330 JAMES CLERK MAXWELL. [CHAP. XL 



If you can put us in the way of diminishing the deficit 

 we shall be grateful, and I will see that the money goes to 

 the fund, and that the names are duly entered, however 

 small the contributions. 



... I have nothing to do in King's College till Jany. 

 20, so we came here to rusticate. We have clear hard frost 

 without snow, and all the people are having curling- 

 matches on the ice, so that all day you hear the curling- 

 stones on the lochs in every direction for miles, for the 

 large expanse of ice vibrating in a regular manner makes a 

 noise which, though not particularly loud on the spot, is very 

 little diminished by distance. I am trying to form an 

 exact mathematical expression for all that is known about 

 electro-magnetism without the aid of hypothesis, and also 

 what variations of Ampere's formula are possible, without 

 contradicting his expressions. All that we know is about 

 the action of closed currents that is, currents through closed 

 curves. Now, if you make a hypothesis (1) about the mutual 

 action of the elements of two currents, and find it agree 

 with experiment on closed circuits, it is not proved, 

 for 



If you make another hypothesis (2) which would give, 

 no action between an element and a closed circuit, you may 

 make a combination of (1) and (2) which will give the 

 same result as (1). So I am investigating the most general 

 hypothesis about the mutual action of elements, which 

 fulfils the condition that the action between an element 

 and a closed circuit is null. This is the case if the action 

 between two elements can be reduced to forces between the 

 extremities of those elements depending only on the distance 

 and + or - according as they act between similar or 

 opposite ends of the elements. If the force is an attraction 



= < (r) SB* (cos w + 2 cos cos 0') 



where o> is the angle between s and s', r the distance of s and 

 s' and and Q' the angles s and /, the elements, make 

 with r, then the condition of no action will be fulfilled. 



