362 POPULAR LECTURES AND ADDRESSES. 



for adjusting the compasses of iron ships. Mr. 

 Smith found that this watch was going well, until 

 one day he observed it had gained fifteen seconds, 

 the reason of which he could not explain until he 

 had recollected that instead of its having been put 

 under the pillow as usual, it had been hung up in 

 a suspended watch-case. 



The question now arises, What is the cause of 

 these variations, and how on dynamic principles 

 are they to be explained ? The dynamics of the 

 subject are indeed very simple, and can be easily 

 reduced to a well-known general problem. 



A simple pendulum when it vibrates through a 

 very small arc, vibrates according to the law of 

 simple harmonic motion. Take a spiral spring, 

 with a heavy weight hanging by it, stretch it a 

 little and let it go, and it vibrates according to the 

 same law. The vibrations of a tuning-fork, or any 

 other instrument giving a similar musical sound, 

 arc also according to the law of simple harmonic 

 motion. A case of roughly approximately simple 

 .harmonic motion we have when the piston moves 

 to and fro in a cylinder, the head of the piston-rod 



