ACCORDANCE OF QUANTITATIVE THEORIES, &c. 193 



take the mean of all those in which the effect to be mea- 

 sured is present, and compare it with the mean of the 

 remainder in which the effect is absent, or acts, it may 

 be, in the opposite direction. The difference will then 

 represent the amount of the effect, or double the amount 

 respectively. Thus, in the case of the atmospheric tides, 

 we take the mean of all the observations when the moon 

 was on the meridian, and compare it with the mean of all 

 observations when she was on the horizon. In this case 

 we trust to chance that all other effects will lie about 

 as often in one direction as the other in the drawing of 

 each mean, and will neutralise themselves. It will be a 

 great advantage, however, to be able to decide by theory 

 when each principal disturbing effect is present or absent ; 

 for the means may then be so drawn as surely to separate 

 each such effect, leaving only very minor and casual di- 

 vergences to the law of error. Thus, if there be three 

 principal effects, and we draw means giving respectively 

 the sum of all three, the sum of the first two, and the 

 sum of the last two, then we gain three simple equations, 

 by the solution of which each quantity is determined. 



Explained Results of Measurement. 



The second class of measured phenomena contains those 

 which, after being determined in a direct and purely empi- 

 rical application of measuring instruments, are afterwards 

 shown to agree with some hypothetical explanation. Such 

 results are turned to their proper use, and several dif- 

 ferent advantages may arise from the comparison. The 

 correspondence with theory will seldom or never be abso- 

 lutely precise ; and, even if it be so, the coincidence must 

 be regarded as accidental. If the divergences between 

 theory and experiment be comparatively small, and vari- 

 able in amount and direction, they may often be safely 



VOL. n. o 



