From Giambatista Beccaria
MS not found; reprinted and translated from Latin pamphlet: De Electricitate Vindice Joannis Baptistae Beccariae ex Scholis Piis Ad Beniaminum Franklinium Virum de Re Electrica, & Meteorologica optime meritum. Epistola. Taurini, Typis Joannis Baptistae Fontana Impressoris, & Bibliopolae in Palatio Urbis. Facultate obtenta.  (Yale University Library).6
Beccaria’s letter is known only in the form of a four-page pamphlet, quite probably printed very soon after the indicated date of the letter. It is not clear whether he actually sent a hand-written copy to Franklin, or, following a rather common practice of the time with scientific writings intended for many readers, cast the paper into the form of a letter addressed to one individual well known among students of the particular subject.
The text of this letter offers difficulties, both because of the somewhat cumbersome style of the Latin in which it was written and the unfamiliar terminology Beccaria employed, and also because the scientific concepts and theories that he presented and discussed have, during the last two centuries, become increasingly irrelevant to the progress of electrical science. Because of these difficulties the editors have decided to print both the Latin original and an English translation, so that possibly interested readers may use either one version or the other, or both in combination, when seeking to understand the author’s presentation. Limited annotation is attached to the translation rather than to the Latin original.
The editors gratefully acknowledge the help they have received in preparing the translation from David O. Ross, Jr., assistant professor of Classics in Yale University, and from Alan E. Shapiro, graduate student in the Yale Department of the History of Science and Medicine. It should be made wholly clear, however, that these gentlemen have not seen the final text of the translation before its dispatch to the printer, and that the editor of this series is, here as always in the pages of these volumes, ultimately responsible personally for all errors and shortcomings in the editorial work.
[20 Februarii 1767.]
De Electricitate Vindice
Joannis Baptistae Beccariae ex Scholis Piis
Ad Beniaminum Franklinium
Virum de Re Electrica, et Meteorologica optime meritum
1. Quod die 11. Septembris 1766. scribebam tibi, FRANKLINI clarissime: Existimare me, errare eos, qui putarent, Simmeriano experimento theoriam infirmari tuam; experimenta ea omnia, queis ego, et Pekinensis, et Simmeriani experimenti analysim eram prosequutus, et totam de electricitate vitrorum historiam auxeram, novum dumtaxat principium postulare, quod tuis adjungeretur, et cum iisdem apprime consentiret; id fusius nunc tandem demonstrare constitui, quum primum per valetudinem licet mihi.
2. Itaque addendum principium est hujusmodi: Facies vitri post explosionem, dum denundatur, electricitatem vindicat sibi, quam habuit ante explosionem. Atque principium hoc est, cui nomen indere placet mihi, rem proxime significans Vindicem Electricitatem.
3. De principii caussa, ipso constituto, quaeremus. Interea nonne magnam Physicae accessionem ii facere sunt censendi, qui experimenta numero longe plurima specia distractissima inveniant, a quo uno principio pendeant omnia, et mutua veluti cognatione colligari singula cum singulis demonstrent, quae disjunctissima videbantur, et quasi pugnantia? Imo vero nonne in omni demum caussarum vestigatione phaenomeno alicui est denique acquiescendum, cujur ulteriorem caussam assequi non licet? Porro principii hujus mei, quod Vindicem Electricitatem appello, caussam proximan explorari posse confido; sed eo ignorato hanc ignorari debere certum est.
4. Id itaque agam in singulari libello, ut demonstrem: Experimenta omnia, quae protuli, Electricitatem Vindicem postulare tamquam constans phaenomenum, ad quod referantur. Hoc posito ilia explicari omnia, et reliqua vere divinari, quae, et qualia debeant existere pro infinita, quae potest occurrere, adjunctorum varietate.
5. Sed tibi interea, Vir clarissime, si prima innuam, et ea certe necessaria principii consectaria, faciam satis abunde. Neque haec memorabo, quo doceam; sed quo facias Tu solidiora, quae natura ipsa compellit nos fundamentis superstruere a Te constitutis.
6. Itaque, si hoc ponatur: Faciem vitri, dum denundatur post explosionem, vindicare sibi electricitatem, quam habuit ante explosionem, consectarium primum est: Eam Electricitatem praepollere debere in faciem adversam; qua voce intelligere me vides, quod est consentaneum theoriae tuae.
7. Ex Te enim ignis extraneus, qui init in unam vitri faciem, dispellit tantumdem ignis proprii ex facie adversa; similiterque ignis proprius, qui eliciatur ex una vitri facie, tantumdem extranei facit, ut affluat in faciem adversam, cujus proprius erat veluti fulcrum. Quamobrem, si facies vitri, quae ante explosionem redundabat, dum post explosionem denudatur, vindicat sibi excessum ignis, quem habebat ante explosionem, hic excessus praepollebit in faciem adversam, quae per hypothesim ab explosione omnem amisit electricitatem; nempe tantumdem ignis nitetur dispellere ex facie adversa, adeoque excitabit in facie adversa atmosphaeram redundantem; scilicet excessus in eam immissus dicetur praepollere in faciem hanc, quatenus faciet, ut haec, quae caeteroquin non haberet nisi ignem nativum proprium, ipsa etiam redundare videatur ob partem ignis proprii, quae pellitur, et explicatur.
8. Similiter, si facies vitri, quae ante explosionem deficiebat, dum post explosionem denundatur, vindicat sibi defectum, quem habebat ante explosionem, hic defectus praepollebit in faciem adversam, quae item per hypothesim ab explosione omnem amisit electricitatem; nempe tantumdem ignis extranei alliciet in faciem adversam; adeoque excitabit in facie adversa atmosphaeram deficientem; scilicet defectus in earn denudatione inditus dicetur praepollere in faciem hanc, quatenus faciet, ut haec, quae caetoroquin haberet ignem nativum suum, ipsa etiam deficere videatur ob partem ignis extranei, quem jam plane expostulat, atque allicit ad sese.
9. Itaque, quo multa paucis, eaque satis perspicue omnia eloqui valeamus, nomina licebit condere aliqua, quibus has, affinesque alias in vitris electricitatum habitudines significemus: Et primo quidem summam ignis redundantis in facie una, et deficientis in facie adversa, quae explosione nullescit tota, et cui adeo proportione respondet explosionis magnitudo, appellabiums nomine, uti puto, satis consentaneo Electricitatem vitri absolutam, et veram; unde similiter totus excessus, aut totus defectus in facie una vitri, dicetur absoluta, et vera ejus faciei Electricitas.
10. Deinde ipsam, quae intercedat aliqua, inter excessum faciei unius, et defectum alterius differentiam, Electricitatem relativam sive apparentem dicemus; quod ea sola appareat, et agat, quum vitrum aut indutum, aut exutum exploratur, quin attrectetur facies utraque simul ad explosionem ciendam.
11. Sed haec iterum apparens electricitas distinguetur excessus adjuncto, si excessus faciei unius sit major defectu adversae, vel contra, si defectus sit major excessu; Sic si vitri facies A, excessum majorem habeat defectu adversae faciei B, in vitro inerit Electricitas apparens excessus; sin defectus faciei B sit major excessu faciei A, vitrum erit electricum defectu apparente.
12. Atque ad singulas distinguendas in singulis faciebus electricitates hujusmodi, faciem A in primo exemplo electricam dicemus excessu determinante, et faciem B excessu determinato electricam dicemus. Contra in exemplo altero faciem B appellabimus electricam defectu determinante, faciem A electricam defectu determinato.
13. Unde etiam universe eae voces obvenient familiares Electricitas, aut Facies determinans, et Electricitas, aut Facies determinata.
14. Neque demum erit supervacaneum electricitatem apparentem aliam dicere solitariam, aliam conjugatam: Ceu cum facies una vitri excessum ignis habet sine ullo respondente in facie adversa defectu, aut contra facies una defectum habet sine ullo respondente in facie adversa excessu, vitrum excessu, aut defectu solitario electricum dicetur. Sin excessui majori aliquis jam respondeat in facie adversa defectus, aut majori defectui excessus aliquis: vitrum excessu, aut defectu apparente conjugato erit electricum.
15. Quibus quidem in partitionibus non vereor, ne videar Tibi ineptire, Franklini clarissime, utpotequi videas, eas vocum differentias expostulari a differentiis rerum, ceu alterum demonstrat, quod ex constituta vindice electricitate sequitur consectarium.
16. Scilicet: Apparens a denundatione electricitas, si coetera constent eadem, maxima sit oportet: Est enim electricitas solitaria excessus, aut defectus, qui primo existit in facie una, dum facies adversa ab explosione egnem nativum habet; prima autem, auqe init in faciem vitri electricitas, maxima est, et maximam habet vim determinandae contrariae in facie adversa electricitatis; sunt enim datae caussae effectus initiales, qui sunt semper maximi. Itaque quemadmodum (ne a re discedamus nostra) cum principio vitrum obijcimus catenae, ut fiat electricum, prima, quae in contiguam vitri faciem init scintilla, est maxima, et maxima est prima, quae a facie adversa dispellitur in solum, et scintillae consequentes decrescunt usque, et usque magis; ita prima, et solitaria, quae a denundatione vitri emicat iterum post explosionem electricitas, maxima sit oportet, et maxima vi contrariam determinet in facie adversa electricitatem.
17. Atque hinc manifestum existit consectarium tertium: Electricitates homologas a denundatione post explosionem apparentes in utraque vitri facie vi maxima tendere ad aequalitatem. Scilicet electricitas determinans vi maxima tendit ad nihilum: intereaque facit, ut electricitas apparens determinata vi maxima nitatur abire in absolutam ipsi sibi contrariam, et aequalem. Quod abstractum consectarium singulari exemplo est omnino perspicuum: Nam, si ponas, post explosionem denundari faciem A, quae ante explosionem redundabat, ipsa vindicabit sibi vi maxima pristinum excessum, qui vi maxima partem ignis nativi pellet ex facie adversa (16); adeoque maxima erit mutua, et contraria ejus excessus in ignem hunc nativum, et ignis hujus nativi in eum excessum actio. Igitur ille excessus ab igne hoc nativo vi maxima retropelletur, ut discedat, et abeat in nihilum, atque interea ille excessus dispellet aequali vi ignem nativum, ut discedat, et defectus ita existat excessui aequalis.
18. Exempli contrarii eadem est ratio. Phaenomena enim omnia ilia tenenda docent principia tua. I. Ignem in vitro librari utrinque cum igne nativo corporum extraneorum, quotiescumque summa ignis in vitro sit utlibet aequalis summae nativae. II. Ignem in vitro praepollere utrinque in ignem nativum corporum extraneorum, quotiescumque summa ignis in vitro sit utlibet major igne nativo. III. Ignem corporum extraneorum praepollere utrinque in ignem vitri, quotiescumque ignis in vitro sit utlibet minor igne nativo.
19. Quare, cum post explosionem denudatur facie vitri B, quae ante explosionem igne deficiebat, ipsa a denundatione sibi vindicat pristinum defectum, quin facie adversa, quae disjuncta est a corporibus deferentibus, respondentem excessum possit comparate sibi; summa ergo ignis nativi vitro contingentis toto eo defectu erit minuta; igitur ignis extraneus praepollebit undique, et nitetur se expandere in faciem deficientem, quo defectum minuat, atque in adversam, quo excessum producat defectui aequalem, itaque nativam ignis dosim restituat vitro. Quae omnia vi contingent maxima ex allata caussa.
20. Reenimvera, quae post explosionem a denudatione reviviscunt electricitates, signa electrica pro sua magnitudine edunt maxima omnia, scintillas, motus, auram.
21. Quae ipsa res quartum ferme facit Electricitatis Vindicis consectarium, nempe: Si facies post explosionem denudata iterum induatur, et vitrum attrectetur, aut amittit electricitatem vindicatam, si attrecteur in facie determinante, quae suit denudata, aut absolutam acquirit, et illi contrariam, et aequalem, si attractetur in facie adversa; etenim attrectare, seu universe objicere corpus deferens corpri, cujur electricitas vi maxima tendat in nihilum, est quasi viam electricitati ipsi facere, qua evanescat; Itaque quando ex proximo consectario electricitas determinans denudatione excitata vi maxima tendit in nihilum, attrectatione facei ipsius determinantis in nihilum abibit.
22. Similiter attrectare, seu corpus deferens objicere corpori electricitatem appetenti est viam facere, qua ipsam assequatur; sed ex proximo consectario facie vitri determinata vi maxima appetit electricitatem absolutam contrariam, et aequalem determinanti; igitur attrectatione hanc assequetur.
23. Neque vero in sola denudatione obtinet electricitas vindex; sed adhuc magis universe decremento ipsi, quod capit electricitas dati corporis cohibentis, dum admovetur ad datam a dato corpore distantiam, electricitas respondet, quae ipsi a vi vindice restituitur, cum iterum removetur.
24. Atque ex his paucis, quae ab uno fluunt omnia principio, quasi necessariis consectariis reliqua jam fluunt omnia, quae scribebam in specimine altero. Quemadmodum enim, denudata una facie, invalescit utrinque in vitro ejus faciei electricitas, quae obtinebat ante denudationem; Ita liquet, denudata altera, invalescere debere utrinqué alterius electricitatem; Unde intelligitur, quemadmodum a denudatione facierum vitri, aut vitorum plurium, quae ante et post explosionem fiat ordine eodem, electricitates ante et post explosionem appareant contrariae; quam rem primam appellabam ex explosione electritatum oscillationem; quae tamen appariturae sin eaedem, si facies vitri, aut vitrorum ante et post explosionem denudentur ordine contrario.
25. Atque huic rei si addas Vis Vindicis constantiam, qualem experientia demonstrat, ut nempe duret dum vitra ad horas integras denundantur, et iterum induuntur; perspicua est ratio electricitatis in vitro, vel in vitris admirabiliter horas integras oscillantis ex indusii a vitro, aut vitri a vitro disjunctione, et conjunctione.
26. Evanescit similiter omnis earum oscillationum admirabilitas, quas inveni contingere ex inversione vitri tenuioris. Quam tamen ad rem hoc facit experimentum.
27. Duas laminas vitreas tenuem aliam, aliam crassiorem, caetera aequales singulis catenae ramis objicio singulas, ut eodem tempore vi eadem electricaefiant; Turn praehensas angulis subtraho ambas laeva unam, dextera aliam. Socius adest, qui bacillis cerae signatoriae separatos singulis singulos duos habet in promptu arcus ex metallicis virgis sinuatos in formam literae S. Continuo uno eorum arcuum communicationem insert inter facie duas unam redundantem in vitro uno, aliam in alio deficientem; Similiter alio eorum arcuum facit, ut communicent reliquae duorum vitrorum facies duae: Singulis singulorum arcuum ad vitrorum facies appulsibus scintillulae existunt, quas theoria tua postulat, atque appulsu ultimo, quo communicatio absolvitur, explosio existit. Sed turn, si digitis attrecto utrinque vitrum crassius, ipsum quidem jam nullatenus explodit; si tenujus, explosionem experior ab ipso reliquam crassitiei vitri alterius proportionalem:
28. Quamobrem pro majore vitri crassitie major necessaria est ad inferenda electricitates contrarias in oppositas ejus facies. Quidni igitur quod tenuius est vitrum majore vi pristinam sibi a mutua, quae fiat post explosionem, interiorum facierum per disjunctionem denudatione, vindicet electricitatem? Atqui dum vitrum tenuius invertitur, interior quae fit ab inversione facie, ante explosionem electricitatem habebat illi contrariam, quae faciei contingebat antea interiori.
29. Adde demum ultimum, quod est plane necessarium, Vis Vindicis consectarium: Electricitati primo immissae ipsam magnitudine respondere; et jam liquet, quamobrem in experimento Pekinensi longe omnium pulcherrimo, utpote primo in eo genere, abeant in contrarias electricitates inversione vitri, quod unum principio electricum factum est, non item inversione alterius, quod electricitatem accepit illius communicatione.
30. Atque ex his, ut inquiebam, non experimenta ipsa solum, sed et experimentorum limites, atque varietates omnes facile intelliguntur. Non vereor vero ego, ne obscurior videar Tibi, dum studui esse brevior, qui paucis assueveris docere longe plurima. Vale.
Augustae Taurinorum die 20. Februarii 1767.
31. P. S. Quae de vitro dixi, eadem constituenda de corporibus cohibentibus omnibus, quae non transmeat electricus ignis, et analoga de aliis cohibentibus, quae transmeat, ceu sunt tibialia Simmerii, ad quae omnia latissime pertinet Electricitas Vindex, ceu necessaria vis cohibentis affectio pro ipsius vis modo, et magnitudine.
32. Fit inde, ut etiam ante explosionem vitra, ubi jam semel sunt denudata, Vim Vindicem habeant aliquam.
33. Ad modum vero quod attinet ejus Vis Vindicis, cum nitor ego electricum facere vitrum, vel vitra, quae calent admodum, scintillae utrinque existunt perpetuae. Ignis ergo electricus tum vel permeat, vel circuit. Experimentum habeo, quo rem plane definiam. Interea id videre videor: Electricitates in vitro, vel in vitris hujusmodi, quae admodum caleant, per explosionem neutiquam abire in contrarias, neque per inversionem.
34. Episcopus Mutinensis vir doctissimus aeque, et spectatissimus, et Pater Troilius e Societate Jesu nuper scripserunt de lapide, qui superiore aestate observatus est Alboreti dilabi e caelo. Perspecta observationum historia, opinatus sum: Lapidem hunc a fulmine in aerem disjectum, similiter ac electrica scintilla aquae guttulam disjiciente explodere ego soleo ligneum globulum ad hexapedas duas, aut etiam quatuor. Reenimvera eo tempore fulminabat, tonabat, tonitru exauditum, observata fulguratio socia fulminis phaenomena, perspectae scintillae in facie proximi rivi. Similia fulminantis caeli adjuncta consectabantur similes lapidum lapsus, quorum historiam apte refert Troilius. Placuit opinio mea, et visa scientiam facere portenti naturae, quod summan omni aevo habuit adjunctam admirabilitatem aeque, ac vanam superstitionem. Atque, uti addit doctissimus Episcopus, id etiam perbelle congruit, solum Mutinense scatere undique proxima aqua. Quare fulmen per lapidem, qui erat metallicus, effundens se in subiectam aquam debuit disjicere hanc, efferre ilium in sublime obvolutum luce sua, ne cerneretur, nisi postmodum cum relaberetur.
On Vindicating Electricity
Of Giambatista Beccaria of the Sacred Schools
A Letter to Benjamin Franklin
A Man of Great Merit in Electrical and Meteorological
Turin, February 20, 1767.7
1. I wrote to you, my distinguished Franklin, on September 11, 1766,8 that I thought they are wrong, who think your theory is invalidated by Simmer’s experiment; that all those experiments (in which I followed up the analysis of the Pekin and Simmer’s experiment,9 and furthered the whole investigation of the electricity of glasses) demand a new principle, which may be joined with yours, and which especially agrees with yours. This I have now at last decided to demonstrate more fully, when my health first allows me.
2. Thus the principle to be added is as follows: A surface of glass after an explosion, while it is discharged, frees [vindicat] for itself the electricity which it had before the explosion. And this is the principle to which I am pleased to give the name, closely expressing the effect: Vindicating Electricity.
3. Now that the principle has been set up, we shall seek to learn its cause. Are not they to be regarded as having made a great advance in Physics, who devise experiments, the greatest in number and most diverse in appearance, and show from what one principle all of them depend, and that separate phenomena are bound with each other as if by a mutual relationship—[phenomena] which before appeared most independent and almost contrary? Indeed, in every investigation of causes, must one not be finally content with any phenomenon, the more remote cause of which one cannot pursue? Hence I trust that I am able to explore the immediate cause of my principle, which I call Vindicating Electricity; but while the principle itself remains unknown, it is certain that the cause must remain unknown.
4. Therefore I shall do that in a special book, to demonstrate: That all the experiments that I have devised demand that we postulate Vindicating Electricity as a constant phenomenon to which the experiments may be referred; once this is posited, all those things are explained, and others truly deduced, what and of what sort ought to exist in relation to the infinite variety of adjuncts that can occur.
5. But if in the meantime, illustrious Sir, I sketch for you my basic propositions and the really important inferences, I shall certainly have done enough.
6. Thus, if this is posited: that a surface of glass, after an explosion, frees [vindicare] for itself the electricity it had before the explosion, the first inference is: that electricity ought to charge [praepollere] into the opposite surface—by which word you see that I understand what agrees with your theory.
7. For, according to you, the excess fire,1 which enters one surface of a glass, drives out from the opposite surface the same amount of fire; and likewise its own fire which is drawn out of one surface of a glass makes the same amount of excess fire flow into the opposite surface, of which its own [fire] was like a fulcrum. Wherefore, if the surface of a glass, which had an excess before the explosion, frees for itself the excess fire it had before the explosion, the excess charges into the opposite surface, which according to the hypothesis set free all its electricity with the explosion; for, of course, it will try to drive out the same amount of fire from the opposite surface, and so will produce in the opposite surface an excess atmosphere; obviously the excess sent into it will be said to charge into that surface, with the result that what would otherwise have only its own natural fire seems itself to have an excess on account of its own fire that is driven out and set free.
8. Similarly, if the surface of a glass that was deficient before the explosion is discharged after the explosion, it frees for itself the deficiency it had before the explosion, this deficiency will charge into the opposite surface, which, likewise according to the hypothesis, has set free all its electricity with the explosion; for, of course, it will attract the same amount of fire into the opposite surface; and so will produce in the opposite surface a deficient atmosphere; of course, the deficiency imposed on it by the discharging will be said to charge into that surface, with the result that that which otherwise would have its own natural fire, seems itself even to be deficient because of the part of the excess fire it now clearly demands and attracts to itself.
9. Therefore, to speak briefly but clearly, it will be desirable to invent some terminology by which we may signify these and other related conditions of electricity in glasses: First, even the total sum of excess fire in one surface and of deficient fire in the opposite surface, all of which is nullified by the explosion and to which the magnitude of the explosion corresponds proportionately, we shall call by a name appropriate enough, I think: the absolute and true electricity of glass; whence similarly the total excess or total deficiency in one surface of a glass will be called: the absolute and true electricity of that surface.
10. Then the difference itself, which somehow occurs between the excess of one surface and the deficiency of the other, we shall call relative or apparent electricity, because that only appears and acts when a glass charged by excess or deficiency is tested, unless both surfaces are touched simultaneously to produce an explosion.
11. But again this apparent electricity will be distinguished by the characteristic of excess if the excess of one surface is greater than the deficiency of the opposite one, or on the contrary, if the deficiency is greater than the excess; thus, if the surface A of the glass has a greater excess than the deficiency of the opposite surface B, there will be in the glass apparent excess electricity; but if the deficiency of surface B is greater than the excess of surface A, the glass will be electric by apparent deficiency.
12. In order to distinguish the different electricities of this sort in each of the surfaces, we shall call surface A in the first example electric by the determining [determinante] excess, and surface B electric by the determined [determinato] excess. On the other hand, in the other example we shall call surface B electric by the determining [determinante] deficiency, and surface A electric by the determined [determinato] deficiency.
13. Whence will come the universally familiar terms: determining Electricity or the determining surface, and determined Electricity or the determined surface.
14. Nor finally will it be superfluous to call one apparent electricity simple [solitariam], the other conjugate [conjugatam]: just as when one surface of a glass has an excess of fire with no corresponding deficiency in the opposite surface, or on the other hand one surface has a deficiency with no corresponding excess in the opposite surface, the glass will be called electric by simple excess or deficiency. But if to a greater excess some deficiency responds on the opposite side, or to a greater deficiency some excess, then the glass will be electric by apparent conjugate excess or deficiency.
15. In these definitions I have no fear that I might seem silly to you, illustrious Franklin, since you will see that these distinctions in terminology are demanded by real distinctions, as the other inference shows, which follow from the posited principle of vindicating electricity.
16. Obviously, electricity arising from discharge, if other things are constant, must be the greatest; for there is simple electricity by excess or by deficiency, which exists in one surface while the opposite surface has natural fire from the explosion; the first electricity, however, which enters the surface of the glass is the greatest and has the greatest power of determining contrary electricity in the opposite surface; the initial results of a given cause are always the greatest. Thus, according to our principle (lest we depart from our present subject) in whatever way we touch the glass to the chain to make it electric, the first spark to enter the contiguous surface of the glass is the greatest, and the first to be driven out from the opposite surface into the ground is the greatest, and subsequent sparks decrease more and more; thus the first, simple electricity which flashes forth from the discharge of the glass again after the explosion must be the greatest and must determine with the greatest force the contrary electricity in the opposite surface.
17. And from this there exists a third inference: homologous electricities arising from the discharge after an explosion tend toward equality in each surface of the glass with the greatest force. For of course determining electricity tends with the greatest force to nothing; and meanwhile it causes apparent determined electricity with the greatest force to try to pass into absolute [electricity] equal and opposite to itself. Which abstract inference is altogether clear from a single example: for, if you assume that surface A is discharged after the explosion and that before the explosion it had an excess, then it frees for itself with the greatest force its original excess, which drives with the greatest force part of the natural fire from the opposite surface (16); and thus the mutual action of its excess upon its natural fire, and of its natural fire upon its excess, will be contrary and maximum. Therefore that excess will be repelled with the greatest force by the natural fire, so that it vanishes and passes into nothing, and meanwhile that excess drives out the natural fire with an equal force, so that it vanishes, and thus a deficiency exists equal to the excess.
18. The reason for the opposite example is the same. All these phenomena show that your principles must be maintained. I. The fire in a glass is held in balance on both sides with the natural fire of external bodies, whenever the total of the fire in the glass is equal to the natural quantity. II. The fire in a glass charges from both sides into the natural fire of external bodies, whenever the total of the fire in the glass is greater than the natural fire. III. The fire of the external bodies charges from both sides into the fire of the glass, whenever the fire in the glass is less than the natural fire.
19. Therefore, when after the explosion the surface B of the glass is discharged, which before the explosion had a deficiency of fire, it frees for itself by the discharge the original deficiency without the opposite surface, which has been separated from conducting [deferentibus] bodies, being able to obtain for itself a corresponding excess; therefore, the quantity of natural fire touching the glass will be decreased by that total deficiency; and therefore, the excess fire will discharge everywhere and will try to expand itself into the deficient opposite surface, by which it lessens the deficiency and produces an excess equal to the deficiency, and thus restores to the glass its natural quantity of fire. All which things happen with the greatest force from the assumed cause.
20. For indeed, the electricities which are recovered from the discharge after an explosion give all the greatest signs in proportion to their magnitude, sparks, movements, wind.
21. Which thing itself makes the fourth inference of Vindicating Electricity, that is: If a surface discharged after an explosion is again charged by excess, and the glass is touched, either it loses the vindicating electricity, if it is touched in the determining surface that was discharged, or it acquires absolute electricity contrary to that and equal, if it is touched on the opposite surface; for to touch, or generally to present a deferent body to a body whose electricity tends with the greatest force into nothing is as it were to make a path for the electricity itself through which it vanishes; and thus since from the previous inference determining electricity excited by discharge tends with the greatest force into nothing, by the touching of the determining face itself it will pass into nothing.
22. Likewise to touch, or to present a deferent body to a body seeking electricity, is to make a path by which it may obtain [electricity]; but from the previous inference the determined surface of the glass seeks with the greatest force absolute electricity contrary and equal to the determining electricity; therefore it follows this by the touching.
23. Nor indeed does vindicating electricity hold in discharge, but still more generally the electricity corresponds to the decreasing of itself, which the electricity held by a given body within itself experiences, while it is moved to a given distance from a given body; and this electricity is restored to it by the vindicating force when it is again removed.
24. And now from these few, if necessary, inferences, all of which follow from one principle, all the remaining inferences follow, which I wrote about in another publication. For just as, once one surface is discharged, the electricity of that surface, which was acquired before the discharge, grows stronger on each side of the glass, so it will follow that when the other surface is discharged the electricity of the other on each side ought to grow stronger; whence it is understood how, from the discharge of a glass, or of several glasses, which discharge came about before and after the explosion in that same order, opposite electricities appear before and after the explosion, which phenomenon I first called from the explosion oscillation of electricities; which nevertheless would appear the same, if the surface of a glass, or glasses, are denuded before and after the explosion in the opposite order.
25. And if you add to this phenomenon the constancy of the Vindicating Force, which constancy, experiment shows, lasts for whole hours while the glasses are discharged and charged again, the reason is clear for the oscillation of the electricity in glass (it lasting surprisingly for whole hours in glasses) whether by the separation of cloth from glass or of glass from glass, or their conjunction.2
26. Likewise all the wonder of their oscillations disappears, which [oscillations] I found to happen from the inversion of a thinner glass. This is shown by this experiment:
27. I connect two glass plates, one thinner, the other thicker, but equal in other respects, individually to separate branches of a chain, so that they become electric at the same time and with the same force. Then I remove both of them, taking them by the corners, one on the left, the other on the right. An assistant is present, who has ready two separate curved metal rods, each with a handle of sealing wax, bent into the shape of the letter S. With one of these rods he promptly establishes communication between two surfaces, one charged to excess in one glass, the other charged by deficiency in the other glass. Likewise, with the other of these rods he connects the remaining two surfaces of the glasses. From each contact of each of the curved rods sparks arise to the surfaces of the glasses, which your theory demands, and at the final contact, by which the communication is ended, an explosion takes place. But then, if I touch with my finger the thicker glass on each side, it now does not explode at all; but if I touch the thinner, I experience a subsequent explosion proportional to the thickness of the other glass.
28. Wherefore, in proportion to the greater thickness of the glass a greater force is necessary to bring contrary electricity into its opposite surfaces. Is it not, therefore, because a thinner glass frees for itself with greater force the original electricity from the mutual discharge that occurred after the explosion of the interior surfaces through separation? Then, while a thinner glass is inserted, the surface, which becomes the inner from the inversion, had, prior to the explosion, electricity contrary to that which was previously on the inner surface.
29. Add a final inference of Vindicating Force that is clearly necessary: The Force corresponds in magnitude to the electricity first admitted. And now one can see why in the Pekin experiment (that most splendid of all, as well as the first of its kind) electricities change into the contrary by the inversion of the glass that alone was made electric in the beginning, not similarly by the inversion of the other that receives electricity by the communication with it.
30. And from these things, as I was saying, not only are the experiments themselves easily understood, but the boundaries of the experiments and all their variety. In truth, I do not fear that, while I am eager to be concise, I will seem to you rather obscure, you who are accustomed to teach many things in a few words. Farewell.
31. P.S. What I have said about glass must also be established for all insulating [cohibendibus] bodies through which electric fire does not pass, and is analogous to other insulating bodies through which electric fire does not pass, just as Symmer’s stockings, to all which things Vindicating Electricity most broadly pertains, as a necessary aspect of restraining force in relation to the manner and magnitude of the force itself.
32. It happens then that once glasses are discharged they have some Vindicating Force even before an explosion.
33. In connection with the manner of this Vindicating Force, when I try to make a very warm glass or glasses electric, continual sparks arise on both sides. Therefore the electric fire either goes through or around. I have an experiment by which I clearly define the phenomenon. Meanwhile, I seem to see this: electricities in glass or glasses of this sort, which are very warm never change into contrary electricities by an explosion or by inversion.
34. The Bishop of Modena, a man equally learned and revered, and the Jesuit Father Troilius recently wrote about a stone which was observed last summer to fall from heaven at Alboretium.3 When the history of these observations is reviewed I believe that the stone was cast into the air by a thunderbolt, just as I am accustomed to explode an iron ball a distance of two or even four rods by an electric spark dispersing a drop of water. For indeed at that time it was thundering and lightning, thunder was heard, lightning (the allied phenomenon of the bolt) was observed, sparks were seen on the surface of a nearby stream. Similar effects of lightning in the sky accompanied similar falling stones, of which Troilius gives a good account. My judgment is that these sights explain the portent of nature, which in every age has excited the greatest wonder as well as vain superstition. And, as the learned bishop adds, this confirms remarkably that the soil at Modena is everywhere full of the nearby water. Wherefore the bolt, driving through the stone, which is metallic, into the water beneath should scatter the water and hurl the stone into the air while covered in its own flash, so that it be not seen until afterwards, when it falls back down.
6. One other copy of this pamphlet has been located in the N.Y. Pub. Lib.
7. The date line is transferred to this point in the translation from its position in the Latin between the end of the main body of the letter and the postscript. Beccaria used the classical name for Turin, which, literally translated, means “The August [City] of the Taurini.”
8. No letter from Beccaria to BF of this date is known. There is, however, a letter of October 11, 1766 (above, XIII, 450–3), and it is probably to this one that Beccaria, through a lapse of memory, refers. While it does not speak directly of Symmer’s experiment, it refers to the work of Gian Francesco Cigna, who, like Symmer, held theories on electricity contrary to those of BF and Beccaria.
9. The experiments of a group of Jesuit priests at Pekin in 1755 and those of the English experimenter, Robert Symmer (d. 1763; above, IV, 276–7 n; VIII, 417), in 1759 with silk and worsted stockings, tended to support Nollet’s theory of two electrical “fluids,” rather than BF’s theory of a single “fluid,” with positive and negative electrical charge readily observable. The whole of Beccaria’s present communication was intended to support the Franklin theory.
1. It would appear that wherever in this paragraph or later in the letter Beccaria uses the expression “excess fire” or “excess charge,” or words to the same purport, he means what BF would have called a “positive charge,” or “charged positively, or plus.” Similarly, in the next paragraph and elsewhere in the paper Beccaria uses such terms as “deficient” or “charged with a deficiency” where BF would have referred to a “negative charge,” or “charged minus.” For BF’s first use of this terminology, see above, III, 131–2.
2. Readers are warned that the editors are far from satisfied that they have provided a correct and comprehensible translation of this paragraph. Each reader is invited to cope directly with the Latin here.
3. The present Italian name of this town has not been identified.