826 On Unijorm Rotation, Sfc. 



hundredth o£ the order t> 2 /C 2 . The analysis provides for this 

 result. But it is not correct to suppose that the effect is 

 non-existent, in the absence of the principle of relativity. 

 The effect of the earth's orbital motion is of course smaller. 



A brief treatment of the same problem by the Cartesian 

 method is of analytical interest. If z is the axis of rotation, 

 and (X, fjb, v) is any vector referred to the axes which rotate 

 round z with uniform angular velocity co, then its rate of 

 change with respect to fixed axes coinciding instantaneously 

 with the moving axes, has components 



d/(V' (X, fi, v)—a(fi, — X, 0), 



where B/cK denotes a differentiation referred to moving- 

 axes, as against "dfot referred to axes fixed in the gether. 

 These must be identical with 8/~dt (\, &, v) or 



(d[dt—a>y T d/'d.'e-\-a>a;'d/"dy)(\, p, v). 

 Thus 



0/3*) (/> 9, A) = 0/3*' + <»y 3/dff -©a 'dl'dy) (/, g, h) 



-•(?,-/,<>). . (14) 

 But, with fixed axes, 



4-7T "dfdt (/, g, h) = curl (a, b, c), . . . (15) 



so that, with respect to axes moving with a terrestrial 

 observer and with his instruments, we obtain on reduction 



47rd/df" (/,#, //) = curl (a, b, c) + 4™ curl ( — foe, — hy,fx+gy), 



or 47rO/B*' (f,g, h) = curl {a', V, c f ), . . (16) 



where a' = a — 4:7r(oxh, b ! = b — ^ircoyh, 



c' = c-\-A'ir(o(fx+gy) (17) 



Aftor the same manner 



^1^ {a, b,c))=- 4:irC 2 curl (f,g',h'), . . (18) 



where f ; =f -hcoxc/^irC 2 , g' ~ g + oyyc/^irC 2 , 



h' = h-a>(ax + by)/4wC 2 (19) 



