■i'ii! Woolard — Generalized Relativity and Gravitation. 



remains the same, and hence our equations regarding it 

 should remain essentially the same in form. 



2, From a consideration oi* Newton's law of gravita- 

 tion, and of his three laws of motion, there may be formed 

 certain well-known differential equations which describe 

 the motion of bodies under the influence of forces. 1 In 

 building up his system of mechanics, Newton postulated 

 the existence of a definite frame of reference, fixed in 

 space, to which motion might be referred. In practice, 

 motion is usually measured relative to the earth consid- 

 ered as fixed; we know that the earth, as well as every 

 other celestial body, is in motion in space ; . hence we can 

 observe no absolute motion ; Newton considered such as 

 existing, however, even though unattainable. The New 

 tonian equations are invariant in form for any uniform 

 translatory motion of the axes of reference. 2 If the 

 same arbitrary velocity were suddenly added to every 

 body in a system, it would be impossible to detect it. 

 The frame of reference assumed at the beginning is not 

 unique, but only one of an infinite number, all moving 

 relative to one another with a constant velocity of trans- 

 lation without rotation. It is possible to detect relative 

 motion only. 



3. The introduction of the all-pervading luminiferous 

 aether gave rise to many difficulties. It seems to be neces- 

 sary to postulate, however, on account of aberration, 

 etc., that the aether is not entrained by bodies moving 

 through it. 3 Hence, if we could measure the velocity of 



1 See, for example, Dadourian, Analytical Mechanics, New York, 1913; 

 Moulton, Introduction to Celestial Mechanics, New York, 1914; Jeans, 

 Theoretical Mechanics, New York, 1907; Watson, Theoretical Astronomy, 

 1881. 



- Jeans, Theoretical Mechanics, p. 33 ; Cunningham, Eelativity and the 

 Electron Theory, 1915, pp. 2-11; Watson, Theoretical Astronomy, sec. 10: 

 the equations of motion referred to two systems of coordinates respectively, 

 (x, y, z.) and (x,„ y„, z,„) moving relative to one another are: 



2 A 



and 



<Py d?x \ 



- '^ (Yx- 

 etc., 



■ Xy) = 



o ; J/o r 1 



- 3», ( Yx ° 



- Xy )=0 



illustrating what we mean when we say the form of equations remains 

 unchanged. 



3 See, e. g., Cunningham, Relativity and the Electron Theory, pp. 12-16. 



