706 



240./ 3a>A 2to,/ 3wA 



Sto," 5ü)/ 5ü),(o, tu.tu, (o.v),] 



If now we put 



/ 3to, a)„\ / 3a>„ toA 



'y ^ 5B, 21 J ' 'y^ 11^^21 J 



we nvAY replace Wj-.to,/- and vi^o)^ by /(;/ : c'S k^'^-.c^ and kjc,:c* 

 ill (he (ei'ins 5w,- : 2/'i", Sw,^ : 2/-2^ and 5uj,a»„ : j-j/',, and so we have 



1 I 2 //.■ l-\ 5 //,• A, , , 



and from tliis 



--l-l(^^)^ï(^^)■! ■ <") 



§ 4. We now proceed to the calculation of the field of the 

 equations of motion of a particle in the field of the two fixed centres. 

 We put for abbreviation 



4^ + 4^=^" (12) 



io is a function of the coordinates. Let v be the velocity of the 

 particle and .i', //, : the cartesian coordinates. For L we then get the 

 expression 



L= Ve — 2c''fü + I ïü^ — ü" 



and from tliis, expanding the root and neglecting terms of higher 

 order than the second, 



«^ 



i^ = c^ (1 -Ljc) — \v'\ c-w — ^ chv" + I tvv' 4- -- . 



Of' 



Instead of L we may use F in the principle of H.\milton and 

 thus we find 



d /ÖP\ _dP d /dP\ _dP d /dP\ _ dP 

 dt \d.v ) Ö.V ' dt \dy J öy dt \dz ) dz 



The first of these equations is 



r- .. . f ■ bw ■ div ■ dw\ 



vv ■ die dio dip 



+ —.v = c'' i c\v — + {v" --. 



c OiB o.» Oj; 



(18) 



