NEW MECHANICS AND ASTRONOMY. 241 



Tisserand found that if the Newtonian attraction 

 took place in conformity with Weber's law, there would 

 result, in the perihelion of Mercury, a secular variation 

 of 14", m the same direction as that tvhich has been 

 observed and not explained, but smaller, since the 

 latter is 38". 



Let us return to the hypotheses A, B, and C, and study 

 first the motion of a planet attracted by a fixed centre. 

 In this case there will be no distinction between 

 hypotheses B and C, since, if the attracting point is 

 fixed, the field it produces is a purely electrostatic 

 field, in which the attraction varies in the inverse 

 ratio of the square of the distance, in conformity with 

 Coulomb's electrostatic law, which is identical with 

 Newton's. 



The vis viva equation holds good if we accept the 

 new definition of vis viva. In the same way the 

 equation of the areas is replaced b\' another equivalent. 

 The moment of the quantity of motion is a constant, 

 but the quantity of motion must be defined in the 

 new way. 



The only observable effect will be a secular motion 

 of the perihelion. For this motion we shall get, with 

 Lorentz's theory, a half, and with Abraham's theory 

 two-fifths, of what was given by Weber's law. 



If we now imagine two moving bodies gravitating 

 about their common centre of gravity, the effects are 

 but very slightly different, although the calculations 

 are somewhat more complicated. The motion of 

 Mercury's perihelion will then be 7" in Lorentz's 

 theory, and 5.6" in Abraham's. 



The effect is, moreover, proportional to w'a", n being 



the mean motion of the planet, and a the radius of its 

 a.v77) id 



