ON THE STUDY OF PHYSICS. 55 



tracing out similarities in very diverse things. One consequence of 

 this process when systematically carried out was the early recognition 

 of the fact that although the forms of nature were seemingly infinite 

 and exceedingly complex, yet there was discernible throughout some- 

 thing like patterns that had been followed, as though nature were 

 not infinitely varied after all. In anatomy, for example, the similarity 

 in the structural form of fishes, birds and mammals was the subject of 

 attention long before the doctrine of evolution furnished a satisfactory 

 explanation for the resemblance. 



Not less striking are the formal resemblances between the laws in 

 widely differing departments of physics, so that, for example, if we 

 have solved a certain problem in the distribution of heat in conductors, 

 the same relation between the symbols furnishes the solution for an 

 important case of electrical currents in conductors, as if the forms of 

 the laws in nature were less complex than the phenomena, the most 

 diversified things having been built up after exactly the same pattern. 

 The recognition of these far-reaching and surprising analogies is 

 found to be most helpful. As Hertz once said, 'it seems as though an 

 independent life and reason of its own dwelt in these mathematical 

 formulas; as if they were wiser than their discoverer, and gave out 

 more than had been put into them. ' But one caution is necessary. It 

 must always be remembered that the analogies obtain between the 

 relations and not between the things themselves. Thus we derive 

 valuable mental assistance from the observation that electricity in its 

 relation to potential behaves the same as an incompressible fluid with 

 respect to pressure, but it is a great mistake to think that the thing 

 electricity is like the thing water. Or, to take another illustration, the 

 vibrations which give rise to the sensations of light occur with a 

 rapidity which in an elastic solid would require an enormous rigidity; 

 yet here, just as before, the analogy consists in the relations and not in 

 the things, and those who try to think of an ether at once more rigid 

 than steel and at the same time so tenuous that it produces no per- 

 ceptible retardation of the planets show that they have missed the 

 point of all analogies which is to furnish a mold in which we can cast 

 our thought concerning the sequence of events. 



In like manner, a law in science is now regarded simply as a con- 

 venient formula by which we express an observed correlation of prop- 

 erties or a uniformity in the order of nature, and the assumption that 

 a law expresses a compelling and inviolate principle is wholly disclaimed. 



The fundamental entities of physics, the ultimates in terms of 

 which it is possible to express all other facts and phenomena of the 

 science, are space, time, energy, matter, electricity and ether. It 

 should, however, be said that it is doubtful whether there is necessity 

 for both electricity and ether. There is a growing tendency at present 

 to explain the properties of matter in terms of electricity. 



