364 POPULAR LECTURES AND ADDRESSES. 



as the vibration of the case is in the opposite 

 direction to that of the balance-wheel, or in the 

 same direction ; and the amount whether of ac- 

 celeration or retardation, may be as much as a 

 minute an hour, as I hope to demonstrate to you 

 practically. 



If a watch or chronometer be allowed extreme 

 freedom to move, it has always a faster rate than 

 when the case is held quite fixed. Mr. Archibald 

 Smith has made experiments on this point upon a 

 pocket-watch, with chronometer escapement and 

 compensated balance, and found that the moment 

 of inertia of the frame was 650 times that of the 

 balance-\vhccl, from having observed that when 

 hung horizontally by a long thread it had a gaining 

 rate of some sixty-seven seconds in the day. 



Observations made by Daniel Bernoulli on the 

 sympathy of vibrations l manifested by the pans 

 hanging from the two ends of a common balance, 

 and the solution by Kulcr of the particular 



1 Sec n Paper (May, 1840', "On the Sympathy of Pendulums," 

 l>v Mr. Archil ).iM Smith, in Vol. II. of the Cambridge Mathematical 

 Journal. 



