C. Bancs — Contractions of Fitzgerald- Lor entz Effect. 353 



y = 



10-' X -25 X 10- 

 2 X 10 a 



= 1-25 X 10- 



so that per vanishing interference ring, a differential expansion 

 of 4 X 10~ 10 would be registered. Similar relations hold if any 

 one of the rods v, b, A, expand. Since an ordinary coefficient 

 of expansion is of the order of 10" 5 , the precision of the 

 method, apart from instrumental considerations (which are 

 experimental questions), is manifest. As a second example, 

 such small apparent elongations as occur in the Michelson- 

 Morley experiment may be considered. 



The problem may be stated with reference to fig. 2, where 

 PP is the polar EE, an equatorial diameter of the earth, p and 



m 



t 



$ 



\i 



^3 



V \-u ' 



r 



t A 



CL \ 



7th 



p' diameters of 23*5° of latitude. The earth moves along the 

 diameter p' with the speed of 3 X 10~ 6 cm./sec. Hence the 

 A, v, o triangle with 6 = 47° is placed with the side v vertical 

 in latitude 23'5°, the base, o, horizontal and the plane in the 

 meridian as shown. The horizontal pendulum is carried by 

 the post v, with its plane normal to the meridian and observed 

 along win in it, as mentioned above. 



Twelve hours of rotation bring the triangle h, v, b into the 

 position h', v\ b f and it is required to find the change of angle 

 da, seeing that the motion is now along v' instead of h. For 

 convenience in computation let the angle be taken as 45° in 

 place of 2 X 23'5°. Let /3= 10" 4 be the velocity of the earth 



in terms of that of light, so that \/l — ft 2 is the longitudinal 

 contraction coefficient. Hence the lengths A, v, b, for the earth 



at rest, are to be multiplied respectively by a/1 



\/l - /3 2 /2 ; A', v\ V by Vl - /3 2 /2, VT^ 

 expanding 



/3 2 ,a/1-/3 2 /2 

 and on 



/3 J , l; 



