MOTION OF A BODY EXPOSED TO EATS OF HEAT AND LIGHT. 
721 
2. For the enclosure 
( 2 ) 
These equations can be easily integrated, yet it would be difficult to determine the 
constants occurring in the final equation. If we consider, however, that i is very small 
compared to I, and that, therefore, the velocity produced by the force L on the mill is 
very great compared to that produced on the vessel, we can in equation (1) neglect 
^ in comparison with and we then get as integral 
dx L / 
dt x y 
1 — e 
( 3 ) 
This equation means that the velocity of the mill gradually increases until it reaches 
the final velocity Putting the value of ^ from (3) into (2), we have 
1 ^?+( K +*) J+ H ^— ** ( 4 ) 
The solution of this equation is 
^=Ae _w sin(^+c4)-l-Be _ ^, (5) 
with the conditions 
I(tf_ w »)_(K+*)x+ H=0 (6) 
2Ia-(K+*)=0 (7) 
b(i£-(K+*)?+h) = -L; (8) 
from (6) and (7) we can determine K +* and I, as A and n are found by observation, 
and H is given by the data of the bifilar suspension. In order to determine L from 
equation (8) we must find j and B. 
For t—0 we have «/=0 and^|=0. 
This gives the boundary conditions, 
Asin«+B=0 (9) 
A (a sin a— w cosa) + B|=0 (10) 
Eliminating A and B out of these equations, we get 
A sin a — ncosa. 
K : 
i 
sin a=0, 
( 11 ) 
It is found by experiment that after a few swings the vessel vibrates round its position 
of rest. The motion then is given by 
y=Ae~ xt sin (nt -f-a). 
