402 THE PRINCIPLES OF SCIENCE. 



separately for each apparatus by suitable experiments. 

 Thus Smeaton, in his admirable but now almost forgotten 

 researches concerning water-wheels, eliminated friction in 

 the most simple manner by determining by trial what 

 weight, acting by a cord and roller upon his model water- 

 wheel, would make it turn without water as rapidly as 

 the water made it turn. In short, he ascertained what 

 weight concurring with the water would exactly com- 

 pensate for the friction 8 . In Dr. Joule's experiments to 

 determine the mechanical equivalent of heat by the con- 

 densation of air, a considerable amount of heat was pro- 

 duced by friction of the condensing pump, and a small 

 portion by stirring the water employed to measure the 

 heat. This heat of friction was ascertained by simply 

 repeating the experiment in an exactly similar manner 

 except that no condensation was effected, and observing 

 the change of temperature then produced*. 



We may describe as test experiments any in which we 

 perform operations not intended to give the quantity of 

 the principal phenomenon, but some quantity which would 

 otherwise remain as an error in the result. Thus in 

 astronomical observations almost every source of error 

 may be avoided by increasing the number of observations 

 and distributing them in such a manner as to produce 

 in the final mean as much error in one way as in the 

 other. But there is one source of error, first discovered 

 by Maskelyne, which cannot be avoided, because it affects 

 all observations in the same direction and to the same 

 average amount, namely the Personal Error of the ob- 

 server or the inclination to record the passage of a star 

 across the wires of the telescope a little too soon or a 

 little too late. This personal error was first described in 

 the * Edinburgh Journal of Science/ vol. i. p. 178. The 



8 'Philosophical Transactions/ vol. li. p. 100. 



'Philosophical Magazine/ 3rd Series, vol. xxvi. p. 372. 



