Intensities of Powerful Magnetic Fields. 147 
Hence (2) becomes 
#0 PVVdO 47T 2 
d? + -W~dt + ^F -° < 3) 
The motion represented by this differential equation Mall 
be oscillator j or non- oscillatory, according as the roots of 
the auxiliary quadratic are imaginary or real — that is, ac- 
/ & 2 I 2 L 2 
cording as -™- > or < — p— . Hence, if E be the critical re- 
sistance at which the motion just ceases to be oscillatory, we 
W v= A -^ (4) 
When L and b are expressed in centimetres, fi in grammes 
and centimetres, T in seconds, and R in centims. per second, 
I is given by this equation in absolute C.Gr.S. units of mag- 
netic field-intensity. 
The method of experimenting consisted in first finding the 
value of T, the free period of vibration of the coil with 
its circuit uncompleted, then finding the resistance which, 
being placed in circuit with the coil, just brought the needle 
to rest without oscillation. This resistance was conveniently 
obtained by means of a resistance-box included in the circuit, 
and therefore added no self-induction to that in the coil. An 
aluminium arm attached to the coil, and carrying the siphon, 
served as an index to render the motions of the coil visible. 
The resistance R was first made much too great, so as to give 
a slow subsidence, then gradually diminished until the value 
which just prevented oscillation was reached; and it was 
found that this value could be determined easily within 50 
ohms, and, with great care, to 20 ohms. As the experiments 
on the recorders had to be made somewhat hurriedly, and, on 
account of the disturbances, neglected, and, further, as fi was 
taken as equal to Wb 2 , where W is the mass of the coil, 
the results could not be taken as giving more than a rough 
approximation to I ; but those for two instruments are given 
below in illustration of the method. For both instruments 
the values of W, L, and b were the same, and were respec- 
tively taken as 3*343 grammes, 3338 centim., and "95 centim. 
Each coil had a mean vertical length of 5*3 centim., a mean 
breadth of 1*9 centim., and contained 45 - 72 metres of fine wire 
T. R. I. 
(1) -465 sec. 3330 x 10 9 centim. per sec. 5150 C. G. S. 
(2) -500 „ 3530 xlO 9 „ „ 5120 „ 
(/3) The second method is one which was adopted in mea- 
surements which I made of the fields of some experimental elec- 
