520 DR. LAMONT ON THE MAGNETIC OBSERVATORY 
axis of the telescope is again perpendicular to the plane of the 
mirror; then a! ¢ a is the angle of deflection, which we will call 
o. If we call the distance c a! =e, the magnetic moment of the 
deflecting magnet = M, and the magnetism of the earth= X, 
theory gives the following equation, 
M ; 
y= sin $f (e), 
where f (e) denotes a function of the distance. It need scarcely | 
be remarked that ¢ must be measured four times, in such man- 
ner that the middle of the deflector must be brought on two 
corresponding divisions « and , 2! and £', and so on, first with 
the north pole, and then with the south pole, turned towards 
the suspended magnet. The mean of the four angles measured 
- 1 1 : 
then corresponds to the distance re B, > # B',&c., in the above 
formula. 
It should further be noticed, in reference to the function / 
(e), that it depends also on the magnetic moment of the deflec- 
tor; and if this suffer any alteration, either by gradual loss, or 
by change of temperature, such alteration must be taken into 
account, 
Ff (e) must now be determined, for which purpose deflections 
must be taken at the different distances a a! «", B 6! 6". 
Theory gives the following as the most convenient form of 
Sf (es 
1 
log f (e) = log = & 4 P+4s 
where p and g must be determined by equations of the form 
ee 
M : i 
log——= log sin > + log > ee + 2 +» 
sage 
M 1 
log —— ~ = log sin ¢! + log = es 4 5. 
The value of f (e) being ascertained, = is determined. In 
order then to obtain M X, the deflecting magnet is suspended 
by a silk thread under a bell glass, and its time of vibration 
determined : calling this time T, we have 
ay 
where K is the moment of inertia of the 
magnet including the suspension appa- == 
ratus. For determining K, I employ a 
