92 Prof, Challis on a Theory of Magnetic Force. 
We next deduce an n-ic in y, in which 
dz 
y= (1 a") Ta? 
and, hence, we pass to an n-ic in 2’, in which 
a'=P+Qy+ Ry?+ .. + Ty”, 
where m is not greater than n—1, and P, Q, R,.. T are so de- 
termined that the n-ic in 2! is of the form 
ai” —nz' + (n—I1)a'=0. 
Irom the equations in 2 and a! we obtain | 
L—= oi, 2 = 0 B= 00", 2.1 tO= one 
whence the form of ¢ is to be sought. 
Mr. Jerrard’s trinomial transformation indicates that this 
process is applicable (primd facie) to equations as high as the fifth 
degree inclusive. Beyond that degree a trimomial cannot be a 
general equation. But possibly the properties of trinomial equa- 
tions, or of equations involving only one parameter, may enable 
us to extend the process further by obtainmg the n-ic in a’, 
4 Pump Court, Temple, London, 
January 12, 1861. 
XVI. A Theory of Magnetic Force. 
By Professor Cuaruis, /R.S, 
[Continued from p. 73.] 
N art. 6 of the foregoing part of the Theory of Magnetic 
Force, certain laws of the motion of an elastic fluid, essential 
both to that theory and to the previous theories of electric and 
galvanic forces, were enunciated without being supported by 
mathematical evidence. Before proceeding further with the ex- 
planation of magnetic phenomena, I.propose to adduce the 
mathematical investigation of those laws. 
15. It was stated that the resultant of the composition of 
steady motions is steady motion. The proof of this theorem is 
as follows :—For cases of steady motion, the general hydrody- 
namical equation which expresses constancy of mass, viz. 
dp ai. pu, d.pvd. pu 
Be de dy dz 
becomes, to the second order of approximation, 
du, dv , dw 
—+—_+-—=0 
da pate ; 
because for that kind of motion dp =0(0, an dp dp dp 
de pd? py? plz 
