106 REPORT—1885. 
fo ong ts Gia ole ce dr dyt : 2) 
r2 ds\d8y y y rds, aga” dsy 
(h+g) adr { afl danny 4) , se 
a9 ae (y'-y) dss (z'—2) ag 
h L—f dr dy \ 
+ ot & {w@-n -@—2 2h 
dy dz dy dz 6 
i a 2) A Oe I] is, dso, 
g { dsy ds, ds, ds, \ age 
‘with similar expressions for the components of couple around the axes of 
y and z. 
By making the force between two closed circuits have the same value 
as that given by Ampére’s theory, Korteweg finds that 
a+ 2b—d—c = — 3A?, 
where A is a constant quantity whose value depends upon the unit of 
-eurrent adopted. 
By making the couples produced by one closed circuit on another 
have the same value as that given by Ampére and the potential theory, 
he finds that 
d rh) + (q—h) r—c + 2A?= 0. 
dr J 
Korteweg considers that the experiments of v. Ettingshausen, quoted 
above, prove (1) that the force on an element of circuit produced by a 
closed circuit is at right angles to the element, and (2) that the couple on 
an element due to a closed circuit has the value given by Ampere’ 8 theory. 
The first condition gives 
c— b= 2A?; 
the second the two conditions 
S (rk) —f=0 
h+g=0. 
And he points out that we cannot get any more conditions. by consi- 
dering the action between two closed circuits, or the action of a closed 
circuit on an element of another. ; 
It should be noticed that since, according to this theory, part of the 
action of one element of a cireuit on another consists of a couple, the 
condition that the force due to a closed circuit on an element of another 
‘should be at right angles to the element is not, asin Stefan’s theory, iden- 
tical with the condition that the expression for the couple exerted by one 
-closed circuit on another should be the same as that given by Ampére. 
This theory is valuable because it is the most general one of the class 
we are considering which has been published. It is the only one which 
takes into account the couples, and by giving special values to the quan- 
tities a, b, c, d, f, g, h, wecan get any of the other theories of this class. _ 
om ~- 
