4 INTRODUCTION 



have to choose those which give the smallest values 

 of the probable errors. In this manner the ex- 

 actitude of our scientific methods are improved, and 

 thereby the accuracy of our conclusions. On the 

 other hand, the experimental laws found and ex- 

 pressed by our formulae very often are true only for 

 a limited region of the field examined. By means 

 of the deviations between the calculated and the 

 observed values it is possible to form an idea of 

 the cause of the said deviations — which in this 

 case ought to exceed the experimental errors — and 

 thereby to find new laws of a wider application than 

 the old ones, and even to discover new, i.e. pre- 

 viously unknown phenomena. 



In the following pages I have made extensive 

 use of a graphical illustration of the mathematical 

 formulae, representing the laws accepted, as com- 

 pared with the observed data, marked by crosses 

 or points. Now there is only one line, for deviations 

 from which the eye is extremely sensible, so that 

 it may be used to prove the corresponding law 

 with a great strictness, and this line is the straight 

 one. If now a variable quantity y is dependent 

 upon another quantity x, which we may change as 

 we wish, for instance temperature or concentration, 

 so that the formula expressing this dependency 

 possesses the form 



y = a + bx, 



where a and b are two experimentally determined 

 constant values, then the graphical interpretation 



