524 WEBER ON THE MEASUREMENT 



Consequently it becomes 



\d¥^'^~dF~~de dF)~^^ \di~~dt~~dt~~dt) 



, . Jd®' de' d@L d&'A 



""^'"""^ydt^ dt dt dt) 

 and 



(ddry ddr^ ddr^ ddr\_ (dQ.de.,d®,,d&A 



VdF~~di^-^'W'~~dt^)-'^^^^\dl+~dt^'dT^'dFj 



du 



—4 cos© . -rr- 



dt 



The differential coefficients -~, -^, -~, &c. are easily deve- 



dt dt dt 



loped according to the well-known laws of trigonometry; and 



we thus obtain the following expressions, viz. — 



d®, •,./•, 



rj —— = + u sm & — u' sm 0' cos co — v sin ij cos 7, 



r, — TT* = —u' sm 0' + w sm cos w — i? sm >] cos (w + y), 

 d^ _ _ 



r, — ry = — t; sin )j + « sin © cos y — u' sin 0' cos (w + y), 



rf©2 



rg ~rj = — u sin © + «' sin ©' cos w — w sin >) cos y, 



7*2 -TT^ = + ?<' sm 0' — M sm cos CO — w sm ij cos (w + y), 

 r^ -~ = — V sin >j — w sin © cos y + u' sin ©' cos (w + y), 



rg -~ = + M sm © + m' sm 0' cos co — v sm >j cos y, 



d®\ I • ^, ■ ^ • , 



r^ —T^" = + tt' sm ®' + u sm © cos co — v sm ij cos (co + y), 



dr 



r^ -~ = — v sin ») 4- w sin © cos y + u' sin 0' cos (eo + y), 



