EXPERIMENT. 47 



balance to the top of the Dome of St. Paul's, and tried 

 whether the balance remained in equilibrium after one 

 weight was allowed to hang down to a depth of 240 feet. 

 No difference could be perceived when the weights were 

 at the same and at different levels, but Hooke rightly 

 held that the failure arose from the insufficient difference 

 of height. He says, * Yet I am apt to think some difference 

 might be discovered in greater heights V The radius of 

 the earth being about 20,922,000 feet, we can now readily 

 calculate from the known law of gravity that a height of 

 240 would not make a greater difference than one part in 

 40,000 of the weight. Such a difference would doubt- 

 less be inappreciable in the balances of that day, though 

 it could readily be detected by balances now frequently 

 constructed. Again, the mutual gravitation of bodies at 

 the earth's surface is so small that Newton appears to 

 have made no attempts to demonstrate its existence ex- 

 perimentally, merely remarking that it was too small to 

 fall under the observation of our senses 8 . It has since 

 been successfully detected and measured by Cavendish, 

 Baily and others. 



The smallness of the quantities which we can now 

 observe is often very astonishing. A balance will weigh to 

 one millionth part of the load or less. Sir Joseph Whit- 

 worth can measure to the one millionth part of an inch. 

 A rise of temperature of the 8 Sooth part of a degree 

 centigrade has been detected by Dr. Joule. The spectro- 

 scope can reveal the presence of the one 1 80, 000,000 th 

 part of a grain of soda, and the sense of smell can probably 

 feel the presence of a far less quantity of odorous matter *. 

 We must nevertheless remember that effects of indefinitely 



r Hooke's 'Posthumous Works/ p. 182. 

 8 ' Principia/ bk. Ill, Prop. vii. Corollary i. 



t Keill's ' Introduction to Natural Philosophy.' 3rd ed., London, 

 *733, PP- 48-54- 



