Intelligence and Miscellaneous Articles. 457 
distance of the induced mass is sufficiently great, the action due to 
asin gle circular current is calculated by the formula 
-D K di TTO' 2 • , 
2 dt R 2 
in which R' is the distance from the point O to the centre c of the 
current under consideration, e' the angle which R' makes with the 
axis of the solenoid, p the radius of the circular current of which 
c is the centre. I designate by u the latitude of the circuit C in 
regard to the plane drawn from the centre G- of the sphere per- 
pendicularly to the axis of the system; by S the distance Gee; 
By p the radius of the sphere ; by R the distance OGr ; and by e 
the angle which R makes with the axis of the solenoid. Whence 
follow the formula? : — 
$=psintt; R sine' =R sin e; 
R' 2 =R 2 + 2SRcose + 3 2 ; 
B= — m 
K di 7rp 2 . cos 2 u 
sine 
2 dt B aB1 "Vi LO p _ . , , p 3 • , \t 
1 + 2^ cose sintt + £— sin 2 «) ; 
R R / 
u varies only when the transition is made from one circuit to the 
other, since the momentary variation di has been supposed the 
same throughout the current. Designating by u' the measure of 
the angle whose vertex is at Gf and whose sides intercept the con- 
stant distance Z, which separates two consecutive circuits upon the 
sphere, we have pu' = Z, and we see that vl will be very small in 
conformity with the ratio of I to p. If we represent by f(u) the 
general value of B, and by T the resultant of the forces analogous 
to this last, which forces proceed from the currents comprised be- 
tween the values u^ and u % of u, we have 
Y=f(u 1 )+f(u 1 +u')+f(u 1 + 2u')+.:.+f(u 2 y. 
When u' is very small the second member differs little from a defi- 
nite integral ; and designating this correction by A, we have 
y^f+A. 
An approximate value of A is given by the well-known formula, 
to be found at the commencement of Poisson's Traite deMecanique : — 
A=J[/K)+/K)]+ g [/'K)-/'K)]- 
The limits which we shall take for the integral will be — -, -= ; and 
