M. Ampére on @ new Electro-dynamic Experiment. 37 
To enable us to judge of the validity of this supposition, 
put y =y + (7—,y) m the formula (3); then 
y (P—a)adé sind da’ 
Y= oe f3 —— 
1 (r?#—a?) a(y/—y) dé sin’ da 
LAF Laas ergata 
Now, the first term in the value of y is what results from 
M. Poisson’s supposition, that the thickness of the molecule 
femains constant. ‘That supposition therefore virtually ad- 
mits the equality of the second term to zero. It is very plain 
that, if the second term be not equal to zero, we shall not ob- 
tain the exact value of the double fluent by integrating on the 
supposition that the thickness of the molecule is constant. 
Now it is to prove that the second term in the foregoing value 
of y is evanescent, that Laplace has taken so much pains with- 
out having given a satisfactory demonstration of it. It has 
likewise been shown above, that the evanescence of the same 
quantity is in reality the foundation of the whole analytical 
theory. It would be superfluous to add another word re- 
specting M. Poisson’s demonstration, which affords no addi- 
tional evidence of the proposition to be proved. 
An attentive reader who considers the foregoing observa- 
tions must allow that some material inadvertencies and inac- 
curacies have originally slipt into the analysis of Laplace. But 
the theory having been published, it has been deemed advisa- 
ble to repel all objections, and to defend it to the utterance. 
Jan. 6, 1826. JAMES Ivory. 
[To be continued.] 
IV. Sequel of the Memoir of M. AMPERE on a@ new Electro- 
dynamic Experiment, on its Application to the Formula re- 
presenting the mutual Action of the two Elements of Voltaic 
Conductors, and on new Results deduced from that Formula. 
(Concluded from vol. Ixvi. p. 387.] 
WE have found, in the applications which we have just 
made of the formula which expresses the mutual action 
of two infinitely small portions of voltaic conductors, (see 
page 385 of this memoir in the preceding volume of the Philo- 
sophical Magazine) 
dM 
Y : 1 
25, dé == aii (cos # —sin#) ( 
sin? é cos* @ 
+ jong ti)ds 
sin é cosé 
for the differential momentum of rotation in virtue of which a 
rectilinear conductor, of which the length is 2a, moveable 
around 
