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\DOI{10.5802/crmeca.346}
\datereceived{2025-11-26}
\dateaccepted{2026-01-12}
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\dateposted{2026-02-24}
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\editornote{Article submitted by invitation}
\alteditornote{Article soumis sur invitation}

\title{At the origins of electroculture: a retrodictive modelling of
Bertholon's 18{th}-century electrovegetometer in the pre-corona regime}

\alttitle{Aux origines de l'\'{e}lectroculture : mod\'{e}lisation
r\'{e}trospective de l'\'{e}lectrov\'{e}g\'{e}tom\`{e}tre de Bertholon
au XVIII\textsuperscript{e} si\`{e}cle dans le r\'{e}gime de pr\'{e}-d\'{e}charge corona}

\author{\firstname{Thierry} \lastname{Dufour}\CDRorcid{0000-0002-0397-368X}}
\address{Laboratoire de Physique des Plasmas (LPP), Sorbonne
Universit\'{e}, \'{E}cole Polytechnique, CNRS, 75005, Paris, France}
\email{thierry.dufour@sorbonne-universite.fr}

\begin{abstract}
Pierre-Nicolas Bertholon's 18th-century electrovegetometer was
conceived to harness ``atmospheric electricity'' for plant growth, yet
its physical capabilities have never been quantified within the context
of today's understanding of the Earth atmospheric electric system. This
study addresses the lack of quantitative assessment of such a
historical ``electroculture'' device and its plausible influence on the
near-canopy electrical environment. It aims to reinterpret Bertholon's
apparatus using contemporary atmospheric electrodynamics, asking under
which realistic fair-weather and storm-like conditions a purely passive
collector-distributor could generate fields and ion fluxes of physical
significance. A two-dimensional, quasi-steady ohmic model has been
developed in which the atmosphere is a resistive column carrying the
global conduction current, the metal structure is a floating conductor
supported by leaky wooden insulators and space charge and corona are
excluded so that all results describe pre-onset upper bounds. The
simulations show that in fair weather the single upper point and the
lower multi-point crown of the electrovegetometer enhance the
background field by two to three orders of magnitude, yet only within
millimetric-centimetric regions around the tips and with total currents
limited to the pA--nA\tralicstex{\textperiodcentered{m}\textsuperscript{−2}}{${\cdot}$m$^{-2}$} range. Under storm-like forcing,
peak fields at the crown reach 10\textsuperscript{5}--10\textsuperscript{6} V\tralicstex{\textperiodcentered{m}\textsuperscript{−1}}{${\cdot}$m$^{-1}$},
approaching or exceeding empirical corona-onset thresholds, while
remaining largely insensitive to uncertainties in apex angle or
collector geometry as long as an elevated mast is present. These
results make Bertholon's reports of luminous ``aigrettes'' physically
plausible, but suggest that any fair-weather agronomic impact was
subtle and highly localized and that modern ``electroculture'' claims
require careful, coupled electrostatic and biological studies beyond
the pre-corona regime. 
\end{abstract}

\begin{altabstract}
L'\'{e}lectrov\'{e}g\'{e}tom\`{e}tre du XVIII\textsuperscript{e} si\`{e}cle de
Pierre-Nicolas Bertholon a \'{e}t\'{e} con\c{c}u pour exploiter 
\og l'\'{e}lectricit\'{e} atmosph\'{e}rique \fg au profit de  la
croissance des plantes, mais ses capacit\'{e}s physiques n'ont jamais
\'{e}t\'{e} quantifi\'{e}es dans le contexte de la compr\'{e}hension
actuelle du syst\`{e}me \'{e}lectrique atmosph\'{e}rique terrestre.
Cette \'{e}tude comble le manque d'\'{e}valuation quantitative d'un tel
dispositif historique d'\og \'{e}lectroculture \fg et de son
influence plausible sur l'environnement \'{e}lectrique \`{a}
proximit\'{e} de la canop\'{e}e. Elle vise \`{a} r\'{e}interpr\'{e}ter
l'appareil de Bertholon \`{a} l'aide de l'\'{e}lectrodynamique
atmosph\'{e}rique contemporaine, en se demandant dans quelles
conditions r\'{e}alistes de beau temps et de temp\^{e}te un
collecteur-distributeur purement passif pourrait g\'{e}n\'{e}rer des
champs et des flux ioniques ayant une signification physique. Un
mod\`{e}le ohmique bidimensionnel quasi stationnaire a \'{e}t\'{e}
d\'{e}velopp\'{e}, dans lequel l'atmosph\`{e}re est une colonne
r\'{e}sistive transportant le courant de conduction global, la
structure m\'{e}tallique est un conducteur flottant soutenu par des
isolants en bois non \'{e}tanches, et la charge spatiale et l'effet
corona sont exclus afin que tous les r\'{e}sultats d\'{e}crivent les
limites sup\'{e}rieures avant le d\'{e}but. Les simulations montrent
que par temps clair, le point sup\'{e}rieur unique et la couronne
multipoints inf\'{e}rieure de l'\'{e}lectrov\'{e}g\'{e}tom\`{e}tre
amplifient le champ de fond de deux \`{a} trois ordres de grandeur,
mais uniquement dans des r\'{e}gions millim\'{e}triques \`{a}
centim\'{e}triques autour des pointes et avec des courants totaux
limit\'{e}s \`{a} la gamme pA--nA\tralicstex{\textperiodcentered{m}\textsuperscript{−2}}{${\cdot}$m$^{-2}$}. Dans des conditions de
force semblables \`{a} celles d'un orage, les champs maximaux au niveau
de la couronne atteignent 10\textsuperscript{5}--10\textsuperscript{6} V\tralicstex{\textperiodcentered{m}\textsuperscript{−1}}{${\cdot}$m$^{-1}$},
approchant ou d\'{e}passant les seuils empiriques de d\'{e}clenchement
de l'effet corona, tout en restant largement insensibles aux
incertitudes li\'{e}es \`{a} l'angle au sommet ou \`{a} la
g\'{e}om\'{e}trie du collecteur tant qu'un m\^{a}t sur\'{e}lev\'{e} est
pr\'{e}sent. Ces r\'{e}sultats rendent les rapports de Bertholon sur
les \og aigrettes \fg lumineuses physiquement plausibles, mais
sugg\`{e}rent que tout impact agronomique par temps clair \'{e}tait
subtil et tr\`{e}s localis\'{e} et que les affirmations modernes sur
l'\og \'{e}lectroculture \fg n\'{e}cessitent des \'{e}tudes
\'{e}lectrostatiques et biologiques coupl\'{e}es et minutieuses
au-del\`{a} du r\'{e}gime pr\'{e}-corona. 
\end{altabstract}

\keywords{\kwd{Abb\'e Bertholon}\kwd{Electroculture}\kwd{Cold
atmospheric plasmas}\kwd{Corona}\kwd{Retrodictive model}}

\altkeywords{\kwd{Abb\'e Bertholon}\kwd{\'{E}lectroculture}
\kwd{Plasmas froids atmosph\'erique}\kwd{D\'echarge corona}
\kwd{Mod\'{e}lisation r\'{e}trospective}}

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\section{Introduction}\label{sec1}
\subsection{An interdisciplinary impetus: from the Montpellier
colloquium to the present study}\label{ssec11}

The present study was initiated in the aftermath of the French
colloquium \og{}~\textit{Hommage \`{a} Pierre Bertholon, savant et
\'{e}lectricien des Lumi\`{e}res~}\fg{}, held in Montpellier in October
2023 thanks to Alumni-ONERA and the University of Montpellier. This
event gathered historians of science, physicists,
atmospheric-electricity specialists and scholars of 18{th}-century
natural philosophy, communities that rarely interact even though their
combination holds unsuspected and significant interdisciplinary
potential. Discussions with participants during and after the meeting
revealed a shared interest in reassessing Bertholon's
electrovegetometer using the tools of modern atmospheric
electrodynamics, while remaining faithful to its historical context and
material constraints. The present article is therefore partly a product
of this interdisciplinary encounter, illustrating the scientific value
of such colloquia in bridging distinct research cultures and
stimulating new lines of inquiry across disciplinary boundaries.

\subsection{Historical framing}\label{ssec12}

To situate this renewed interest within its original scientific
context, it is necessary to revisit the historical foundations of
Bertholon's work. In 1783, Pierre-Nicolas Bertholon de Saint-Lazare,
commonly known as Abb\'{e} Bertholon, published \textit{De
l'\'{e}lectricit\'{e} des v\'{e}g\'{e}taux}, a treatise in which he
asserted that ``atmospheric electricity'' acts continuously on plants
and might be harnessed to improve germination, growth, flowering and
fruiting~\cite{Bertholon1783}. His key practical proposal, the
electrovegetometer (\textit{\'{e}lectro-v\'{e}g\'{e}tom\`{e}tre)}, was
a passive apparatus intended to collect charge from the atmosphere and
redistribute it gently over crops through ``aigrettes lumineuses'': a
historical French expression that can be understood today as faint,
luminous corona discharges.

Although Bertholon interpreted the operation of his apparatus through
the 18{th}-century notion of an ``electric fluid'', the physical
principle he was appealing to can be expressed clearly in modern
electrodynamic terms: sharp conductors immersed in an ambient electric
field can act as sources (or sinks) of space charge, modifying local
ion densities and weak airflows and thereby altering the microphysical
environment near leaves and soil. In Bertholon's descriptions, the
electrovegetometer consisted essentially of a vertical, insulated mast
that elevated a collecting structure into the atmospheric electric
field. A conductive path brought the intercepted charge down to a
distribution arm, which terminated in a crown of fine points suspended
over crop rows. The points were intended to release charge via
non-disruptive discharges, subtly modifying the potential gradient and
charge environment around the canopy.

Bertholon described two closely related configurations of this
electrovegetometer:
\begin{itemize}
\item The Configuration I ``single-point rod, articulated arm''
(Figure~\ref{fig1}a), combined a relatively simple collector with a
mechanically versatile diffuser. A tall wooden mast, carefully
insulated from the soil by tar, resins and glass elements, carried a
single iron point at its head, shielded by a tin funnel to favour
upward collection. A suspended chain conducted the intercepted
``electric fluid'' to a small iron disk where the collected charge was
expected to accumulate before being redistributed. From there, a hinged
metal arm, horizontally supported on insulated trestles, could be swung
over selected rows of crops. At its far end, a crown of fine points
could release charge like a diffuse corona just above the canopy. A
removable grounding chain allowed the whole device to be neutralized
when the air was judged ``overcharged''. 
\item The Configuration II ``multi-point crown, rotating and extendable
arm'' (Figure~\ref{fig1}b) is characterized by a crown of sharp points
mounted on a resin-treated, glass-insulated hub, to increase the
effective collection area of \textit{electrical fluid} while
maintaining high insulation. A bent lever and chain connected this hub
to a rotary, telescopic arm that could sweep a full circle and be
extended or retracted to adjust the treated footprint. As in
Configuration I, a terminal crown of points was expected to diffuse
charge gently onto the vegetation.
\end{itemize}
In both configurations, the apparatus was entirely passive: it neither
measured voltage nor current and it injected no external power. Since
modern concepts such as electrical potential, current and standardized
units were not yet available, Bertholon reasoned qualitatively with
notions of ``more'' or ``less'' electricity. The individual components
of each configuration are detailed in Table~\ref{tab1}.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Bertholon's electrovegetometer, a passive
apparatus intended to channel ``atmospheric electricity'' toward crops.
(a) Configuration I, featuring a single-point rod collector (E) at the
mast head and an articulated arm that distributed charge through a
multi-point crown (N). (b) Configuration II, equipped with a
multi-point crown collector (E), a rotating and extendable arm and a
larger treatment footprint terminating by a multi-point crown
distributor (N). A neutralization device (Z), shown in the inset of
(b), could provide safety and on/off control. Adapted
from~\cite{Bertholon1783}.}
\end{figure}

%tab1
\begin{table}
\caption{\label{tab1}Comparison between the design and operation of
Bertholon's electrovegetometer (Figure~\ref{fig1}): Configuration I
(``single-point rod, articulated arm'') and Configuration II
(``multi-point crown, rotating and extendable arm'')}
\begin{tabular}{cll}
\thead
& \parbox[t]{12pc}{\centering Configuration I\Lbreak Single-point rod, articulated arm} 
& \parbox[t]{12pc}{\centering Configuration II\Lbreak Multi-point crown, rotating and extendable arm} \vspace*{2pt}\\
\endthead
Purpose & \multicolumn{2}{c}{\parbox[t]{25pc}{\raggedright Passive capture ${\rightarrow}$  Insulated
conduction ${\rightarrow}$ Gentle diffusion over crops (no
measurement)}} \vspace*{5pt}\\ 

Mast/Base & 
\parbox[t]{12pc}{\raggedright Wooden mast (A--B): buried section fire-dried, tarred,
wrapped in charcoal dust/cement, then masonry footing; above-ground
part painted/bitumen-coated for weather resistance} & 
\parbox[t]{12pc}{\raggedright Mast (A--B) with
resin-saturated head cylinder (C) treated with tar/pitch/turpentine to
improve insulation from ground} \vspace*{5pt}\\ 

Top insulation & 
\parbox[t]{12pc}{\raggedright - Thick glass tube packed with bituminous
mastic (D) \Lbreak
- Second glass insulator downstream (H)} & 
\parbox[t]{12pc}{\raggedright Insulated rotary
interface via resin insert (D) and glass/mastic sleeve~(H)} \vspace*{5pt}\\ 

\parbox[t]{6pc}{\centering Collector (at mast head)} & 
\parbox[t]{12pc}{\raggedright Single-point rod (E) mounted in D;
protected by a tinplate funnel (F)} & 
\parbox[t]{12pc}{\raggedright Multipoint crown (E) to maximize
charge capture} \vspace*{5pt}\\ 

\parbox[t]{6pc}{\centering Conduction path (vertical)} & 
\parbox[t]{12pc}{\raggedright Conducting chain (G) suspended from E,
guided through H to prevent leakage} & 
\parbox[t]{12pc}{\raggedright Bent iron lever (C) carrying
chain (G) to the arm interface} \vspace*{5pt}\\ 

Regulation/buffer & 
\parbox[t]{12pc}{\raggedright Chain terminates at iron disk (K) acting as a
small ``condenser/regulator'' to buffer atmospheric variations} &
\parbox[t]{12pc}{\raggedright No
separate disk; regulation implicit (focus on mobility and reach)} \vspace*{5pt}\\ 

\parbox[t]{6pc}{\centering Horizontal arm/distribution} & 
\parbox[t]{12pc}{\raggedright Articulated conductor arm (K--L--M--N)
hinged at L and Q, supported on insulating trestles (O, P) with
stretched silk cords} & 
\parbox[t]{12pc}{\raggedright Telescoping conductor arm (L--M) with its
telescoping conductor (Q), supported on insulating trestle (P) with
stretched silk cords} \vspace*{5pt}\\ 

Terminal diffuser & 
\multicolumn{2}{c}{\parbox[t]{25pc}{\raggedright Crown of sharp metal
points at the arm tip (N, R), releasing charge as non-disruptive corona
over the crop canopy/soil}} \vspace*{5pt}\\ 

Mobility/coverage & 
\parbox[t]{12pc}{\raggedright Arm swings on hinges (L, Q) to cover a sector
(row/strip)} & 
\parbox[t]{12pc}{\raggedright Full 360\textdegree\ rotation via I--L--M and extend/retract
(Q) to sweep a full circle and vary reach} \vspace*{5pt}\\ 

\parbox[t]{6pc}{\centering Neutralization (on/off control)} & 
\multicolumn{2}{c}{\parbox[t]{25pc}{\raggedright Apply a chain (or
vertical rod) between K and the ground to break insulation and bleed
charge. Also used to null effect when ``excess'' of electricity is
presumed}} \vspace*{5pt}\\ 

\parbox[t]{6pc}{\centering Operation (per Bertholon)} &
\multicolumn{2}{c}{\parbox[t]{25pc}{\raggedright Use when the air was 
``poor in electric fluid''; distributed via N; grounded at K when
``excess'' was observed}} \vspace*{5pt}\\ 

Safety & 
\multicolumn{2}{c}{\parbox[t]{25pc}{\raggedright Sharp points released corona glows (no
sparks). ``C-shaped exciter'' (copper/iron frame with glass handle ${+}$\ 
trailing ground chain) recommended to shunt charge during handling}}
\botline
\end{tabular}
\tabnote{The letters (A--Z) correspond to the captions of the original
figures. Both devices were passive collectors-distributors (no
field/charge/current measurement).}
\end{table}

\subsection{From enlightenment ideas to modern atmospheric
electrodynamics}\label{ssec13}

By the late 18{th} century, several essential aspects of atmospheric
electricity were already recognised. Experiments by Stephen Gray and
Charles Fran\c{c}ois de Cisternay Du Fay had already distinguished
conductors from insulators and introduced the idea of two opposite
electrical states, later renamed ``positive'' and ``negative''
\cite{Bailey2001}. Benjamin Franklin synthesised these ideas, defined
the polarity convention and argued, on the basis of laboratory
similarities and field experiments, that lightning was an electrical
discharge of the same nature as sparks from machines
\cite{Williams2009}. His proposals were confirmed in France by
Dalibard and Le Monnier who utilized elevated and well-insulated iron
conductors to draw sparks during thunderstorms, hence confirming that
storm clouds carry electrical charge \cite{Winkleretal1898}. Soon
afterwards, systematic electroscope measurements by John Canton in
London and Giambattista Beccaria in Turin showed that even cloudless
air was rarely neutral: slow ``silent'' discharges, diurnal variations
of the field and luminous glows such as sailors' St Elmo's fire
revealed that the lower atmosphere was persistently electrified
\cite{Herbert2012}. From a modern standpoint, St Elmo's fire was
understood as a low-current corona discharge from sharp conductors in a
strong ambient field \cite{McGinness2025}. Yet these 18{th}-century
insights were local and qualitative. A quantitative, global framework,
in which thunderstorms, fair-weather regions and the ionosphere are
coupled through a single atmospheric electric circuit, emerged only in
the early 20{th} century, particularly through C. T. R. Wilson work and
later syntheses of the ``global atmospheric electrical circuit''
\cite{Aplin2008}. 

Modern atmospheric electrodynamics frames these phenomena in terms of
the global electric circuit (GEC). The Earth-ionosphere system behaves
as a leaky spherical capacitor: thunderstorms and electrified clouds
maintain the ionosphere at roughly ${+}$250/${+}$300 kV relative to the
surface, while ``fair-weather'' regions close the circuit through the
weak electrical conductivity of the air \cite{Tinsley2007,Mareev2014}. 
Under clear undisturbed conditions, the atmospheric column carries a
small, nearly steady downward conduction current density, described
locally by Ohm's law:
{\begin{equation}\label{eq1}
J_{z}(z) = \sigma (z)E_{z}(z),
\end{equation}}\unskip
where $\sigma(z)$ is the electrical conductivity and $E_{z}(z)$ the
vertical electric field (taken positive upward). Near the surface,
typical values of $E_{z}(0) = E_{0,\mathrm{atm}}$ are comprised between
${-}$150 to ${-}$100~V${\cdot}$m$^{-1}$ and $J_{z}(0)=J_{0,\mathrm{atm}}$
between ${-}$3 and $-1$ pA${\cdot}$m$^{-2}$ \cite{Guha2010}. Conductivity
increases by many orders of magnitude with altitude (from about
10$^{-14}$ S${\cdot}$m$^{-1}$ near the ground to 10$^{-7}$
S${\cdot}$m$^{-1}$ in the lower thermosphere), so that $|E_{z}|$
decreases correspondingly and the potential $V(z)$ rises from 0~V to
the ground toward the ionospheric level of a few ${\times}10^{5}$ V
\cite{Kudintseva2016}.

Under disturbed or stormy conditions, this simple vertical structure is
strongly modified. Charge separation in thunderclouds produces large
quasi-static fields at the surface (up to several kV${\cdot}$m$^{-1}$),
enhances ion production and alters the conductivity profile
\cite{Kundt1999}.  The vertical current density can increase into the
nA${\cdot}$m$^{-2}$ range and strong, locally variable fields develop
near sharp objects, creating conditions favourable for corona
discharges and leaders \cite{Standler1979}. These disturbed states form
the storm branch of the global circuit are crucial for interpreting how
a protruding conductor, such as Bertholon's electrovegetometer, might
experience both modest fair-weather forcing and episodic, much stronger
storm-time forcing.

Owing to its limited height (Figure~\ref{fig1}), Bertholon's apparatus
can only interact with the lowest few meters of the atmosphere, where
the idealised one-dimensional GEC picture breaks down and local
processes dominate. Topography, aerosol loading, vegetation, humidity,
surface conductivity and proximity to storm charge all influence the
local electric field. For a passive collector-distributor such as the
electrovegetometer, this near-surface layer controls both the magnitude
of intercepted current and the likelihood of initiating discharges at
the tips. For clarity, two idealized regimes can be distinguished, as
summarized in Table~\ref{tab2}:
\begin{itemize}
\item Fair-weather (``sunny'') conditions, representing undisturbed
atmospheric states with weak fields and very small conduction currents;
\item Stormy-weather conditions, representing periods beneath
electrified clouds or near active storm cells, where fields and
currents can increase by orders of magnitude. 
\end{itemize}

%tab2
\begin{table}
\caption{\label{tab2}Idealized near-surface regimes used as atmospheric
boundary conditions}
\begin{tabular}{cccc}
\thead
\multicolumn{2}{c}{Parameter} &
\parbox[t]{9.5pc}{\centering Fair weather conditions} & 
\parbox[t]{9.5pc}{\centering Stormy weather conditions} \vspace*{2pt}\\ 
\endthead
\multicolumn{2}{c}{Electric field direction} & Downward (negative) &
Upward (positive) \vspace*{5pt} \\ 

\multicolumn{2}{c}{Vertical electric field $E_{0,\mathrm{atm}}$} & 
$-100\rightarrow -150$ V${\cdot}$m$^{-1}$ & 
$+1\rightarrow +10$ kV${\cdot}$m$^{-1}$ \vspace*{5pt} \\ 

& & Increases with altitude & Decreases with altitude \\

\morerows{2}{Electric potential} & $V(z)$ & 
$\dfrac{\mathrm{d}V}{\mathrm{d}z} = -E_{z} > 0 $ & 
$\dfrac{\mathrm{d}V}{\mathrm{d}z} = -E_{z} < 0$ \\

& $V$ (1 m)  & ${+}$100 V  $\rightarrow +150$ V  & ${-}$1 kV  $\rightarrow -$ 10 kV \\

& $V$ (10 m) & ${+}$1000 V $\rightarrow +1500$ V & ${-}$10 kV $\rightarrow -$ 100 kV \vspace*{5pt} \\ 

\multicolumn{2}{c}{Conductivity at surface $\sigma$ (0)} & (1--5) 
${\times}$ 10$^{-14}$ S${\cdot}$m$^{-1}$ & (1--10) ${\times}$ 10$^{-12}$ 
S${\cdot}$m$^{-1}$ \vspace*{5pt} \\ 

\multicolumn{2}{c}{$\sigma$ variation with
height (0--20 m)} & \parbox[t]{9.5pc}{\centering Increases gradually (${\approx}$10${\times}$) due
to ionization by cosmic rays and radioactivity} & \parbox[t]{9.5pc}{\centering Increases sharply
(${\approx}$100${\times}$) near ground due to field-induced ionization
and space charge} \vspace*{5pt} \\ 

\multicolumn{2}{c}{Conduction current density $J$} & 
\parbox[t]{9.5pc}{\centering ${\approx}-2$ pA${\cdot}$m$^{-2}$ (downward, negative)} & 
\parbox[t]{9.5pc}{\centering ${+}$0.1 ${\rightarrow} +10$ nA${\cdot}$m$^{-2}$ (upward, positive)} \vspace*{5pt} \\ 

\multicolumn{2}{c}{Surface potential reference $V$ (0)} & 0 V (by
convention) & 0 V (by convention) \vspace*{5pt} \\ 

\multicolumn{2}{c}{Breakdown electric field ($E_{\mathrm{bd}}$)} & ${\approx}$3.0
MV${\cdot}$m$^{-1}$ & 2.5--2.8 MV${\cdot}$m$^{-1}$ 
\botline
\end{tabular}
\end{table}

\vspace*{-6pt}

\subsection{Knowledge gap and research questions}\label{ssec14}

Historical accounts describe Bertholon's electrovegetometer as a purely
passive apparatus: the ambient atmospheric conduction current was
collected on a sharp upper point and redistributed through a conductor
by a lower crown of points, without any external power source or means
of regulating or measuring the electrical state. What remains uncertain
is whether such a passive configuration could, even in principle,
generate ion or charge fluxes large enough to have physical
significance at canopy height. No previous study has embedded the
electrovegetometer explicitly in the framework of the global
atmospheric electric circuit, with realistic fair-weather and
storm-time fields, currents and conductivity profiles, nor quantified
how far from the tips its influence on the electrical microenvironment
of crops can extend.

A second gap concerns the absence of a systematic distinction between
fair-weather and storm-affected regimes. Modern atmospheric electricity
recognises that typical fair-weather conditions (e.g.\ 
$E_{0,\mathrm{atm}}\approx -120$ kV${\cdot}$m$^{-1}$,
$J_{0,\mathrm{atm}}\approx -2$ pA${\cdot}$m$^{-2}$) are associated with
weak, quasi-steady conduction currents, whereas storm-time conditions
can support much stronger and more structured electric fields. Yet,
existing historiographical and experimental discussions of the
electrovegetometer do not quantify how these regimes would
differentially drive a floating metal structure, nor do they estimate
pre-corona upper bounds on the fields and currents attainable at the
upper collector and the lower crown. This makes it difficult to judge
whether historical reports of luminous ``aigrettes'' correspond to
fields that plausibly exceed diffuse-corona onset thresholds.

Finally, the electrodynamic consequences of geometric uncertainty
remain unexplored. Historical engravings constrain the general
architecture of the electrovegetometer but not the precise mast height,
arm length, tip spacing or apex angles. It is therefore unknown how
strongly the background column current can be concentrated into the
canopy layer by a realistic crown, over what distance above the soil
the enhanced electric field and current density persist (e.g.\ within
the first 0.2--0.5 m) and how sensitive these quantities are to
collector and mast geometry.

The present work addresses these gaps by developing a simplified
two-dimensional conduction model of the air-device system, in which the
electrovegetometer is treated as a floating metal structure polarised
by the global electric circuit. Within this pre-corona, ohmic
framework, we calculate the potential, electric field and current
density around idealised reconstructions of Bertholon's device under
both fair-weather and storm-like forcing, for several plausible
combinations of mast height, arm length and tip spacing. The
simulations quantify (i) the maximum local fields and enhancement
factors at single-point and multi-point collectors, (ii) the
concentration of background column current into the canopy layer and
the resulting vertical and horizontal gradients of $|E|$ and $|J|$ and
(iii) the atmospheric and geometric conditions under which the computed
fields approach or exceed empirical diffuse-corona onset criteria.
Because space charge accumulation and ionisation feedback are not
modelled, these results should be interpreted as controlled, pre-onset
upper bounds rather than predictions of discharge behaviour.

These considerations lead to the following research questions:
\begin{itemize}
\item Under realistic fair-weather forcing, what potentials,
electric-field magnitudes and current densities are established around
the upper collector and lower crown and over what length scales do
these perturbations decay above the canopy?
\item Under enhanced background fields representing pre-storm or
storm-affected conditions, can a purely passive electrovegetometer
reach electric-field levels at its tips that approach diffuse-corona
onset thresholds, making historical luminous ``aigrettes'' physically
plausible?
\item How do field enhancement, current concentration into the canopy
layer and proximity to corona-onset thresholds depend on mast height,
arm length, tip spacing and collector design within the range
consistent with historical descriptions?
\end{itemize}

\section{Model}\label{sec2}

All numerical computations were performed using GNU Octave (version
10.3.0), employing custom scripts for the finite-difference
discretization, relaxation scheme, and post-processing.

\subsection{Physical assumptions and scope}\label{ssec21}

The electrostatic environment around Bertholon's electrovegetometer is
modeled as a quasi-steady, ohmic atmosphere carrying the global weather
conduction current. The key assumptions are as follows:
\begin{itemize}
\item The atmosphere behaves as a linear, resistive medium
characterized by a prescribed conductivity $\sigma (x,z)$,
dominated by its altitude dependence $\sigma (z)$.
\item The vertical conduction current is approximately conserved ($\vec
{\nabla}{\cdot}{\mathrm{J}}=0$) in the absence of sources or sinks.
\item Space charge $\rho $ and ionization feedback are not explicitly resolved; instead, their net effect on conductivity is encoded in $\sigma (z)$.
\item The metallic parts of the device are treated as perfect conductors, each connected metallic region being equipotential. The structure is electrically floating: no external voltage is imposed, and its potential adjusts self-consistently under the imposed global-circuit forcing.
\item The ground is represented as a conducting, equipotential boundary. The crop canopy is not explicitly resolved (fields are evaluated in the air above flat ground), so fine-scale field distortions by individual plants are neglected.
\item The problem is solved in two-dimensional Cartesian geometry, assuming invariance in the out-of-plane direction. As a consequence, the computed enhancement factors are specific to this 2D approximation; a truly axisymmetric or fully 3D representation of the device would generally yield quantitatively different near-tip field concentrations, although the qualitative trends discussed here are expected to remain the same. The wooden supports are represented as weak conductors (very low $\sigma _{\mathrm{wood}}$) that can leak current but are highly resistive compared to metal.
\end{itemize}

\subsection{Governing equations and conductivity profile}
\label{ssec22}

The electric potential $V(x,z)$ satisfies the stationary conduction
Equation~(\ref{eq2}) throughout all materials, while the electric field
and current density are given by Equations~(\ref{eq3}) and~(\ref{eq4}).
The atmosphere is described using the altitude-dependent conductivity
profile of Equation~(\ref{eq5}), where $\sigma _{0} =
{J_{0,\mathrm{atm}}}/{E_{0,\mathrm{atm}}}$ is determined by the imposed
near-surface atmospheric electric field $E_{0,\mathrm{atm}}$ and the
corresponding column current density $J_{0,\mathrm{atm}}$.
Figure~\ref{fig2}a displays the resulting isopotential structure for
values of $E_{0,\mathrm{atm}}$ ranging from $-$0.4 kV${\cdot}$m$^{-1}$
to 10 kV${\cdot}$m$^{-1}$. Two physically distinct atmospheric regimes
appear in this range and are therefore considered in the simulations:
\begin{itemize}
\item Fair-weather conditions, characterized by
$E_{0,\mathrm{atm}}\approx -120$ V${\cdot}$m$^{-1}$ and
$J_{0,\mathrm{atm}}\approx -2$ pA${\cdot}$m$^{-2}$, yielding weak
potential gradients and gently curved isopotentials (left side of
Figure~\ref{fig2}a).
\item Stormy-weather conditions, associated with much stronger positive
electric fields, are here represented by
$E_{0,\mathrm{atm}}=+5$ kV${\cdot}$m$^{-1}$ and
$J_{0,\mathrm{atm}}=5$ nA${\cdot}$m$^{-2}$, which produce steep potential
drops with altitude and tightly packed isopotentials (right side of
Figure~\ref{fig2}a).
\end{itemize}

\begin{figure}
\vspace*{2pt}
\includegraphics{fig02}
\vspace*{2pt}
\caption{\label{fig2}(a) Electric potential $V(E_{z},z)$ in the
atmosphere above the ground, shown as colored contours (in kV) and
black isopotential lines. The horizontal axis represents the imposed
vertical electric field $E_{z}$, ranging from fair-weather values 
($E_{z} < 0$) to storm-time values ($E_{z} > 0$). The two white
vertical lines correspond to the fair-weather and stormy-weather
atmospheric conditions for this study. (b) Geometrical model of
Bertholon's electrovegetometer as implemented in configuration I, which
includes the wooden insulating mast and supports (brown), the
conductive L-shaped structure (red) and the multi-point crown. The
computational domain represents a 2 m ${\times}$ 4 m vertical
cross-section of the surrounding atmosphere.} 
\vspace*{2pt}
\end{figure}

A conductivity scale height of $H_{\sigma}=6$ km is adopted. In a
vertically uniform atmospheric column, current conservation~(\ref{eq6})
then leads to the electric-field profile of Equation~(\ref{eq7}).
Through Gauss law, the corresponding diagnostic space charge density is
given by Equation~(\ref{eq8}).
{\begin{eqnarray}
\vec{\nabla} \cdot [\sigma (x,z)\,\vec{\nabla}V(x,z)] &=& 0 \label{eq2} \Seqnsplit
\vec{E} &=& -\vec{\nabla}V \label{eq3} \Seqnsplit
\vec{J} &=& \sigma \vec{E} \label{eq4} \Seqnsplit
\sigma_{\mathrm{air}}(z) &=& \sigma _{0}\exp \left(\dfrac{z}{H_{\sigma}}\right) \label{eq5} \Seqnsplit
J_{z}(z) &=& \sigma (z)\cdot E_{z}(z) = J_{0,\mathrm{atm}} \label{eq6} \Seqnsplit
E_{z}(z) &=& -E_{0,\mathrm{atm}}\exp \left(-\dfrac{z}{H_{\sigma}}\right) \label{eq7} \Seqnsplit
\rho (z) &=& \varepsilon _{0}\dfrac{\mathrm{d}E_{z}}{\mathrm{d}z} = -\varepsilon _{0} \dfrac{E_{z}(z)}{H_{\sigma}}. \label{eq8}
\end{eqnarray}}\unskip
The space charge density $\rho(z)$ is not explicitly solved. Instead,
$\sigma(z)$ is prescribed and the solver remains purely ohmic and
pre-corona. For storm-like surrogate cases, the same form is considered
although the magnitudes of $|E_{0,\mathrm{atm}}|$,
$|J_{0,\mathrm{atm}}|$ and $\sigma_{0}$ are increased to match the
idealized values in the ``storm-like'' regime. The solid regions are
air with $\sigma_{\mathrm{air}}(z)$ given by  Equation~(\ref{eq5}),
wood supports with $\sigma_{\mathrm{wood}} \approx 10^{-15}$
S${\cdot}$m$^{-1}$ (strongly insulating but not perfectly) and metal
conductor: $\sigma_{\mathrm{metal}} = 1 \times 10^{7}$
S${\cdot}$m$^{-1}$.  Owing to this strong conductivity mismatch, the
metallic structure is treated as a single floating conductor with an
effectively uniform internal potential.

\subsection{Geometry and computational domain}\label{ssec23}

The problem is solved in two dimensions over $x\in [-0.4,2.0]$ m and
$z\in [0.0,4.0]$ m on a uniform grid of $N_{x}=6000$, $N_{z}=$ 10~000
nodes ($\Updelta x = \Updelta z = 400~{\upmu}$m).  This 2D formulation
represents an infinitely long structure in the out-of-plane direction;
results are therefore cross-sections with unit depth.

The Bertholon-type apparatus is modeled as shown in
Figure~\ref{fig2}b. A vertical wooden mast, 2.0~m high and 0.15 m
wide, forms the central support. A short horizontal wooden element is
placed at $z=1.5$ m and two wooden feet, each 0.5 m high and 1.5 cm
thick, provide support at ground level beneath the conductor. The
metallic conductor is represented by an L-shaped structure with
triangular tips. At the top, a 0.30-m-high, 0.02-m-wide triangular tip
located at $z=2.2$ m serves as the upper single-point collector, with
an apex angle of 4\textdegree. From the base of this tip, a vertical
metallic segment extends 1.70 m downward with a thickness of 0.02 m.
This segment connects to a horizontal arm 1.50 m long positioned
approximately 0.5 m above the ground. At the end of this arm, a
terminal crown composed of five triangular points (each 0.30 m high and
0.02 m at the base) is arranged with angular orientations of
${-}$40\textdegree, ${-}$20\textdegree, 0\textdegree, ${+}$20\textdegree\
 and ${+}$40\textdegree\ relative to the vertical. This stylized geometry
corresponds to sharp apex radii of order 1~mm.

\subsection{Boundary conditions and numerical implementation}
\label{ssec24}

The top and bottom boundaries enforce the imposed vertical current
density $J_{0,\mathrm{atm}}$ following Equations~(\ref{eq9})
and~(\ref{eq10})  while lateral boundaries are symmetric, as expressed
by Equation~(\ref{eq11}).
{\begin{eqnarray}
\left.\dfrac{\partial V}{\partial z}\right| _{z=0} &=& -\dfrac{J_{0,\mathrm{atm}}}{\sigma (0)} \label{eq9} \Seqnsplit
\left.\dfrac{\partial V}{\partial z}\right| _{z=H} &=& -\dfrac{J_{0,\mathrm{atm}}}{\sigma (H)} \label{eq10} \Seqnsplit
\left.\dfrac{\partial V}{\partial x}\right| _{\mathrm{left}/\text{right}} &=& 0.               \label{eq11}
\end{eqnarray}}\unskip
One air node is fixed at $V=0$ to set the reference potential. This
choice enforces the column current but does not impose a perfectly
equipotential Earth at $z=0$; near-ground potentials can therefore vary
horizontally, an approximation acceptable here but not exact.

The governing Equation~(\ref{eq2}) is discretized on a
two-dimensional five-point finite-difference stencil. To ensure
continuity of the current density across sharp changes in conductivity,
the conductivity at each cell face is computed with 
Equation~(\ref{eq12}) which provides the harmonic mean between adjacent
cells. This averaging scheme preserves flux conservation and numerical
stability in regions where materials of very different conductivities
meet (e.g., air/wood or air/metal interfaces). The resulting discrete
system is solved by Jacobi relaxation, in which the potential at the
node $(i,j)$ is updated iteratively according to 
Equation~(\ref{eq13}) with boundary updates and gauge enforcement after
each sweep.
{\begin{eqnarray}
\sigma _{\mathrm{face}} &=& \dfrac{2\sigma _{1}\sigma _{2}}
{\sigma _{1}+\sigma _{2}+\varepsilon} \label{eq12} \Seqnsplit
{V}_{i,j}^{(n+1)} &=& \dfrac{\sigma _{e}V_{i,j+1}+\sigma _{w}V_{i,j-1}+\sigma _{n}V_{i+1,j}+\sigma _{s}V_{i-1,j}}
{\sigma _{e}+\sigma _{w}+\sigma _{n}+\sigma _{s}}. \label{eq13}
\end{eqnarray}}\unskip
Initialization uses the analytic fair-weather profile in 
Equation~(\ref{eq14}) and metal regions are seeded with the average
potential of neighbouring air cells. Iterations stop once
Equation~(\ref{eq15}) is satisfied or when 2000 iterations are reached.
This criterion yields good agreement with the 1D analytic column and
current conservation (top vs bottom flux differ by ${<}$0.01\%),
but peak fields remain somewhat sensitive to grid resolution and tip
geometry. They should be interpreted as approximate pre-corona values
rather than fully converged quantities. Iterations continue until the
maximum change in $V$ between two successive steps falls below a
prescribed tolerance, ensuring convergence of the electrostatic
potential field.
{\begin{eqnarray}
&& V^{(0)}(z) = E_{0,\mathrm{atm}}H_{\sigma} \left(1-\mathrm{e}^{-\frac{z}{H_{\sigma }}}\right)
\label{eq14} \Seqnsplit
&& \mathrm{Max} |V^{(n+1)}-V^{(n)}| < 10^{-3}. \label{eq15} 
\end{eqnarray}}\unskip
Electric field and current density are computed after convergence using
centered finite differences. The horizontal and vertical components of
the electric field follow directly from the potential gradients
(Equations~(\ref{eq16}), (\ref{eq17})) and the field magnitude is
obtained from  Equation~(\ref{eq18}). The current-density components
are then derived from Ohm's law (Equations~(\ref{eq19}), (\ref{eq20}))
using the local conductivity and the total current-density magnitude is
computed from Equation~(\ref{eq21}). These quantities are visualized in
units of kV${\cdot}$m$^{-1}$ for the electric field and pA${\cdot}$m$^{-2}$
or nA${\cdot}$m$^{-2}$ for the current density, with solid regions
masked.
{\begin{eqnarray}
E_{x} &=& -\dfrac{\partial V}{\partial x}              \label{eq16} \Seqnsplit
E_{z} &=& -\dfrac{\partial V}{\partial z}              \label{eq17} \Seqnsplit
|E| &=& \sqrt{{E}_{x}^{2}+{E}_{z}^{2}}                 \label{eq18} \Seqnsplit
J_{x} &=& -\sigma \cdot \dfrac{\partial V}{\partial x} \label{eq19} \Seqnsplit
J_{z} &=& -\sigma \cdot \dfrac{\partial V}{\partial z} \label{eq20} \Seqnsplit
|J|   &=& \sqrt{{J}_{x}^{2}+{J}_{z}^{2}}.               \label{eq21} 
\end{eqnarray}}\unskip

\subsection{Mesh and convergence}\label{ssec25}

To verify that the reported results are not sensitive to the grid
spacing, a mesh-refinement study has been performed using five
successively refined meshes (Figures~\ref{fig3}a, \ref{fig2}b--f) while
keeping the physical domain size and all model parameters unchanged.
For each mesh, the key quantities discussed in the manuscript are
monitored: (i) the floating potential of the metallic structure
$V_{\mathrm{cond}}$, (ii) the maximum electric field magnitude in air
$E_{\max}$ and (iii) the maximum current density in air $J_{\max}$.
Since the field at an idealized sharp apex may exhibit mesh-dependent
amplification, near-tip values were evaluated either (i) after
excluding the metal region and its immediate neighboring cells, or (ii)
at a fixed physical distance above the apex (e.g., 5--10 mm), which
provides a mesh-consistent diagnostic. The differences between the
baseline (Resolution ${=}$\ 400 ${\upmu}$m) and fine meshes were below
6.5\% for $V_{\mathrm{cond}}$, 4.8\% for $E_{\max}$, and 4.9\% for
$J_{\max}$, indicating mesh independence within the accuracy required
for the present pre-corona, ohmic upper-bound analysis. In addition,
the iterative solver is run until the maximum change in potential
between two successive iterations satisfied $\Updelta V_{\max} = \max
\vert V^{(n)} - V^{(n-1)}\vert < 5V$, ensuring numerical convergence on
each mesh, as supported in Figure~\ref{fig3}g.

\begin{figure}
\includegraphics{fig03}
\caption{\label{fig3}(a) Zoomed view of the modeled tip geometry
(black) in the ($x$, $z$) plane. (b--f) Computed potential distribution
$V(x,z)$ in the air around the tip in fair weather conditions, and for
progressively finer spatial resolutions (1 mm, 600~${\upmu}$m,
400~${\upmu}$m, 200~${\upmu}$m and 100~${\upmu}$m). As the grid is
refined, the representation of the tip and the associated near-tip
potential gradients become sharper; the potential pattern changes
markedly from 1 mm to 400~${\upmu}$m, while the 200~${\upmu}$m and
100~${\upmu}$m results are visually very similar, indicating
grid-independence at these resolutions. (g) Convergence of the
iterative solver for a 400~${\upmu}$m resolution: the maximum absolute
change in potential between two successive iterations decreases
monotonically with iteration number, showing rapid initial reduction
followed by a slower asymptotic approach to a converged solution.}
\end{figure}

\section{Results}\label{sec3}
\subsection{Fair-weather (``sunny'') conditions}\label{ssec31}

Here, we examine Configuration I of the electrovegetometer
(Figure~\ref{fig1}a), which consists of a conductive L-shaped structure
combining a single-point collector at the upper extremity with a
five-point crown near ground level. The response of this geometry is
evaluated under fair-weather forcing, characterized by an imposed
downward conduction current $J_{0,\mathrm{atm}}\approx -2$
pA${\cdot}$m$^{-2}$ and a background electric field
$E_{0,\mathrm{atm}}\approx -120$ V${\cdot}$m$^{-1}$ applied at the lower
boundary.

The steady-state potential, electric-field magnitude and
current-density magnitude in the vicinity of the upper single-point
collector are shown in Figure~\ref{fig4}. Figure~\ref{fig4}a
illustrates that the atmospheric potential ranges from approximately
260--305 V over the vertical extent of the domain. Near the metallic
point, the potential drops sharply to ${\approx}$260--265 V, whereas
the surrounding air at the same altitude lies around 290--300 V. This
30--40 V lateral depression is tightly confined to a region only a few
millimeter wide, forming a narrow potential funnel aligned with the
tapered geometry of the rod. Because the conductor is electrically
floating, its potential (${\approx}$240 V at the base of the point)
emerges self-consistently as the value required to satisfy the imposed
column current. Outside the immediate tip region, equipotential
contours relax back to their nearly uniform fair-weather spacing.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Pre-corona response of the upper single-point rod
collector (apex angle $\theta=$\ 4\textdegree) under fair-weather
forcing ($E_{0,\mathrm{atm}} \approx -120$ V${\cdot}$m$^{-1}$,
$J_{0,\mathrm{atm}} \approx -2$ pA${\cdot}$m$^{-2}$). (a) Steady
potential $V$ showing strong equipotential compression near the
floating metal apex. (b) Electric-field magnitude $|E|$ with geometric
enhancement to $E_{\max} = 20.9$ kV${\cdot}$m$^{-1}$. (c) Current-density
magnitude $|J|$ peaking at $J_{\max} = 1.36$ nA${\cdot}$m$^{-2}$ and
relaxing to the background within centimeters.}
\end{figure}

Figure~\ref{fig4}b reveals the resulting electric-field enhancement.
The gradient associated with the 30--40 V drop over sub-centimeter
distances produces local fields exceeding 20 kV${\cdot}$m$^{-1}$ with the
simulation giving a peak value of $E_{\max}=20.9$ kV${\cdot}$m$^{-1}$. 
This corresponds to an enhancement factor of roughly:
{\begin{equation*}
\dfrac{E_{\max}}{|E_{0,\mathrm{atm}}|} \approx 
\dfrac{2.1\times 10^{4}}{1.2\times 10^{2}}\sim 175.
\end{equation*}}\unskip
This value is purely due to geometric concentration at the apex. The
elevated field decays rapidly: within 1 cm of the tip it falls to the
kV/m range and within a few centimeters it returns to ambient
fair-weather values.

Figure~\ref{fig4}c shows the associated current-density magnitude.
The strongest currents are confined to a narrow axial plume emerging
from the single-point rod, with a peak of $J_{\max} = 
1.36$~nA${\cdot}$m$^{-2}$. This value is consistent with Ohm's law $J=\sigma
E$, using the local fair-weather surface conductivity $\sigma
_{0}\approx 1.7\times 10^{-14}$ S${\cdot}$m$^{-1}$.  Although small in
absolute terms, such a current corresponds to a microscopic flux of:
{\begin{equation*}
\dot{N}\approx \frac{J_{\max}}{e} \approx 8 \times 10^{9}
~\mathrm{charges}{\cdot}\mathrm{s}^{-1}{\cdot}\mathrm{pm}^{-2},
\end{equation*}}\unskip
showing that even nanoampere currents involve billions of charge
carriers per second. As expected in the ohmic, pre-corona regime, the
spatial pattern of $|J|$ mirrors that of $|E|$ and merges smoothly into
the background atmospheric current $J_{0,\mathrm{atm}}\approx -2$
pA${\cdot}$m$^{-2}$ over centimeter scales.

The steady-state potential, electric-field magnitude and
current-density magnitude surrounding the lower multi-point crown are
represented in Figure~\ref{fig5}. On the scale of the entire crown
(Figure~\ref{fig5}a), each of the five metallic points produces a
distinct depression in the potential field. These local ``funnels'',
typically 20--40 V deeper than the surrounding air at the same height,
merge into a single broader perturbation a few centimeters away from
the crown. The zoom near the central point (Figure~\ref{fig5}b) shows a
narrow, vertically elongated potential channel whose minimum lies
around 250--260 V, corresponding to a lateral potential drop of 30--40
V over millimeter-to-centimeter scales. This results from both the
sharp curvature of the central apex and the lateral confinement imposed
by neighboring points of the crown.

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5}Pre-corona response of the lower five-point crown
under fair-weather forcing ($E_{0,\mathrm{atm}} \approx -120$
V${\cdot}$m$^{-1}$,  $J_{0,\mathrm{atm}} \approx -2$ pA${\cdot}$m$^{-2}$)
with apex angle $\theta=4$\textdegree.  (a,b) Potential $V$ showing
local depressions around each apex and a narrow, deep potential funnel
at the central tip. (c,d) Electric-field magnitude $|E|$ forming five
interacting high-field lobes, with a localized maximum $E_{\max} =
80.9$ kV${\cdot}$m$^{-1}$. (e,f) Current-density magnitude $|J|$
revealing five focused conduction channels and a peak $J_{\max} = 
1.34$~nA${\cdot}$m$^{-2}$. All values remain within the linear,
conduction-dominated regime.}
\end{figure}

The electric-field magnitude (Figure~\ref{fig5}c and especially
\ref{fig5}d) exhibits five distinct high-field lobes, one per apex.
Their superposition forms a structured envelope rather than an isolated
maxima, reflecting strong inter-point interactions. Within the central
zoom (Figure~\ref{fig5}d) the field reaches $E_{\max}\approx 80.9$
kV${\cdot}$m$^{-1}$, nearly 700 times the ambient fair-weather field.
This field drops to a few kV/m within about 1 cm, returning to
near-ambient values within several cm. The enhancement remains at least
one order of magnitude below typical corona-onset thresholds for sharp
conductors at ground pressure, confirming operation in the pre-corona,\break
ohmic regime.

The current-density maps (Figure~\ref{fig5}e,f) indicate
the structure of the electric field. Each point of the crown generates
a narrow current plume that diffuses downward and merges with the
background conduction current. The central apex again produces the
highest value, $J_{\max}\approx 1.34$~nA${\cdot}$m$^{-2}$ which
corresponds to a microscopic flux similar to that estimated at the
single-point rod collector, {i.e.}\ $\dot{N}\approx 8\times 
10^{9}~\mathrm{charges}{{\cdot}}\mathrm{s}^{-1}{{\cdot}}\mathrm{m}^{-2}$.
Because the conductivity varies only weakly within the 5--15 cm region
surrounding the crown, the structure of $|J|$ is governed almost
entirely by geometric field shaping rather than atmospheric
stratification.

Under fair-weather forcing, all simulated fields remain well below
air-breakdown thresholds, confirming operation in a linear, ohmic
pre-corona regime. Field enhancement arises solely from geometric
concentration at the metallic points, producing smooth, monotonic
patterns of electric field and current density consistent with
$J=\sigma E$. These results define a quantitative baseline for
potentials, enhancement factors and conduction plumes, against which
stronger forcing can be compared. We now examine how the geometry
responds under idealized storm-like conditions, where ambient fields
increase dramatically.

\subsection{Stormy weather conditions}\label{ssec32}

The response of the upper single-point rod is studied under an
idealized storm-like forcing, using the parameters of Table~\ref{tab2}.
The background electric field is increased to $E_{0,\mathrm{atm}}
\approx 5000$~V${\cdot}$m$^{-1}$ and the imposed conduction current
reverses direction, reaching $J_{0,\mathrm{atm}}\approx +5$
nA${\cdot}$m$^{-2}$. This configuration provides a linear surrogate for
storm-enhanced fields without explicitly modelling cloud charge, space
charge or the three-dimensional electrostatic structure of
thunderclouds. As a consequence, the fields obtained near the points
represent the upper bounds of the pre-corona state; a real atmosphere
would transition to space charge dominated corona before such fields
are maintained.

Figure~\ref{fig6} shows the steady potential, electric-field magnitude
and current-density magnitude around the upper tip for this storm-like
scenario. The potential well around the apex (Figure~\ref{fig6}a) is
significantly deeper and more compressed than under fair weather,
reflecting both the stronger forcing and the higher upward current.
Local potential near the single point apex falls below ${-}12$~kV,
compared with the ${-}260$ V  range seen previously, indicating an
order-of-magnitude intensification of the gradients. The resulting
electric field (Figure~\ref{fig6}b) reaches a peak of $E_{\max}\approx
735$~kV${\cdot}$m$^{-1}$  localized to a sub-centimeter region. This
value is still below canonical breakdown estimates for air at ground
pressure (${\sim}$2.5--2.8 MV${\cdot}$m$^{-1}$) but it falls within the
lower range of empirical corona-onset measurements for sharp conductors
under humid or pre-storm conditions. Within 1 cm of the apex, the field
drops to a few hundred kV/m and returns to background values within a
few centimeters, preserving the strongly localized enhancement pattern
observed in fair weather.

\begin{figure}
\includegraphics{fig06}
\caption{\label{fig6}Response of the single-point rod collector under
idealized storm-like forcing ($E_{0,\mathrm{atm}} \approx 5$
kV${\cdot}$m$^{-1}$, $J_{0,\mathrm{atm}} \approx 5$ nA${\cdot}$m$^{-2}$).
(a) Steady potential $V$ showing deep compression of equipotentials
near the floating metal apex. (b) Electric-field magnitude $|E|$
reaching  $E_{\max} = 735$ kV${\cdot}$m$^{-1}$, approaching empirical
corona-onset ranges. (c) Current-density magnitude $|J|$ peaking at
$J_{\max} = 5.4~\upmu$A${\cdot}$m$^{-2}$. Values represent pre-corona
upper bounds within the linear, space-charge-free model.} 
\end{figure}

The corresponding current-density magnitude (Figure~\ref{fig6}c) peaks
at $J_{\max}\approx 5.4~\upmu$A${\cdot}$m$^{-2}$ consistent with the
scaling $J=\sigma E$, given the elevated conductivity at the tip
altitude. This represents an increase of nearly three orders of
magnitude relative to fair-weather values (${\sim}1.36$
nA${\cdot}$m$^{-2}$), yet the spatial structure remains a narrow axial
plume diffusing smoothly into the background upward current.

Despite the large absolute fields and currents, the computed solution
retains the qualitative signature of a linear conduction regime:
equipotential surfaces continue to converge monotonically, $|E|$ 
increases smoothly toward the apex and no field clamping or plateau
forms. This behaviour indicates that, within the limitations of a space
charge free model, the system remains mathematically ohmic even at
intensities where a real atmosphere would have already initiated
corona. The results should therefore be interpreted as a near-threshold
pre-corona state, with physical discharge onset inferred from external
criteria, not from deviations within the simulated fields.

The response of the five-point crown distributor under storm-like
forcing is shown in Figure~\ref{fig7}. Compared with the fair-weather
case, the stronger background field and reversed conduction current
produce a markedly deeper and more confined potential well around each
apex. On the scale of the full crown (Figure~\ref{fig7}a),
equipotential surfaces collapse tightly around all five metallic
points, with local potentials in the zoom region (Figure~\ref{fig7}b)
falling to around ${-}$10 kV. As in the previous single-point rod, these
minima form narrow, vertically elongated channels, but the lateral
confinement imposed by neighbouring peaks sharpens the gradients even\break
further.

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Response of the lower five-point crown under
idealized storm-like forcing ($E_{0,\mathrm{atm}}\approx 5$
kV${\cdot}$m$^{-1}$, $J_{0,\mathrm{atm}}\approx 5$ nA${\cdot}$m$^{-2}$)
with apex angle $\theta=4$\textdegree.  (a,b) Potential $V$ showing a
deeply collapsed well and strong confinement of equipotentials around
each apex. (c,d) Electric-field magnitude $|E|$ with a localized
maximum $E_{\max} = 2.84$~MV${\cdot}$m$^{-1}$, approaching empirical
breakdown ranges. (e,f)  Current-density magnitude $|J|$ peaking at
$J_{\max} = 2.8~\upmu$A${\cdot}$m$^{-2}$.  These values represent
upper-bound, pre-discharge fields within the linear, space charge free
model.}
\end{figure}

The corresponding electric-field magnitude (Figure~\ref{fig7}c,d)
displays a set of 5 high-field lobes. Their superposition produces a
structured envelope of enhanced field, with the central peak reaching
$E_{\max} \approx 2845$ kV${\cdot}$m$^{-1}$. This value is roughly 40
times larger than the storm-like single-point rod maximum and lies
squarely within the empirical breakdown range for humid air at ground
level. It also exceeds typical diffuse-corona onset estimates for sharp
conductors. Because the model is strictly linear and excludes space-charge 
or ionization processes, these simulated fields should be
interpreted as upper bounds on the pre-discharge state; a real
atmosphere would begin corona formation and field clamping before such
values were sustained. Spatially, the enhancement remains confined to a
sub-centimeter region around the apex, decaying to the 100-of-kV/m
range within ${\sim}$1 cm and to background levels within a few
centimeters.

The current-density maps (Figure~\ref{fig7}e,f) reproduce this
structure. A sharply focused axial jet emerges from each point, with
the central one producing $J_{\max} \approx 5.4~\upmu$A${\cdot}$m$^{-2}$,
over three orders of magnitude above its fair-weather counterpart and
consistent with the elevated $E_{\max}$ through $J=\sigma E$. Although
extremely large for a conduction-only model, the spatial pattern
remains smooth and monotonic, without the field clamping or non-linear
features that would accompany real corona onset.

Taken together, these results show that the multi-point crown acts as
an exceptionally efficient field concentrator under storm-like forcing,
much more so than the upper single-point collector. However, because
the model neglects space charge, ionization and discharge physics, the
predicted MV/m-scale peaks represent idealized upper limits rather than
realistic operational values; in practice, corona, streamer activity
and associated charge regulation would intervene well before the
simulated fields could be reached.

\subsection{Influence of apex angle}\label{ssec33}

To evaluate the sensitivity of the electrovegetometer response to the
sharpness of Bertholon's upper collector, a parametric sweep is
achieved for different values of the apex angle $\theta$ of the
single-point rod, keeping all other geometric and atmospheric
parameters unchanged. The angle $\theta$ is defined here as the full
opening angle of the triangular tip in the 2-D configuration
(Figure~\ref{fig2}b). Values from 2\textdegree\ to 90\textdegree\ 
(blunt, right-angle wedge) were explored. For each $\theta$, the
maximum electric-field magnitude ($E_{\max}$) is extracted from the air
adjacent to the upper tip and to the lower crown. Besides, the maximum
conduction current density ($J_{\max}$) is also extracted in those same
regions. The results are summarized in Figure~\ref{fig8}.

\begin{figure}
\includegraphics{fig08}
\caption{\label{fig8}(a) Maximum electric field $E_{\max}$ and (b)
current density $J_{\max}$ as functions of apex angle for the upper
single-point rod ($\theta$), under fair-weather (red) and storm-like
(blue) forcing. Fair-weather values show weak dependence on tip
geometry, whereas storm-like conditions produce strong geometric
amplification. The lower crown achieves the highest fields (2.8
MV${\cdot}$m$^{-1}$) and currents (5 mA${\cdot}$m$^{-2}$), representing
upper-bound pre-discharge estimates in the linear ohmic model.}
\end{figure}

Figure~\ref{fig8}a shows that the peak field near the single-point
rod decreases monotonically as the tip is blunted. Under fair-weather
forcing (red triangles), $E_{\max}$ drops from roughly 20 kV/m for very
sharp apices to 13 kV/m at 90\textdegree. The dependence is smooth and
relatively weak: over the entire 0--90\textdegree\ range, the variation
remains within a factor ${\lesssim}1.5$. The same trend holds under
storm-like forcing (blue triangles), with $E_{\max}$ decreasing from
800 kV/m for acute tips to 450~kV/m for the bluntest wedge. Thus,
sharpening the apex enhances the local field, but only at the
tens-of-percent level for realistic angles. This mild angular
sensitivity is expected in a floating-conductor configuration dominated
by large-scale column forcing: changing $\theta$ modifies the local
curvature, hence the geometric amplification factor, but the overall
potential of the metal adjusts self-consistently to satisfy the imposed
atmospheric conduction current. In other words, the tip sharpness
controls how a nearly fixed potential drop is concentrated into
millimeter--centimeter gradients, rather than changing the global
voltage available to the structure.

For comparison, Figure~\ref{fig8}a also reports the maximum field at
the five-point crown (stars). In both atmospheric regimes, the crown
peak field remains essentially constant as $\theta$ varies. Under
fair weather, it stays near 80 kV/m and under storm-like forcing near
2700--3000 kV/m. This insensitivity indicates that the lower crown is
controlled almost entirely by its own apex geometry and by the ambient
forcing, with only negligible coupling to the sharpness of the distant
upper collector. Practically, this means that uncertainties in the
historical manufacturing of the top point do not propagate into the
near-canopy field enhancement produced by the terminal crown.

The corresponding maxima in conduction current density is shown in
Figure~\ref{fig8}b. As predicted by the ohmic relation, $J_{\max}$
near the upper tip follows the same monotonic decrease with $\theta$ as
$E_{\max}$. In fair weather (red triangles), the peak current density
decreases gently (again by less than a factor of two) between sharp and
blunt apices. In storm-like conditions (blue triangles) the same
reduction occurs, but at values that are three orders of magnitude
higher than in fair weather, reflecting the imposed increase in both
background field and conductivity. As for the electric field, the crown
current maxima (stars) are essentially flat with $\theta$, confirming
that the lower distributor behaviour is decoupled from the collector
sharpness in this pre-corona regime.

An additional feature of Figure~\ref{fig8}b is that, under storm-like
forcing, the upper tip exhibits a larger $J_{\max}$ than the crown even
though the crown reaches a higher $E_{\max}$. This reversal arises from
conductivity stratification: the upper collector operates at a higher
altitude where $\sigma(z)$ is larger, so a given field produces a
proportionally larger conduction current. In contrast, the stronger
field of the crown sits in a lower-$\sigma$ layer and therefore carries
a smaller ohmic current density despite its higher geometric
amplification.

Altogether, the apex-angle sweep shows that the pre-corona predictions
for the upper collector are robust to plausible uncertainties in tip
sharpness. Whether the 18{th}-century metal point was needle-sharp or
moderately blunt changes $E_{\max}$ and $J_{\max}$ only by a modest
factor, rather than by orders of magnitude. Therefore, the qualitative
conclusions drawn from the baseline $\theta=4$\textdegree\ geometry
(namely that fair-weather operation remains safely sub-coronal while
storm-time forcing can push the tip toward onset ranges) do not depend
critically on an exact reconstruction of point shape. The strong
enhancement produced by the multi-point crown, on the other hand, is
governed by the crown's own sharpness and spacing and is effectively
independent of the collector angle. Finally, it should be recalled that
these angular trends are obtained in a 2-D wedge approximation. A fully
3-D conical tip would yield different absolute amplification factors,
but the monotonic, weak sensitivity to $\theta$ is expected to persist,
since it reflects the floating-potential adjustment and the
localization of the potential drop rather than any peculiarity of the
2-D geometry.

\subsection{Influence of conductor geometry}\label{ssec34}

Configuration I of the electrovegetometer appears effective under
storm-time conditions but essentially inactive in fair weather. To
explore whether alternative geometries could improve its fair-weather
response, four variants of the conductor's layout were examined, as
sketched in Figure~\ref{fig9}a:
\begin{itemize}
\item The configuration I with single-point rod collector and crown
distributor. 
\item The configuration II: the single upper point is replaced by a
small crown of sharp tips mounted at the mast head, while the lower
distributor remains unchanged. 
\item The extended configuration I: it retains a single upper point but
extends the metallic mast by approximately 1 m, so that the tip now
protrudes higher into the atmospheric column. The lower crown and
supports are unchanged. This configuration does not correspond to a
specific historical drawing but serves to test the sensitivity of the
device to collector height and to the associated changes in background
potential and conductivity.
\item The isolated crown configuration: the entire metallic mast-arm
assembly is removed so as to leave only the five-point crown at canopy
height. This ``minimal'' configuration provides a control case in which
the crown interacts directly with the ambient field without any
guidance or concentration by an elevated conductor. 
\end{itemize}
For the four configurations, the maximum electric field values obtained
at the lower crown are presented in Figure~\ref{fig9}b under
fair-weather and storm-like forcing. In fair weather, all
configurations yield nearly identical peak fields of order $10^{2}$
kV${\cdot}$m$^{-1}$, indicating that the local crown geometry dominates
field enhancement and that the presence, shape or height of the upper
collector has only a minor influence in the weak-field regime. Under
storm-like forcing, however, the three mast-bearing configurations (I,
II and extended-I) all reach comparable peak fields of about  2.5--$3
\times 10^{3}$ kV${\cdot}$m$^{-1}$, whereas the crown-only
configuration remains significantly lower (roughly one half of that
value). This contrast shows that the elevated metallic mast efficiently
funnels the storm-enhanced column potential into the crown region, but
that replacing a single-point collector with a multi-point collector or
modestly extending its height does not materially change the local
maximum field at the distributor.

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}(a) Four distinct geometries of the
electrovegetometer used in the simulations. Brown regions denote wooden
supports, red lines metallic conductors. (b) Maximum electric field at
the lower crown distributor, $E_{\max}$, under fair-weather and
storm-like forcing, showing that all mast-bearing configurations
produce similar peak fields while the crown-only case remains lower in
the storm regime. (c) Corresponding maximum conduction current density,
$J_{\max}$, on a logarithmic scale, illustrating the
three-order-of-magnitude increase from fair to storm conditions and the
enhanced currents obtained when an elevated metallic mast is present.}
\end{figure}

The corresponding maxima in conduction current density, $J_{\max}$, are
shown in Figure~\ref{fig9}c on a logarithmic scale. In fair-weather
conditions, all four configurations cluster around \mbox{$J_{\max}\approx
10^{-3}~\upmu$A${\cdot}$m$^{-2}$,} confirming that the weak, sub-coronal
currents are essentially set by the ambient atmospheric conduction
current and by the crown geometry. When storm-like forcing is applied,
$J_{\max}$ increases by nearly three orders of magnitude, reaching a
few $\upmu$A${\cdot}$m$^{-2}$ for the three mast-bearing configurations,
while the crown-only case again remains lower by about a factor of two.
The parallel behaviour of $E_{\max}$ and $J_{\max}$ across the four
configurations is consistent with the ohmic scaling $J=\sigma E$ and
confirms that the main role of the mast and upper collector is to
increase the amount of background current intercepted and channelled
through the crown, rather than to introduce strong qualitative
differences between the specific collector designs.

\section{Discussion}\label{sec4}

The simulations presented above provide a first quantitative bridge
between Bertholon's qualitative description of his electrovegetometer
and modern concepts of the global atmospheric electric circuit and
pre-corona field enhancement. Several points emerge regarding (i) the
physical plausibility of Bertholon's original narrative, (ii) the
expected magnitude and localisation of electrical effects near the
canopy and (iii) the limitations of the present modelling framework and
its implications for both historical interpretation and modern
``electroculture'' claims.

\subsection{Fair-weather operation: localized but modest enhancement}
\label{ssec41}

Under fair-weather forcing, the reconstructed electrovegetometer
behaves as a weak perturbation of the global conduction current. The
upper collector and lower crown both generate strong local field
enhancements (by two to three orders of magnitude relative to the
ambient ${\approx}10^{2}$ V${\cdot}$m$^{-1}$ field) but these enhanced
regions remain confined to millimeter--centimeter neighbourhoods around
the tips. The single upper point concentrates the background potential
drop into a narrow funnel and attains peak fields of order a few
${\times}10^{4}$ V${\cdot}$m$^{-1}$, while the five-point crown reaches
about $8 \times 10^{4}$ V${\cdot}$m$^{-1}$ near the central apex.

From a purely electrodynamic standpoint, these fields are high enough
to significantly distort ion trajectories and to locally increase
ionisation and attachment rates, if the atmosphere is already weakly
ionised. However, the associated ohmic current densities remain in the
pA${\cdot}$m$^{-2}$ to low-nA${\cdot}$m$^{-2}$ range, only moderately above
the background conduction current. The total current that can be
channeled through a realistic crown footprint therefore remains
extremely small.

For the plant microenvironment, this implies that, in undisturbed
weather, the device could plausibly create narrow ``hot spots'' of
enhanced field and ion flux immediately around each tip, but these
perturbations would decay to near-background values over distances
comparable to or smaller than, typical leaf and canopy length scales.
Any direct electrodynamic forcing on plant tissue (through induced
surface charges, field-driven ion flows at the leaf boundary layer or
modification of aerosol deposition patterns) would thus be highly
localised and likely intermittent.

Consequently, the fair-weather regime appears compatible with
Bertholon's qualitative idea of a continuous but ``gentle'' influence
of atmospheric electricity, yet the present results suggest that this
influence is physically subtle: the electrovegetometer does not act as
a strong injector of charge or as a significant sink/source in the
global circuit. Rather, it reshapes the local pre-existing conduction
current into narrow plumes without greatly increasing its magnitude.

\subsection{Storm-time forcing and the plausibility of luminous
``aigrettes''}\label{ssec42}

Under idealised storm-like forcing, the same geometry operates in a
very different regime. When the background field and conductivity are
increased to values representative of pre-storm or storm-affected
conditions, the upper point and lower crown can reach peak electric
fields ranging from several 10\tsup{5} V${\cdot}$m$^{-1}$ up to the
MV${\cdot}$m$^{-1}$ scale in the linear model. These levels are
comparable to or exceed, empirical corona-onset thresholds for sharp
conductors at ground pressure and approach conventional breakdown
estimates.

It is important to emphasise that, because the model neglects space
charge and ionisation feedback, these MV${\cdot}$m$^{-1}$-scale values
should be interpreted as \textit{upper bounds} on the pre-corona state
rather than as realistic sustained fields: in a real atmosphere, corona
would be triggered earlier and the resulting space charge would
partially screen the tips, limiting further field growth. Nonetheless,
the fact that the ohmic pre-corona solution naturally approaches
corona-onset thresholds under enhanced GEC forcing is significant. It
provides a quantitative rationale for Bertholon's reports of faint
luminous glows (``aigrettes lumineuses'') at the points under disturbed
weather and for historical observations of St Elmo's fire on ship masts
and church spires.

In this picture, the electrovegetometer can act as a facilitator for
corona discharges during periods when the atmospheric column is already
highly stressed by nearby storm charge. The elevated mast ensures that
the upper collector samples a region of slightly higher conductivity
and potential, while the lower multi-point crown concentrates this
potential drop at canopy height. The simulations show that storm-time
currents may increase by roughly three orders of magnitude compared
with fair weather while retaining smooth, monotonic conduction-like
profiles around the tips. Once corona onset is reached, ion production
and charge transport near the canopy could be substantially greater
than in the fair-weather regime, potentially producing visible glows
and enhanced ion fluxes.

However, this enhanced operation would remain episodic, tied to the
presence of nearby electrified clouds and may not correspond to the
benign, steady-state ``improvement'' of vegetation that Bertholon had
in mind. Moreover, corona can produce localised chemical and mechanical
stresses (ozone, NO$_{x}$, UV, micro-scale heating and ion-wind shear) whose
impacts on plants are complex and not necessarily beneficial. The
present model cannot address these aspects and thus cannot directly
support or refute any claimed agronomic benefits of storm-time
operation.

\subsection{Robustness to geometric uncertainties and the role of the
mast}\label{ssec43}

The parametric sweeps indicate that several aspects of the device
response are relatively robust to historical uncertainties in geometry.
Varying the apex angle of the upper collector over a wide range only
alters the maximum field and current density near the tip by factors of
order unity, not by orders of magnitude. This reflects the fact that
the global potential available to the floating structure is set by the
imposed atmospheric column, while the tip sharpness controls how that
potential drop is localized on millimeter scales. Likewise, replacing
the single upper point with a small crown or extending the mast
modestly, barely affects the peak fields at the lower crown in either
fair or storm-like conditions. The simulations show that, in the storm
regime, all mast-bearing configurations (Configurations I, II and
extended-I) yield similar $E_{\max}$ and $J_{\max}$ at the canopy-level
crown, whereas an isolated crown with no mast reaches significantly
lower maxima. This suggests that the primary electrodynamic role of the
mast is to intercept an enhanced portion of the background column
current and potential, funnelling it into the distributor, rather than
to sensitively encode the details of the collector design.

From a historical reconstruction perspective, this is reassuring: even
if Bertholon's actual hardware deviated from the stylised geometry used
here, the qualitative conclusions about\unskip\break fair- versus storm-time
operation, localisation of fields and the relative importance of
collector versus distributor are unlikely to change drastically. The
multi-point crown near the crop canopy emerges as the dominant feature
for local field enhancement, while the mast and collector primarily set
the voltage ``voltage'' delivered to it.

\subsection{Limitations of the present model}\label{ssec44}

Despite its usefulness as an exploratory tool, the present 2-D, linear,
ohmic model has several important limitations that constrain the
interpretation of the results:
\begin{itemize}
\item The model assumes a prescribed conductivity profile and linear
Ohm's law, with no explicit treatment of charge production, attachment,
recombination or drift beyond what is encoded in $\sigma (z)$. Once
fields approach corona-onset thresholds, this approximation breaks
down. The simulated peak fields in the storm-like regime should
therefore be viewed as indicative of where onset is likely, not as
literal predictions of sustained MV${\cdot}$m$^{-1}$ values.
\item The cross-sectional configuration of the electrovegetometer
represents an infinitely long structure, leading to wedge-like tips
rather than realistic 3-D conical points. This affects local
amplification factors and field line topology near the apices. A full
3-D simulation would likely yield different absolute $E_{\max}$ values
and possibly broader high-field regions, though the basic trends
(localised enhancement, decimetric decay to background, relative
insensitivity to the collector apex angle) should remain qualitatively
similar.
\item The wooden supports are modelled with fixed, low conductivities
and the soil is treated implicitly through boundary conditions rather
than as a stratified, moisture-dependent conductor. In practice,
however, Bertholon devoted considerable attention to improving
insulation: the buried mast section was fire-dried, tarred, wrapped in
charcoal dust and cement, then set in masonry, while the above-ground
part was painted or bitumen-coated; the mast head was further protected
by resin-saturated inserts and glass/mastic sleeves and the horizontal
arms were carried on insulated trestles with silk cords
(Table~\ref{tab1}). These measures likely reduced leakage and increased
support resistance, yet their properties still depended on humidity,
ageing and contamination, so leakage paths and the floating potential
(and thus $E_{\max}$ and $J_{\max}$) may have shifted only by moderate
factors.
\item The ``fair weather'' and ``storm-like'' regimes are represented
by simple, horizontally uniform profiles with prescribed
$J_{0,\mathrm{atm}}$ and $E_{0,\mathrm{atm}}$. Actual atmospheric
electric environments over agricultural fields are influenced by
topography, nearby structures, aerosol loading and horizontal
inhomogeneities in storm charge. The local field at the
electrovegetometer could therefore deviate significantly from the
idealised profiles adopted here, especially under complex convective
conditions.
\item The simulations do not include explicit representations of
vegetation. Leaves, stems and canopy structure can distort the field
and act as additional conductors or partial insulators, redistributing
currents and modifying the near-surface potential landscape. They can
also participate in charge exchange through surface conduction films,
stomatal apertures or wetting layers. The present results therefore
provide a first-order picture of the field ``in the air'', not a
complete description of plant-field coupling.
\end{itemize}

\subsection{Implications for the history and modern practice of
``electroculture''}\label{ssec45}

Within these limitations, the modelling results support a nuanced
re-assessment of Bertholon's electrovegetometer. On the one hand, the
device is physically capable of generating strong local field
enhancements and, under storm-time conditions, of approaching or
exceeding corona-onset thresholds, making luminous ``aigrettes''
plausible. On the other hand, in its primary fair weather operating
state (which would dominate day-to-day exposure) the structure appears
to act mainly as a passive field concentrator with small total currents
and highly localised perturbations.

This dual picture suggests that Bertholon's conceptual intuition about
the existence of a persistent electrical influence on vegetation was
not entirely misplaced, but that his expectations regarding the
strength and agronomic consequences of this influence might have been
optimistic. The electrovegetometer is better interpreted as a delicate
probe of the global electric circuit in the near-surface layer and as a
demonstrator of field concentration and corona phenomena, than as a
robust agricultural ``enhancer'' in the modern engineering sense.

For contemporary discussions of ``electroculture'', a term that has
recently resurfaced in popular and sometimes pseudoscientific contexts,
the present work underscores the need for careful, quantitative
modelling and controlled experiments. Devices that resemble historical
electrovegetometers may indeed modify the local electric environment
around plants, but the magnitude, sign and biological relevance of
these modifications cannot be inferred from qualitative analogies
alone. They require a combination of atmospheric-electric measurements,
detailed plant-physiology studies and models that extend beyond the
pre-corona, linear regime considered here.

\section{Conclusion}\label{sec5}

Re-examining Bertholon's 18th-century electrovegetometer within the
framework of modern atmospheric electrodynamics, this study has
developed a quasi-steady, two-dimensional, resistive model of the
air-device system, in which the atmosphere is treated as an ohmic
medium carrying the global conduction current and the metallic
structure is represented as a floating conductor supported by leaky
wooden insulators. Solving the stationary conduction  equation with
altitude-dependent conductivity and realistic configurations has
yielded quantitative estimates of potentials, electric fields and
current densities around the electrovegetometer under idealised fair
weather and storm-like forcing.

The main findings can be summarised as follows:
\begin{itemize}
\item Under typical fair weather conditions, the electrovegetometer's
sharp points enhance the local electric field by two to three orders of
magnitude relative to the background atmospheric field, reaching tens
of kV${\cdot}$m$^{-1}$ at the upper single point and about 80
kV${\cdot}$m$^{-1}$ at the lower multi-point crown. The associated
current densities remain in the pA--nA/m\tsup{2} range, consistent with
weak conduction in a slightly ionised medium. Field and current
perturbations are strongly localised and decay to near-ambient values
within cm.
\item When the background field and conductivity are increased to
values representative of pre-storm or storm-affected conditions, the
same geometry yields peak fields in the 10\tsup{5}--10\tsup{6}
V${\cdot}$m$^{-1}$ range. These levels approach or exceed empirical
corona-onset thresholds and encroach on breakdown estimates,
particularly at the lower crown. Within the limits of a linear, space
charge free approximation, these results indicate that Bertholon's
device could have produced corona glows and enhanced ion fluxes during
disturbed weather, providing a plausible physical basis for historical
reports of luminous ``aigrettes''.
\item Parametric variations of the upper apex angle and collector
geometry show that fair weather and storm-time peak fields and currents
near the lower crown are largely insensitive to the fine details of the
collector, as long as an elevated mast is present. The principal
function of the mast is to intercept a portion of the atmospheric
column potential and funnel it to the distributor, while the
multi-point crown near canopy height remains the dominant feature
controlling local field enhancement.
\item The results are contingent on the assumptions of a 2-D geometry,
linear ohmic conduction, prescribed conductivity profiles and
simplified material properties. They should therefore be viewed as
pre-corona upper bounds rather than fully realistic predictions of
discharge behaviour. Within these limits, the study suggests that
Bertholon's \mbox{electrovegetometer} was physically capable of concentrating
atmospheric electricity and occasionally producing visible corona under
storm-time forcing, while its fair weather influence on plants was
likely subtle, localised and difficult to quantify with 18{th}-century
instruments.
\end{itemize}
Finally, this work illustrates how modern numerical modelling of the
global atmospheric electric circuit, even in a simplified pre-corona
form, can sharpen our understanding of historical electrotechnical
devices and their plausible modes of operation. Future extensions could
include fully 3-D simulations, explicit treatment of space charge and
corona dynamics, more realistic representations of soil and vegetation
and coupled experiments in controlled atmospheric-electric
environments. Such studies would not only refine the retrospective
assessment of Bertholon's electrovegetometer but also inform
contemporary debates on the physical and biological significance of
weak atmospheric-electric perturbations in agricultural settings.

\section*{Declaration of interests}

The author does not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and has
declared no affiliations other than their research organization.

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