Edward Jones to Faraday   15 June 1857

Vicarage West Peckham | Maidstone | June 15. 1857

My dear Sir,

I fear when you see this, that you will bitterly repent having condescended to bestow so long and kind a notice¹ upon the paper I sent you the other day, as I now venture to send you another, in part examination of one or two points on which I think you have scarcely apprehended my meaning. First allow me to say that I do not differ with you, but on the contrary entirely concur with you as to the necessity of imagining every possible position in which a case can be put, as the best means of arming yourself against the opposition which will naturally be offered to it. Secondly that I did not consider that you had misstated the “received idea” of Gravitating force, but that you were weakening your position in so far admiting it.- Untill I read your lecture², I am not aware that I ever troubled myself to consider whether “received ideas” either in fact or in toto, were true or no. I took it for granted - but since reading your pamphlet, that part of the received idea which makes the gravitating force of any particle vary with the mass acted upon, has seemed to me so inconsistent that in the ignorance of any convincing proof of its truth, I unhesitatingly reject it, and I would far rather question the correctness of the inferences drawn from the experiments or calculations made for the purpose of proving it, than admit it - But here I must beg it distinctly to be understood that I speak of the whole gravitating force of any particle, I do not mean to assert that any given particle of matter exerts no greater force upon ten particles than upon one - I admit, and it is necessary even to my argument that I should admit that a particle of matter does actually exercise a force upon one or more particles of matter according to and in proportion to their number, but I do not admit that if any particle of matter A exercised its whole force upon any other particle of matter B, that the addition of a second particle C to B would cause A to exercise a similar and equal force also on C, and so to exercise altogether twice the force which it did before. The reason why a given particle exercises ten times more force upon ten than upon one is, I maintain, because it never did and never could exercise upon that one more than a little part of the force which it does upon the ten and that it did always exercise more other nine portions of its force upon the nine.- Now the received idea of the Law of gravitating force in habit varies in two ways, first inversely as the square of the distance secondly in proportion to the mass acted upon - The definition only names one (the first) of those. The first of these I waive for the present because as I said before I have not yet sufficiently considered it - I address myself to the second; and for this purpose restate my problem (I hope more clearly) which was intended to prove that the whole gravitating force of any particle of matter is not increased by the increase of the number of particles acted upon, and therefore that as far as regards mass of matter, gravitating force is conservative. Let A & B be any two particles of matter acting upon each other by gravitation at a given distance AB their tendency is to meet at their common Centre of Gravity G which is at a point equidistant from A & B[.] Let another particle C be added to B, then the tendency would be to meet in their common Center of Gravity at the point E so placed that

AE : EB :: B+C : A :: 2:1

i.e the distance which A tends to draw B + the distance which A tends to draw C are together equal to the distance which B+C tend to draw A. Now if the force of A on B remained unchanged and a new and equal force were to rise up in A to be exercised on C, then the tendency of the three bodies would still be to meet at the original point G; but this, as G is no longer their common Center of Gravity is not the fact.

The gravitating action here of the three bodies is to their common Center E - But now the apparent result is that the force of A has increased as much as the force of B has decreased, and that the force of A now actually equals the combined forces of B+C. and hence that the “received idea” of gravitating force in a particle varying as the numbers of particles acted upon is confirmed (vid last line page I.)

But now let me call into action another principle which I conceive to be the true one - That particles of matter should not be treated individually but as parts also of the mass or system and so that all force, whatever should be referred to common Centers of Gravity of all matter both acting and acted upon. Thus we have two particles A & B or a system A+B whose common Center of Gravity is G. A does not act on B, nor B on A, but A acts on A+B or the whole mass, & B in like manner acts on A+B the whole mass A+B acts on A it also in like manner acts on B.

All at the point G.

Add C to B. Then the system is A+B+C whose Center of Gy is E.

Then A acts on A+B+C at E and the action of A = BE

B+C acts on A+B+C at E and the action of B+C = AE.

and <because> AE = 2BE. therefore the action of B+C = twice the action of A as before[.] But now to compare the force of A with itself under the cases.

A = ½ x A+B and its action AG = ½ x AB in the first case

A = ⅓ x A+B+C and its action BE = ⅓ x AB. in the second case

Hence the whole force of A measured or represented by its action is in proportion to itself the acting body and not in proportion to the body acted upon so also the action of the whole mass A+B+C on A is equal to twice its action on B+C because AE = 2BE

and this line of reasoning agrees I think in a measure with your remark page 5. upon the relation of a lone particle to gravitation or “to something which causes gravitation, and with which whether the particle is alone or one of a universe of particles it is always related.”³. And I think that it shows, if it be correct, and I candidly believe it to be so, that while the Law of Gravitating action remains as it was before. The Law of gravitating force becomes conservative. I do not think that the above view at all militates against the doctrine of the equality of action and reaction. but rather the contrary; for the action of A on A+B+C is BE+CE or 2BE and the action of A+B+C on A is AE = 2BE[.]

I have now put down all that I am prepared to say upon this division of the subject of gravitation, but the papers you have so kindly sent me open an extensive field of enquiry, and tho’ I am sorry to say I know scarcely anything of magnetism & Electricity, & but little of Light & sound, the whole question has now become to me one of such exciting Interest that I cannot refrain from following it so far as my means will permit me. I am not sanguine of success, still not altogether without hope, & should anything strike me as appearing even in a remote degree to assist the enquiry you will perhaps permit me once more to trespass on your patience & kindness. Again pressing my sense of the honour you have done me in noticing my communication

I remain | My dear Sir | Ever faithfully & obliged yours | Edward Jones

P.S. I am going to Town tomorrow untill Saturday⁴[.] My address will be at my brother’s⁵ No. 51 Strand tho’ I shall not be staying with him.

Michael Faraday Esq | F.R.S. &c