112 THE PRINCIPLES OF SCIENCE. 



rule by which from any regular series of observations we 

 may, on the principle of the method of least squares, 

 calculate out with a moderate amount of labour a formula 

 expressing the variation of the quantity observed, in the 

 most probable manner. In. meteorology three or four 

 terms are usually sufficient for representing any periodic 

 phenomenon, but the calculation might be carried to any 

 higher degree of accuracy. As the details of the process 

 have been described by Sir John Herschel in his admirable 

 treatise on Meteorology f , I need not further enter into 

 them. 



The reader might be tempted to think that in these 

 processes of calculation we have an infallible method of 

 discovering inductive laws, and that my previous state 

 ments (Chap. VII.) as to the purely tentative and inverse 

 character of the inductive process are negatived. Were 

 there indeed any general method of inferring laws from 

 facts it would overturn my statement, but it must be 

 carefully observed that these empirical formulae do not 

 coincide with natural laws. They are only approximations 

 to the results of natural laws founded upon the general 

 principles of approximation. It has already been pointed 

 out that however complicated be the nature of a curve 

 we may examine so small a portion of it, or we may ex 

 amine it with such rude means of measurement, that its 

 divergence from an elliptic curve will not be apparent. 

 As a still ruder approximation a portion of a straight line 

 will always serve our purpose ; but if we need higher pre 

 cision a curve of the third or fourth degree will almost 

 certainly be sufficient. Now empirical formulae really re 

 present these approximate curves, but they give us no 

 information as to the precise nature of the curve itself to 

 which we are approximating. In another mode of ex 

 pression we may say that we do not learn what function 



1 Encyclopaedia Britannica, art. Meteorology. Reprint 152-156. 



