354 THE PRINCIPLES OF SCIENCE. 



In the first use all astronomical observations depend 

 upon it. In the second employment it has been almost 

 equally indispensable. The primary principle that gravity 

 is equal in all matter was proved by Newton's and Gauss' 

 pendulum experiments. The torsion pendulum of Mich ell, 

 Cavendish, and Baily, depending upon exactly the same 

 principles as the ordinary pendulum, gave the density of 

 the earth, one of the foremost natural constants. Kater 

 arid Sabine, by pendulum observations in different parts 

 of the earth, ascertained the variation of gravity, whence 

 comes a determination of the earth's ellipticity. The laws 

 of electric and magnetic attraction have also been deter- 

 mined by the method of vibrations, which is in constant 

 use in the measurement of the horizontal force of terres- 

 trial magnetism. 



We must not confuse with the ordinary use of the 

 pendulum its application by Newton, to show the absence 

 of internal friction against space r , or to ascertain the laws 

 of motion and elasticity 8 . In such cases the extent of 

 vibration is the quantity measured, and the principles of 

 the instrument are different. 



Attainable Accuracy of Measurement. 



It is a matter of some interest to compare the degrees 

 of accuracy, which can be attained in the measurement of 

 different kinds of magnitude. Few measurements of any 

 kind are exact to more than six significant figures*, but it 

 is seldom that. such a point of accuracy can be hoped for. 

 Time is the magnitude which seems to be capable of the 

 most exact discrimination, owing to the properties of the 



r ' Principia/ bk. ii. Sect. 6, Prop. 31. Motte's Translation, vol. ii. 

 p. 107. 



s Ibid. bk. i. Law iii. Corollary 6. Motte's Translation, vol. i. p. 33. 

 1 Thomson and Tail's 'Natural Philosophy/ vol. i. p. 333. 



