175 
of Edinburgh, Session 1880-81. 
From some rough calculations I find that the amplitude of y 
increases, but much more slowly in percentage value than does x • 
so that the maximum inclination of the vibrating part of the string 
to the vertical constantly diminishes. 
It would be interesting to obtain an approximate solution of the 
equations (1), and to compare the motion of the vibrating mass with 
that of a simple pendulum icliose cord is uniformly lengthened. The 
equation for the latter case has been fully treated by Fourier in his 
Tlieorie de la Ohaleur. 
When both masses (in the original problem) are simultaneously 
disturbed, it appears from the equations of motion that that mass 
whose end of the cord vibrates through the greater angle will have 
downward acceleration. As this in the former case was found to be 
accompanied by a diminution of the angle, the angle of the ascending 
mass should increase ; and thus it would seem that after a time the 
downward acceleration will change sign. Thus (if the string were 
long enough) the vertical motions of the system would be oscil- 
latory. But this curious result cannot be verified without pro- 
ceeding to a formal approximation. I have not found time to carry 
out this laborious but not difficult work. 
Another variety of the problem is easily formed by seeking the 
requisite ratio of the two masses, so that the motion shall be wholly 
periodic, with a period equal to that of the vibration of the 
disturbed mass. This is, relatively to the above, a very simple 
question. 
BUSINESS. 
The following candidates were balloted for, and declared duly 
elected Fellows of the Society: — Mr John Horne and Mr B. Neeve 
Peach. 
Monday, 21 st March 1881. 
Sir WYYILLE THOMSON, Vice-President, in the Chair. 
The following Communications were read : — - 
VOL. XI. 
z 
