436 THE PRINCIPLES OF SCIENCE. [CHAP. 



Academicians of Florence could not detect, because at a 

 low pressure the effect was too small to perceive, and at a 

 high pressure the water oozed through their silver vessel. 1 

 has now become the subject of exact measurement and 

 precise calculation. Independently of Newton, Hooke 

 entertained very remarkable notions concerning the nature 

 of gravitation. In this and other subjects he showed, 

 indeed, a genius for experimental investigation which 

 would have placed him in the first rank in any other age 

 than that of Newton. He correctly conceived that the 

 force of gravity would decrease as we recede from the 

 centre of the earth, and he boldly attempted to prove it by 

 experiment. Having exactly counterpoised two weights 

 in the scales of a balance, or rather one weight against 

 another weight and a long piece of fine cord, he removed 

 his 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 elevation. He 

 says, " Yet I am apt to think some difference might be dis- 

 covered in greater heights." ' The radius of the earth 

 being about 20,922,000 feet, we can now readily calculate 

 from the 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 doubtless be inappreciable 

 in the balances of that day, though it could readily be de- 

 tected 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 attempt to 

 demonstrate its existence experimentally, merely remark- 

 ing that it was too small to fall under the observation of 

 our senses. 3 It has since been successfully detected and 

 measured by Cavendish, Baily, and others. 



The smallness of the quantities which we can sometimes 

 observe is astonishing. A balance will weigh to one 

 millionth part of the load. Whitworth can measure to 

 the millionth part of an inch. A rise of temperature of 



1 Essayes of Natural Experiments, &c. p. 117. 



Hooke's Posthumous Works, p. 182. 



* Principia, bk. iii. Prop. vii. Corollary . 



