CHAP. XL] AMPERE'S FORMULA. 331 



To THE SAME. 



8 Palace Gardens Terrace, W., 

 24th January 1862. 



. . . When I wrote to you about closed currents, it was 

 partly to arrange my own thoughts by imagining myself 

 speaking to you. Ampere's formula containing n and k 

 is the most general expression for an attractive or repulsive 

 force in the line joining the elements ; and I now find that if 

 you take the most general expression consistent with sym- 

 metry for an action transverse to that line, the resulting 

 expression for the action of a closed current on an element 

 gives a force not perpendicular to that element. Now, 

 experiment 3d (Ampere) shows that the force on a movable 

 element is perp. to the directions of the current, so that I 

 see Ampere is right. 



But the best way of stating the effects is with reference 

 to " lines of magnetic force." Calculate the magnetic force 

 in any plane, arising from every element of the circuit, and 

 from every other magnetising agent, then the force on an 

 element is in the line perp. to the plane of the element and 

 of the lines of force. 



But I shall look up Cellerier and Plann, and the long 

 article in Karsten's Cyclopaedia. I want to see if there 

 is any evidence from the mathematical expressions as to 

 whether element acts on element, or whether a current first 

 produces a certain effect in the surrounding field, which 

 afterwards acts on any other current. 



Perhaps there may be no mathematical reasons in favour 

 of one hypothesis rather than the another. 



As a fact, the effect on a current at a given place depends 

 solely on the direction and magnitude of the magnetic force 

 at that point, whether the magnetic force arises from currents 

 or from magnets. So that the theory of the effect taking 

 place through the intervention of a medium is consistent 

 with fact, and (to me) appears the simplest in expression ; 

 but I must prove either that the direct action theory is 

 completely identical in its results, or that in some conceiv- 

 able case they may be different. My theory of the rotation 



