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experiments to be made with gyroscopes, instead of with Foucaurt’s 
pendulum. 
Take a system of coordinates 2,—7T, 4,=—9%, #;=2, «,= Ch 
the axis of z being the axis of rotation of the earth, 7 and 9 being 
polar coordinates in a plane perpendicular to it, and ¢ the time. 
Now the argument which leads to the introduction of the distant 
masses is the following: If the earth had no rotation, the values 
of gij would be 
—1 0 0 0 | 
On rt 0 o| 
OD ed 0 
ieee, | ae ar ene 
a bt 
If we transform to rotating axes, by putting 0’ = 9 — wl, we 
find for gij in the new system 
—1 0 0 0 
0 0 —l 0 (2) 
0 —rw 0 +1—7’o?'! 
It is found that the set (1) does not explain the observed phe- 
nomena at the surface of the actual earth correctly, and (2) does, 
if we take the appropriate value for @. This value of w we call 
the velocity of rotation of the earth. Then relatively to the axes (2) 
the earth has no rotation, and we should expect the values (1) of 
gij. The g',, and the second term of 4, in (2) therefore do not 
belong to the field of the earth itself, and must be produced by 
distant masses. *) 
This reasoning is however faulty. 
We will here only consider g,,. The differential equation deter- 
mining this quantity, if we neglect the mass of the earth (or if we 
consider only the field outside the earth), is: 
a" Ja, 2 0 
dr? IE acy Jaa wet 
of which the general solution is 
2 k, 
jkr een 
Le 
where &, and &, are constants of integration. The equation as given 
here is not exact, as it supposes g,, to be small, and if 4, is different 
1) Evidently with Newron’s theory no masses will do this. The hypothesis 
therefore implies a change of Newton's law of gravilation. Perhaps it will be 
possible with Einstein's theory to imagine masses producing the desired effect. 
The fixed stars will not do it. 
