CHAPTER VI. 



Development of the passage function. 



37. According to our general formula (86) we have 



(101) Vvx - 1 . p. hu. 



where 



+ •» 



liji; = jjf'^vi'- V(/i) *<i dv^ dw^, 

 or, if the value of V(/i) is introduced 



(1 02) hi, = / i?.yA. (/,' - A /s) ^=-1 - 

 where as usual 



(103) 



zlsg = (^^«2 fivg dw. 



and only one sign of integration is used. (The integral is an eightfold integral). 

 The integral Jyt may be written in a form more conveniant for algebraic work. 

 Using the integral invariant of chapter II we have 



liji; = f Riß, {ii^, v-^, Wj)//// Ab^'-As^' d'\i' dh' 

 — / Riji, {u^ , , tv^) /j /a htûAs^Az^ d'5^ dh . 



But if in the first of these integral the current variables are denoted by 

 *'2' ^'4* (instead of by y/, iv^' etc.) then, according to the 

 theorem Meddel. N:o 69, u^, v^, tv^ must be exchanged for u^, v^, iv^, so that 



( 1 04) lijk — I {Rm — Riß:) A f\ zl J d^ dh , 



where 



(104*) R'iß = Rijk{u^', v/, «(^i'). 



The expression for lyj, may be written in such a form that it is symmetrical 

 in and . 



Lnnds Universitets Åissliiift. N. P. Avd. 2. Bd 28. 7 



