George Biddell Airy to Faraday   22 April 1844

Royal Observatory Greenwich 1844 April 22

My dear Sir

I duly received your letter of 9 March¹ (containing the experimental measures of the attractive force of an electrified and a non-electrified plate), but I have not been able to act upon it, because I am and have been very busy and really have scarcely had my thoughts free for a moment.

There is a difficulty (incidental to all cases where attractive force increases as the distance of the attracting bodies decreases), namely that a counterbalancing force must be provided whose variations are extremely rapid. And this is, practically, very difficult to provide and to control.

In order to explain my meaning, I will take the numbers which you gave me as "attraction in grains" for a certain charge, and I will suppose that for two different charges (one 1/3d and the other 2/3ds of the same charge) the law of attraction as regards distance is the same, the absolute attractions at equal distances being in the proportion of 1, 2, 3. Then we have -

Now suppose that I provide a counteracting force whose magnitude at 3 4/8 is 17, at 1 7/8 is 100, and at 6/8 is 700. Then with a charge 1 the plates would settle at the distance 3 4/8, with charge 2 at the distance 1 7/8, and with charge 3 at the distance 6/8. And the magnitudes of the forces actually in play at these times would be 17, 100, and 700. Thus to indicate charges whose proportion is 3 to 1, I must actually use forces whose ratio is more than 40 to 1. And this inequality of forces must be included in a comparatively small range: at the same time the apparatus must be so arranged that a similar relation shall be predicable for every diminution of distance as well as for every increase of distance.

I am afraid that this will stop the application of this method.

Repulsive forces are not liable to this objection (supposing them to increase as the distance decreases, which they do). A constant counteracting force would there do perfectly well.

But I fear that (according to the theory of electric attraction) repulsive forces cannot be obtained sufficiently great.

Practical information on this point would be valuable.

I am my dear Sir | Faithfully yours | G.B. Airy

Michael Faraday Esq DCL | &c &c &c