322 THE mkciianicm OF THE BASTE'! ATMOSPHERE. 



in wliirh, 



V -( 1 I 6 " v \Ss ' (131 



" V ' (n' fli)( n'-3) (/t' + 2)(///— 1 )(■«'-: :i) //r„. , 



and putting n'+2 tor »' In (12) vreget 



A.. 

 /I 



A' " I /'' 



A "+* /I /'' 



a », ( i 



• 



Phis becomes i».v substituting o>i ," fc? its value derived from the pre 

 ceding expression becomes. 



A „ i • 



A /l " 1 /'' /' 



in ilk*-, manner we get generally 



A' " /I f /' /' (I!) 



' n 



- 



in which the ralues <»r the factors /''., .,„ /''„,», F„ ,„ : " <- given bj (18) 

 by adding 2, i, and J respectively to "' in that expression. 



Now, all these factors are finite, and beoce putting now /r„ for its 

 equivalent, /»',. ,, :m<i A n tot /i„ ,,, ire have 



a .i. iiniic quantity 



lilKK? by (10) 



■ , , /i„ it iinitd quantity. 



from (13) and (iij ii is seen that any coefficient, taken without 

 regard lo *igri 



-I. 



A.,,, '' An'H (''') 



wIk-m /; . ' ' ' ' (10) 



' W M K„. +t t 



since v, inn Mils condition Is satined all H'<- factors /''„■ , ,, /''„• , ,, . 

 /' n<- Icmm iiuiii mill > Therefore, we have, put I Oik « loin' i /, 



• /■'.. -•■■:,- '] A„,orby (10),<-^ (I i :■:■; a„ ) (17) 



when /; o (18) 



lincc this Is what (lo) becomes when I Is infinitely great. This Is simply 

 the limiting condition ■ " nil cases, mi<i the first mi mini <»i ( i / j i : i-rn 



• i.illy lc.-<,ri tbaD the Second wlu-.n /.' im run i<l< i;il»ly Ichh Hi. in o. 



vv<-, have >> <>m ( \) 



■ V /'., I (K (19) 



