Methods of Tlieoretical Physics. 39 



and another which allows of easy measurements (like the dis- 

 tribution of an electric current in a conductor of suitable 

 shape) by observations of the latter, and then to utilize these 

 values for the determination of the constant of friction. 

 We may also remember the graphical utilization of the series 

 and integrals occurring in the theory of tides, in electro- 

 dynamics by Lord Kelvin, who, in his 'Lectures on Molecular 

 Dynamics,' suggests even the establishment of a mathematical 

 institution for such calculations. 



In theoretical physics other models are more and more 

 coming into use which I am inclined to class as a third 

 species, for they owe their origin to a peculiar method which 

 is more and more being applied in this science. I believe 

 this is due rather to practical physical needs than to specu- 

 lations as to the theory of cognition. The method has, 

 nevertheless, an eminently philosophical stamp, and we must 

 accordingly enter afresh the field of the theory of cognition. 



At the time of the French Revolution and afterwards the 

 great mathematicians of Paris had built up a sharply defined 

 method of theoretical physics on the basis laid by Galilei and 

 Newton. Mechanical assumptions were made, from which a 

 group of natural phenomena could be explained by means of 

 mechanical principles which had attained a kind of geometrical 

 evidence. Men were conscious that the assumptions could 

 not with complete certainty be described as correct, yet up to 

 a certain point it was held to be probable that they were in 

 exact conformity with fact, and accordingly they were called 

 hypotheses. Matter, the luminiferous sether for explaining 

 the phenomena of light, and the two electrical fluids as sums 

 of mathematical points were thus conceived. Between each 

 pair of such points a force was supposed to act having its 

 direction in the line joining the two points, and whose 

 strength was a function of their distance, still to be determined. 

 [Boscovich.) 



An intellect knowing all the initial positions, and initial 

 velocities of all these material particles, as well as all the 

 forces, and which could integrate all the differential equa- 

 tions arising out of them, would be able to calculate 

 beforehand the whole course of the universe just as the astro- 

 nomer can predict a solar eclipse. {Laplace.) 



There was no hesitation in declaring those forces, which 

 were accepted as axiom atically given and not further explain- 

 able, to be the causes of the phenomena, and the determination 

 of their values by aid of their differential equations to be 

 their explanation. 



To this was afterwards added the hypothesis that even in 



