OF ELECTRO-DYNAMIC FORCES. 5l7 



d V d T d T d T 

 Now the differential coefficients -y-^, j~^3 ■ ■ '"c^ , —7-"%' have also 



(t St Cv Si €L Si, U Sit 



dr^ 

 the same value, which shall be denoted by -^— 5, as have likewise 



J^^' T$' ^' ^' ""^''^ ^^ ^^^^^ ^^""'^ ^y ^^' ^" 



summation, keeping this in view, we have 



2uu' ( ^''1^'' ' _ ^lu^n + ^^/;y^^//y _ iLmlLlil) 

 \dSidSi' dsjdsj dsudsij dSudsj / 



_drl_drl , dvi^f _ dj^„,^ 

 ~ dt^ df "^ df'' df"" 



On substituting these values in the fifth expression found for 

 the electro-dynamic force, it becomes 



01.6.01.' e' a a F/dr^ drif dvnf ^^/;/\ 

 Vr • lis L \^^ ~ Tf ^ ~dt^ TF) 



\dt'' df' ^ dt" dt^ /J' 



an expression which may be resolved into the four following 

 members : — 



ue.oiJe' aaidrf ddri\ 



V^ * ^ ^~^ ~ " '' ~dW)' 



a.e.a!b' aafdi'if ddvuX 



+ TiiTii ' 16 W/2~ ~ ^ ''" ~dir)' 



_ ae.a'e' oa /d^n^ _ ^ ddr,,! \ 

 Tiiiriii ' IG \dt^' " '" dt^ )' 



I «g-«'e' aa (drill _ l^lm\ 



^nurnn ' 16 \ d t' "" dt' )' 



