WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 579 



Since the body as a whole is subject to the same deformations with 

 change of velocity, we may prove that if its gravitational energy when 

 at rest is —mgC^, its gravitational energy when in motion will be 

 — nigC^Rr''; so that the effect of the negative inertia of the gravitational 

 energy will be to reduce the total inertia in the ratio 1 : {\—mg/m). 



This result is so important that it is well to look at it also from the 

 point of view of inertia as the property of resisting acceleration. In 

 the case of a positively charged body which is accelerated, we see that 

 every element of charge in it will radiate forces which have at all points 

 outside the element components in the direction opposite to that of 

 the acceleration. Therefore, during a constant acceleration each ele- 

 ment will be acted upon by forces radiated from other elements which 

 will hold it back by an amount proportional to the acceleration. But 

 in the gravitational case the corresponding forces will act in the direc- 

 tion of the acceleration, and will therefore help, instead of hinder, the 

 action of the accelerating force. And it will not be noticed that since 

 these forces are inversely proportional to the distance between the ele- 

 ments, the inertias thus obtained will be inversely proportional to any 

 dimension in two similar but unequal bodies with equal charges or 

 masses. We also see that if we extend these considerations to cases of 

 variable accelerations, the electromagnetic effects introduce the ten- 

 dency to increase the rate of change of acceleration which has the ef- 

 fect of a force in the direction of this rate of the order of 



e^ da. 

 c^di 



and independent of the size of the body. Much use has been made 

 of this in the theory of emission and absorption of light. We see, too, 

 that the gravitational energy will introduce a similar force, whose ratio 

 to that of the electromagnetic energy is not nig/m. 



It appears now, on account of these changes in the inertia of bodies 

 by the gravitational energy, that we must modify the statements made 

 above about the lack of radiation of negative energy from bodies mov- 

 ing under the action of gravitation. But the modification is not so 

 great as might be supposed, because the case of the symmetrical body 

 rotating on its axis of symmetry still involves no radiation, and the 

 radiation in other cases is still less than what could be expected with 

 other theories. Hence we see that in spite of this modification of the 

 theory, the arguments for its preference over all others are still valid. 



posed ; but it is only one of many objections to this idea, so that the incon- 

 sistency need not cause much doubt as to the truth of the assumption. 



