H. A. Buimtead — Lorentz-Fitz Gerald Hypothesis. 507 



F t = E cos if/ 



F n = E siii if/ -f | (v + u) X H | 



in which the term enclosed by vertical lines represents the 

 magnitude only of the vector. H is perpendicular to the plane 

 containing r and v ; let u x be the component of u in this plane 

 and let w be the resultant of u x and v. Then 



| (v 4- u) X H I = ioYL = ^-E sin 6 



wv 

 and F n = E (sin if, + -^ sin 0). 



Dividing F t and F n by the longitudinal and transverse masses 

 respectively, we obtain for the accelerations, 



f t = (Lz_£!)"ecos^ 



(1 - /FY* • , wv 

 /» = ^ .„ E (sin if, + -^ sin 0) 



The acceleration perpendicular to the radius vector is 



JL 



n j8 2 ) 2 icu 



,/n cos i// — /t sin ^ = - — E (/3 2 sin \\i cos ^ 4- -r^sin cos i//). 



Recent estimates make the sun's velocity about 20 kilometers 

 per second, so that j3 2 = 0'45xl0 _s ; its direction makes an 

 angle with the plane of the earth's orbit of about 55°. When 

 r is perpendicular to the plane containing v and the normal to 

 the plane of the orbit, cos yfr is nearly zero ; it must in fact be 

 less than e (the eccentricity of the orbit) even in the favorable 

 case when the minor axis falls in this position ; with the major 

 axis in this position it will be zero. In this position, therefore, 

 the acceleration perpendicular to the radius vector cannot be 

 as much as twice that which was found for the sun at rest. 

 When r is in the plane containing v and the normal to the 

 plane of the orbit, = 55°, ijr < 55° and w = v. So that the 

 acceleration perpendicular to the radius vector will be less than 



[ - PJ- E B 2 sin 110° 



that is its ratio to the acceleration in the direction of the 

 radius will be less than 1-4 X10 -9 . 



In order to be quite certain that astronomical facts are not 

 in conflict with the principle of relativity, it will doubtless be 

 necessary to make detailed comparisons between observation 



