OF DENISON UNIVERSITY. 
II3 
on, and deflections taken ; then, r. 1 . a. m. H meaning same as before, 
{r2 + 12 ) =>-2 Tan a. (3) 
The magnetometer is now removed, and the bar magnet sus- 
pended by a single fiber of silk, where the magnetometer stood. 
The ingenuity of the experimenter will best find a way for doing this. 
It is well to fasten a very small mirror to the suspension fiber, so 
that the period may be observed from the reflected light on the scale. 
The fiber in this case should be as long as possible to make the error 
due to its torsional rigidity as near a minimum as possible. If the 
fiber be twenty centimetres long, the error will be so near to zero as 
not to practically effect the result. The equation Mr. Gray gives 
for the determining of T in terms of m and H is -f — ^ a = o 
where N is the moment of inertia of the vibrating system. The 
solution of this equation can be found in Williamson and Tarlton’s 
Dynamics, art. 107. ; or in Dynamics of a Particle by Tait and Steel, 
art. 88. From this T = 2 ii ^ ^^^r magnets one tenth centi- 
metre in diameter N = 
W 12 
where W is the weight of the magnet 
in grammes. Therefore m H = ^ (3) Combining this with 
, o Il2 12 r w , . , Il2 12 w 
(I) H 2 = 8-3 /..o T7 NO and with (2) H2 = 4-: 
T 2 (1-2 -12 )2 Tan a 
(r 2 4- 12 ) 3-2 T 2 Tan a 
The measurements should all be in the metric system and then 
the value of H is given in c. g. s. units. I find that magnets for de- 
flectors made from No. 18 knitting needles and ten centimetres long 
give the best results. If wire of a larger diameter is used, a more 
complicated formula must be used, involving the moment of inertia of 
a right cylinder about an axis through its centre of gravity and perpen- 
dicular to its own axis. The length 1 is the measured half length of 
the bar magnet. Mr. Gray gives a method for determining the actual 
effective length of the magnet; but I have not used it. Corrections 
also might be made for atmospheric resistance to the vibrator, change 
of length due to change of temperature ; but these are so very small 
that, for practical purposes, they may be neglected. 
The angle 2a should be so small that Tan a—yi Tan 2 a. This 
will avoid much labor in making computations. 
As the mean of a considerable number of experiments I find for 
