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 something 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 perceptible 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 convenient formula by which we express an observed correlation of properties 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.