John Baptist Beccaria [of the sacred schools, sends greetings] to Benjamin Franklin Esqr. the first in Electrical Knowledge &c.

1. Learned Sir, I am glad you are safe arriv’d in London from America; and send you an hypothesis which I struck out from experiments concerning electrical motions: This I divide into two parts, as the very difference [between] these kind of motions seems to require; In the first part I treat of attractions, and in the second of repulsions;

2. And I now Comprehend the whole of my consideration of attraction in a few words as follows: “when the Electrical Fire, being in greater quantity in One body, throws it self by the power of Expansion into another; towards an Equilibrium, it removes the greater part of the Interjected, or Interstitial air from its place, according to its own greater [mass (copia)]. Whence it follows, that the air which is near the bodies, for want of the resistance of the intermediate air, rushes, towards that middle place: but not by passing round the bodies, which is a longer way, and more interrupted from the flowing out of the fire, but by rushing in, from nearby. It is by this [displacing (trusione)] of the air, that bodies unequally electrify’d approach [each other]; and while they approach they are accelerated, because the more fire flows in, the greater quantity of intermediate air is thrown out, and therefore the greater the attraction; and thus the momentum of the air [displaced] from nearby will be increased.

3. That the air is [expelled] by the Electrical fire flowing in, is demonstrated by the experiment of the spark which is excited in the middle of the Tube, hermetically seald at one end, and stop’d with [some liquid] at the Other; for while the spark throws out the [liquid], it is [proved (testatur)] the air is thrown out also.

4. Nor indeed can the fire, when it flows in, supply the [support (fulcrum)] of the intermediate air now driven out, whereby the air adjacent to bodies may be sustain’d; for it flows out again very freely, and passes into the Other body, wherfore as it is not itself sustaind or resisted, neither can it act as a [support].

5. The matter is confirm’d by the following [very] clear experiment: I roll’d up a slip of Gilt paper of about eight inches long and four lines broad, so as to form a little solid cillinder D. I suspend this by a silk thread D.G. under [an opening (fornice)] of an air pump I.H.K. thro’ the top of which, H. the mettal rod BC. passes, [descending into (desinens in)] the mettal ball C. I fix the mettal rod LE. arm’d with [a similar] ball [on top], to the plate IK. [Now] the spheres C and E. are in the same plane with the cillinder D. and at equal distances from it; then fixing the Chain A. B. which belongs to the electrical Machine [to] the rod B.C. and consequently the electrical fire being sent into the rod B.C. I observe: 1st. that before the air is remov’d, the paper cillinder D. is agitated with the most violent vibrations between the two spheres E.C. 2dly. that while the air is remov’d the agitation is plainly diminished in proportion to the quantity of air removed. 3dly. [when as much air as possible is removed] the cillinder D. hardly stirs. When I have observ’d these things, I restore the air again by degrees, and observe that the vibrations increase again in proportion to the restored air, and at length become as violent as before. Which circumstances when I contemplate in particular, and consider them also together, I understand that the quantity or greatness of electrical motions is owing to the air, either intire or in part.

6. Because light bodies such as gold leafe, Dust &c. are agitated in rarifyed air with a motion sufficiently sensible, was the reason why I thought, with other [physicists (physicis), from the beginning, that electrical motions, receiv’d in the air, ought not to be attributed to the action of electrical fire. But because, [having now considered the matter more carefully,] I see that motions in the residual air bear not a greater proportion to the first motions that are made in the intire atmospherical air, than that which passes between the residual and the first air, I am inclined to acknowledge this error in my self and others, and adopt the contrary Opinion; which experience verifies.

7. I must not omit a part of my Observation, which is very [opportune] towards confirming this matter: Sometimes I used to bring my Experiment from the last [stage] into a dark room; and then I observed that the fire vibrating the pendulum, before the air was remov’d, shined here and there with crackling, light but short sparks near each ball: afterwards this fire in proportion to the removed air, and also the minuteness of the vibrations of the pendulum, flow’d out in a more ample, gentle, Continual, tho’ not so shining a Radius.

8. And this truely demonstrates a reaction of the air, compelling the electrical fire in a certain density; which [corresponds to] the proportion of its Own density; and this reaction of the air [cannot avoid responding] to the action of the electrical fire, endeavoring to throw out the air; and clearly throwing it out, where it can prevail against the fire with a necessary [force (vi)].

9. To these I shall add no more towards explaining the attractions of bodies unequally electrify’d, I have brought some arguments in my letters to [Beccari] in which however I treated of the mechanical cause of attractions but doubtfully; but a more accurate consideration of the experiments, occasions my discoursing of the cause of attractions with more confidence.

10. Bodies equally electrified repel each other; The cause of which I now proceed to explain:

11. The electrical fire which is in bodies, by what means soever, [sparks in order to balance] the electrical fire which is in the air. (Give me leave to call the one the proper, and the Other the aerial fire.) If both have an equal proportion to the native capacity of the bodies and of the air, the bodies are attracted, or are at rest in their [original position (nativa directione)]; Otherwise if either the proper or aerial fire is excess, it equally [sets free (explicat)] the bodies and compells them to a repulsion.

This is the account:

12. As often as I proceed to electrifie a Chain several times [for a longer period (diutius), in my Chamber which is a very large One [but closed], I find, that part of its electrical fire is diffus’d into the ambient air; and renders [that air, however much there is in the Chamber,] electrical to excess, whilst it is in a dry State either from the weather or from fire. For I carry into any part of the room two flaxen threads which I suspend either between two fingers, or at the end of a stick, and they repel each other; and whether I keep them in the same place or move them to any Other part of the room, yet they continue to diverge for half an hour, an hour, and sometimes longer. Experiment. V.

13. If the threads are seperated from the stick or reed, by the assistance of the glass, and in like manner from the ground, they first diverge, and then return to their [original position]. But these things happen after all the sparks are as much as possible drawn out from the Chain, after all the redundant fire is remov’d from it, after the Connexion of the Chain with the ground.

14. From a long continued electrification of the Machine I find the Phaenomena in all respects the same: But if the long electrification of the machine continually follows a long electrification of the Chain, or vice versa, the threads fix’d to the reed or stick, are constantly observ’d to diverge from the electrification of another body; in the begining I observe that they attract one another, at the begining electrification of another body; and then again to diverge as before.

15. By these experiments, I say, we are in my Opinion taught: I. that while we accumulate several successive fires in the Chain, several successive parts of it passes widely into the ambient air, and adheres to it; and so all the air containd in the chamber becomes electrified to excess. In like manner while we draw out of the machine several successive fires, the machine draws in several successive parts of the fire from the ambient air, and so all the air contain’d in the Chamber becomes deficient of electricity, or electrifyd in Defect. II. The threads carry’d in either the fingers or at the end of the stick, repel each other in the air by the electrical excess from the chain, or the electrical defect from the machine, or by the force of the proper native fire overcoming the aerial if they [come together in] the electrical air from the machine; or by the power of the aerial fire overcoming the native proper fire of the threads, if they [come together] in the electrical air from the Chain. III. That these kind of threads diverging by the electrification of the chain, from the consequent electrification of the machine, or the contrary, first attract; because the machine first takes in from the air the excess it had from the chain; or the chain restores to the air, the fire taken from the machine; and so the fire in the air restored to its Native quantity ought to equilibrate with the native fire remaining in the threads. IV. But furthermore from a longer electrification of the machine consequent to the electrification of the chain, or the contrary, the threads diverge again; because either the machine goes on to take in part of the native fire, or the chain goes on to add more fire to the air than the native quantity. V. that the same threads, when seperated by the glass, diverge in the begining, because they, which have only their Own Native fire, come together in the air which is electric by excess or defect; and then when they are seperated by the glass they at length come to their [original position] because either part of the aerial fire, if the air is electric in excess from the chain, at last pours itself into the threads towards an equilibrium, and also flows by the compelling power of the glass, or part of the native fire, or of the proper fire of the threads pours itself into the air, if the air is electric by defect, [because] it may be supply’d from elsewhere by the compulsion of the glass.

16. From hence the following things seem universally to hold: I. that the air contains in itself, its own Native fire. II. that to the native fire of the air, another fire may be added, that part of the native fire may be subtracted from the air, but slowly, and as it were by force. III. that the air lets go the [excess], and takes in the deficient fire, but that in a very slow manner. IV. If the air has, like other bodies, its own native fire, then these are in a native state, if the air, while their native fire remains in bodies, has a greater or less quantity of fire than its native quantity, the bodies repel each other; but every one of these theorems can be illustrated in a surprising manner by other experiments; and be more fully demonstrated.

17. Two threads, fastened to the chain, after a few turns of the globe, diverge very much: afterwards from a longer-lasting electrification in the chain they begin to diverge less; and this diverging is diminish’d to a certain degree; so that sometimes the angle of the diverging, after a [longer] continuation of the friction of the globe, becomes double that of the diverging which happen’d from the same electrification when first excited. When I percieve this diverging of the threads diminish enough, then I cease the friction of the globe, but gently apply a very sharp stilus to the chain, wherby I slowly draw forth all the redundant fire from it; while this is doing the threads approach each other slowly, then gently again diverge to an angle indeed less than the first, tho’ great enough, which sometimes scarce amounts to forty five degrees; but then they proceed to diverge for a longer time.

18. That is, the greatest angle from the Electrification first excited, because then a very great quantity of fire is sent in to the chain, and in the threads connected with it, but little or none into the air. Afterwards the angle becomes less, as the fire increases and is consequently sent into the air, the same excess of the fire remaining in the chain. While the fire sent into the chain is slowly diminished by the application of the Stilus, the angle is still diminished in proportion as the residual fire in the chain, and the fire, sent in and Joind to the air, approach to an equilibrium; and where both the fires come to an equality the threads resume their [original] direction: when again the fire, yet redundant in the chain, if further diminshd, and the redundant fire in the air not so (for it is Joind to the air, and as we observe is slowly diminished by it,) the threads again repel each other because of the excess of the aerial fire over that in the chain, which aerial fire, in fine, because it is most slowly discharg’d, the threads proceed to diverge [for a very long time (diutissime)].

19. If the threads are connected with the Machine, all the same Phaenomena happen in them from a long electrification of the machine, that they had from a long electrification of the chain when connected with it.

20. Wherefore as I have shew’d in general from the begining, if the proper fire of bodies, whatsoever it’s quantity be, is in equilibrium with the fire of the ambient air, bodies either remain in their native state or return to it; if one fire exceeds the other bodies repel each other by the power of the fire in excess.

21. And hence if I mistake not learn’d Sir you see the reason why those bodies electrify’d as well from the chain as the Machine repel each other: the proper fire in bodies electrified by the chain overcomes the aerial, and the aerial in like manner overcomes the proper fire in bodies electrified by the Machine.

22. As often as the threads mutually repel each Other, and diverge from either the increased or diminishd native fire in them, they are attracted to my finger when advanced to them; as often as they repel each other and diverge preserving their native fire, from the native fire of the air either increased or diminish’d, they fly from my finger.

23. And this indeed is very agreable to the Known laws of electrical attraction, and repulsion; for when the native fire in the threads is either increased or diminished, they become as unequally electrified as my finger, which has its own native fire; but when the native fire stands firm in the threads, and they repel each other from the increased or diminished fire in the air; then as they diverge from one another, so they must be repelled by my finger, having also its native fire, by the power of the air, in which the native fire is increasd or diminished. But besides, this very repulsion of the threads from my finger also proves the cause of repulsions which I assert; for both the finger and threads communicate with the ground, and therefore they have not in them any Other fire but the native, by which because they do not repel each other, it remains that they repel by the native fire, either increased or diminish’d, in the air.

24. When I first fell upon this theory of electrical repulsions, I was doubtful whether the aerial fire could not make repulsions in the machine, equal in velocity and greatness to those which the proper fire makes in the chain; thence I again suspected that the quantity of the fire in the machine and chain (universally conveying to all bodies) might be quickly changed; but that the measure of the fire in the ambient air is but slowly increased or diminished: besides another consideration increased my suspicion: that I could never draw as much fire from the air as from the machine, nor could I ever add as much to the air as to the chain; for I could never come to be able to sustain the whole diverging of the threads by the electricity of the air alone, as much as existed from the intire electricity of the machine or chain.

However hence it came to pass, that I communicated these same experiments, and also Others, by Letters to the most learned president of the Bononian Institute, wherin I establish’d this theory of repulsions at large.

But upon considering the matter more maturely I found that the velocity of the repulsions, caused by the aerial fire, ought not to answer to the velocity whereby its quantity is either increased or diminsh’d; but to that velocity whereby its inherent quantity acts; and that the greatness of the repulsions, which come from the same fire, ought not to answer to its absolute, but to its comparative greatness; I have observ’d both these to happen upon occasion.

25. If in the Sixth experiment, after the diverging of the threads is diminished from a longer electrification of the chain, I draw all the redundant fire, not slowly but immediatly, from the chain (my hand being apply’d to it) the threads indeed begin to come together [as fast as possible] but they suddenly return with equal velocity before they arrive at their [original position]. But this other repulsion, because it happens from the aerial fire overcoming the proper residual fire in the threads, I perceive nevertheless that the very aerial fire (altho’ its quantity is slowly changed) causes repulsions of equal velocity with those that are made without the proper fire.

26. And that these equally great repulsions happen from the aerial fire I thus understand. After the fire receiv’d into the air, as much as may be, that is round the chain, (all the redundant fire being taken away from the chain, and so the threads now diverging from the aerial fire), I substitute a globe of Sulphur instead of glass, and from the friction of this I observe, the angle of divergence to increase in the begining, which the aerial fire effected, and then continually to diminish.

27. And this is certain that the first frictions of the Sulphureous globe takes away part of the native fire from the chain, and does not in like manner take away the excess of fire of the ambient air (for the air, as we observd before, slowly receives the fire of another body and as slowly parts with it) wherefore the greatness of the divergence is increased which is causd by the aerial fire, not changed by the absolute greatness of the aerial fire, but only by its comparative greatness, the proper fire being therefore diminished, and the proportion of the aerial to the proper [fire] being increased. Therefore because as much of the fire as is collected in the chain, so much is drawn from the machine; the proportion of the aerial fire about the machine, to the residual fire in the machine, will be the same as the proportion of the redundant fire in the chain, to the aerial fire about the chain: wherefore the aerial fire about the machine will make repulsions, not only equally swift, but equally great with those made by the proper fire in the chain.

28. Therefore that I may comprehend in a few words all that seem most likely to explain universally all electrical motions, (for you may easily observe that all suspensions, adhesions, vibrations and an infinite number of Other compositions as so many electrical Ludi [games, demonstrations] are comprehended in the repulsions and attractions). This at length is the Sum of my hypothesis: that the attractions of bodies, unequally electrified, are affected by the electric fire of one body, in which it is more abundant, flowing out into another, thro’ the [intermediate] air, and even throwing off that. But that repulsions are caused by the proper fire of bodies expanding it self against the aerial [fire], or by the aerial expanding it self more strongly against the proper fire; which expansion however, of the fire of one body overcoming another, seems to happen without the mutual admixtion of one with the other. For the air contains its own fire whatsoever its quantity be, nor can it discede from it, and drives away the proper fire of conducting bodies that it may not adhere to it.

29. I have I say Learnd Sir, Laid before you this hypothesis, and you will thereby improve it; and if you think it worthy of being laid before the Royal Society, It will be very agreable to me, who, [since] I am not able to add any Ornament, hope my dilligence will be acceptable to it. Be careful of your Health, for it is fit you should be long preserv’d for the improvement of Science, and the amplification of what you have so certainly established.

Dated at Turin 24. Xber. 1757.