578 PROCEEDINGS OF THE AJVIERICAN ACADEMY. 



Therefore we see that in empty space in the gravitational field we have 

 force due to the stresses on the surface of the element (It equal to 



\ 4 7rc2^ ^t ) 



But the vector gxh represents the rate of flow of negative energy per 

 unit volume, and hence it appears that, if the stresses in the electro- 

 magnetic field accelerate positive energy with its ordinary inertia, the 

 stresses in the gravitational field, which act against the acceleration, 

 must accelerate negative energy with its negative inertia. It is now 

 evident that since the system of stresses we have in the gravitational 

 field would give unstable equilibrium in a set of lines of force with pos- 

 itive inertia, they give stable equilibrium in a similar set with negative 

 inertia. And furthermore, it is evident that if we reverse the signs of 

 both stress and inertia, as we do in changing from electromagnetic to 

 gravitational conditions, the motions in free space of the negative grav- 

 itational energy will be exactly like those of the corresponding positive 

 electromagnetic energy. 



To see what effect this negative inertia of the gravitational field has 

 upon the motion of any mass, we may consider its kinetic energy for 

 different velocities. For a small sphere, either positively or negatively 

 charged, and subject to the deformations required by the relativity 

 principle, the electromagnetic energy for any velocity may be shown 

 to be Amc^Ii~^, where Am is the electromagnetic inertia and Avtc^ 

 the electrostatic energy when it is at rest. If we now assume that mat- 

 ter is made up of minute electric charges, we see that if these charges 

 are near enough to each other to have their fields of energy overlap 

 to any appreciable extent, then if m is the sum of the inertias of the 

 particles in a body when separated, and hence the gravitational mass 

 of the whole body, the inertia of the whole body may be a different 

 quantity in. If the overlapping is that of fields of charges of opposite 

 sign, it will make m' less than m, but if it is that of fields from those 

 of the same sign, it will make m' greater than m. But if unbalanced 

 effects of this sort could occur, it is evident that we could expect equal 

 masses of different substances to have different inertias, and since these 

 different inertias have never been observed, we may neglect such effects 

 and say that the electromagnetic inertia of any body is the sum of the 

 inertias of its component charges. This has been tacitly assumed 



in developing the theory, and we now see that it is a reasonable 

 assumption. *2 



^2 This assumption is inconsistent with the idea that positive electricity 

 may be freely penetrable to negative electrons, as has sometimes been sup- 



