574 PROCEEDINGS OF THE AMERICAN ACADEMY. 



currents, the principle of " Least Work " so useful in civil engineering, 

 the principle of " Least Action " or " Hamilton's Principle " in dynamics 

 of matter and of electricity, and many other laws of this sort, it seems 

 highly probable that, if there must be destructive radiation of gravita- 

 tional energy, the laws by which such radiation takes place should be 

 those involving the least amount of it. 



Another argument of the same general nature is furnished by the 

 extreme simplicity of the fundamental equations of natural phenomena, 

 such as the equations of electrodynamics, either in Maxwell's form or 

 in terms of scalar and vector potentials, the equation for the flow of 

 heat in a solid, and many others, that all combine to make us believe 

 that, if there is one set of equations for gravity that are simpler than 

 all other possible equations not involving improbable results, these are 

 the ones that express the phenomena correctly. This argument of 

 eimplicity is all the more striking if we write the electromagnetic equa- 

 tions in the remarkably simple form that they assume when expressed 

 in the four-dimensional vector analysis of Lewis.* This analysis 

 gives us a set of gravitational equations of equal simplicity, if, but 

 only if, we adopt the electromagnetic theory. And for Theory V we 

 have not only a similar set of equations, but, when we consider their 

 meaning, a simpler explanation of their fundamental causes than can 

 readily be found with any other theory. With these considerations 

 combined with the experimental evidence furnished by the planet Mer- 

 cury, it seems as though we could hardly help believing in this theory. 



To see what Theory V means we have only to consider the theory 

 that matter is made up wholly of electrons and the corresponding posi- 

 tive charges. If now we suppose every positive charge at rest to repel 

 every other positive charge with a weaker force than that with which it 

 attracts an equal negative charge in the same relative position, the ratio 

 of the difference between these forces to the attractive force being a 

 very small number G, we see that every particle of matter at rest will 

 attract every other particle with exactly the observed force if G is 

 properly chosen. And if now we suppose that the magnetic force from 

 a moving positive charge has a smaller effect on another moving posi- 

 tive charge than on an equal negative one with the same relative posi- 

 tion and velocity, and that the ratio of the difference between them to 

 the force between those of opposite signs is the same number G, the 

 existence of the vector h is explained. But we must assume forces 

 between two negative charges to be equal and opposite to those between 

 positive and negative, for, as Gans * has shown, this set of assumptions 



* These Proceedings, 46, No. 7, October, 1910. 

 . » Gans, Phys. Zeitsch., 6, No. 23, 803. 



