"WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 577 



energy. For the similarity of the gravitational equations to the 

 electromagnetic tells us that we may expect gravitational energy to 

 have inertia, like that of electromagnetic energy, and also that we may 

 expect to find stresses in the gravitational field like those of the elec- 

 tromagnetic field. By the word "stress" I mean, of course, "force per 

 unit area," but it must be thoroughly understood that "force" is 

 defined merely as " that which produces acceleration in anything pos- 

 sessing inertia," so that the force must be thought of as accelerating 

 the electromagnetic or gravitational energy of the medium rather than 

 the medium itself, which is incapable of motion. 



From the exact similarity of the gravitational field around a distri- 

 bution of moving masses to the electromagnetic field around a similar 

 distribution of charges constrained to move in similar paths, and from 

 the fact that the mechanical forces of the fields in one case are exactly 

 opposite to those in the other, we see that the stresses in the gravita- 

 tional field are exactly opposite to those of the electromagnetic field. 

 This gives us the following set of stresses : a pressure along the lines 



of g with a tension across them, each of intensity - — - , equal to the 



negative energy per unit volume of the vector g ; and a pressure along 



the lines of li with a tension across them, each of intensity ^—7, equal 



to the negative energy per unit volume of the vector h. These results 

 look, at first sight, impossible, especially when we notice that these 

 stresses have such enormous values as six hundred tons per square cen- 

 timeter at the surface of the earth, and forty thousand tons per square 

 centimeter on the sun ; because it appears as if the forces in a static 

 distribution would be in a state of unstable equilibrium, in which the 

 least disturbance would cause the lines of force to crumple into a hope- 

 less tangle, but it will appear presently that this is not the case at all. 

 Negative Inertia. — To see why not, we may again consider our 

 corresponding electrical case, and consider the similarity of the vectors 

 ExH and gxh, which have exactly similar lines with proportional 

 intensities at different points, and, what is most important, the same 

 direction in every case. And, as Lorentz ^^ proves, in space containing 

 no matter, the force due to the stresses on the surface of any element 

 dr in an electromagnetic field is 



/ , a(E:<H) X 



\4 7rc2 dt J 



^^ Lorentz, Theory of Electrons, chapter I, p. 23 et seq. 



VOL. XLVII. — 37 



