194 THE PRINCIPLES OF SCIENCE. 



attributed to various inconsiderable sources of error in the 

 experimental processes. The strict method of procedure 

 is to calculate, if possible, the probable error of the mean 

 of the observed results (vol. i. p. 451), and then observe 

 whether the theoretical result falls within the limits of 

 probable error. If it does, and if, as we may say, the 

 experimental results agree as well with theory as they 

 agree with each other, then the probability of the theory 

 is much increased, and we may employ the theory with 

 more confidence in the anticipation of further results. 

 The probable error, it should be remembered, gives a 

 measure only of the effects of incidental and variable 

 sources of error, but in no way or degree indicates the 

 amount of fixed causes of error. Thus, if the mean results 

 of any two modes of determining a quantity are so far 

 apart that the limits of probable error do not overlap, we 

 may infer the probable existence of some overlooked source 

 of permanent error in one or both modes. We will further 

 consider in a subsequent section the accordance or dis- 

 cordance of measurements. 



Quantities determined by Theory and verified by 

 Measurement. 



One of the most satisfactory tests of a theory consists 

 in its application not only to predict the nature of a 

 phenomenon, and the circumstances in which it may be 

 observed, but also to assign the precise quantity of the 

 phenomenon. If we can subsequently apply accurate 

 instruments and measure the amount of the phenomenon 

 witnessed, we have an excellent opportunity of verifying 

 or negativing the theory. It was in this manner that 

 Newton first attempted to verify his theory of gravitation. 

 He knew approximately the velocity produced in falling 

 bodies at the earth's surface, and if the law of the inverse 



