448 Mr. R. Hargreaves on 



That is, 



the orders being N 'M L ' for % 2 , and M 'L 'N for £ 3 . With 

 the value of 2/?F given by (118), 



jpZ'rfT 4 = ^[^(r^W-^No) +co 2 {pc^ -ra*M.o') 



+ a, 3 0/a 2 M '- / /^ 2 L ')] . (121) 



For the term (4/3 — i y a) / V we have «(1 — £p 2 ) or 

 kx = qZ' — rY' , where X'... belong to the scalar solution, 



^.X'=|(L .. + N ^M ':). Thus 



("J (i/3- v*)^= |JJ *,[(-.# + »,*) (rX'-pZ') 



r-(-» 1 « + » I «)(jZ'-rY')3 



+ a> 3 (p/, 2 L ' -qa 2 M ' + 7-N 'a 2 -6 2 j] . 

 Adding this to (121) we have 



J' 



IpZ' + Y-^p-i^UT^ ^rX^-c^^Lo'. (122) 



10 V 



The quantity under the sign of summation vanishes as 



stated above with the axis of rotation in the direction of 



translation. 7R 



The rate of change of momentum in (59) -=— may be 

 -NT3 dt 



written as -^ g) 9 P + &>iQ ? or for steady motion — oj 2 P + g>iQ. 



ot 



This and similar terms vanish if a*! : co 2 : g) 3 = P : Q : R, or 

 assuming co { : co 2 : (o s =p : q : r the general condition, - " if 

 Fg — Qp and two similar terms vanish, i. e. if (a 2 — b 2 )pgN ' 

 and two other terms vanish. These require the translation 

 to be along a principal axis. 



§ 32. We now consider the condition of things when the 

 translation approaches the velocity of light, and when it 

 exceeds it ; and for simplicity we first attend to the spheroid 

 of revolution with translation along the axis, for which see 

 schedule, p. 440 (110) (ii.). 1 + r 



As r approaches 1, <p becomes infinite as log -,__ -; S has 



