xv. J ANALYSIS OF QUANTITATIVE PHENOMENA. 347 



tended to be operated upon in a definite manner. We 

 should of course reduce the friction in the first place to the 

 lowest possible amount, but as it cannot be altogether pre- 

 vented, and is not calculable with certainty from any 

 general laws, we must determine it separately for each 

 apparatus by suitable experiments. Thus Smeaton, in 

 his admirable but 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 compensate for the friction. 1 In Dr. 

 Joule's experiments -to determine the mechanical equiva- 

 lent of heat by the condensation of air, a considerable 

 amount of heat was produced by friction of the condensing 

 pump, and a small portion by stirring the water employed 

 to absorb the heat. This heat of friction was measured by 

 simply repeating the experiment in an exactly similar 

 manner except that no condensation was effected, and ob- 

 serving the change of temperature then produced. 2 



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 instrumental 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 thus avoided, because it 

 affects all observations in the same direction and to the 

 same average amount, namely the Personal Error of the 

 observer 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 carefully 

 described in the Edinburgh Journal of Science, vol. i. 

 p. 178. The difference between the judgment of observers 

 at the Greenwich Observatory usually varies from ^ to 



1 Philosophical Transactions, vol. li. p. 100. 



2 Philosophical Magazine, 3rd Series, vol. xxvi. p. 372, 



