rUOFES^S(Jl; (I. il. DAEWIX OX ELIJI'.SOTDAL IlAlEMOXIC AXALYSlS. 
•Vi 4 
We now have 
7i, = — k[i, 11 v E 2], 7i, = ir- 4 , 7i) = associated with a cosine luuctioii. 
'/'i,= *• • 7 'i= lA’ v'g = 5 fo, associated Avith a sine function. 
It is Avell to note that these values are •'•Iven Ijv the u’eneral foriniila, because this 
consideration shoAvs that much of tlie preA'ious reductiojis is still applicable. 
Mhectiiio- the reductions I find 
/ + 2 ' 
E'-w = I) + jL/s-[i/s- - + 20 
+ 2 (2i'+ 1)(3S - l)Jj + J/3r+4:{i/5(S+ I) - cos2</,J, 
‘ f! : 0 - s/3 (- - 1 ) + - 1302 + 80 )} 
2 / + 1 / - 2 : 
+ }y^ . _ (aX + t ) — cos 24], 
Tliis Integral will he associated Avitli C/' and C f and in the present case 
X = 1 /(/+!). 
In the same way 
! ' + i /3 p + 3 - (2/ + 1)J + i-,/3- [VS- + -f 92 
- (J(2*' + 1)(S + 5)]} + E + i/3(S + 9) - 008 2,).!. 
— rsX' n i/3 (- + 3) + - 2 - 50 / 5 - (25S- 18GS + 3G8)} 
+ itiTi»~ ~ -a - «« 
This Avill he as.sociated Avith S,“ and Sx 
Xo\A- turning to the cosine and sine functions, A\e find that theA' must he treated 
a])ai’t, l)ut the integi-al iinolving C,“ may he derived from that in by the factor 
o(cos) : and similarly S,'from hA^ tlie factor 
u'h 
I) 
2 l^i") 
factors AAcre 
evaluated in (oG), § t). 
We noAv have /e_i = 0, = •> ; also for tlie sine function /p_.j = p,, = 0. 
Tlien 
((iTr)' = T + k ^ [(^74 “b Pi) “b Pi *^^.1 
+ /3-[( Pu)- + T(7a.j )- + (p(i + Polh) ces 4</) + P^jp^ cos 4^ 
~b {pc, + T(7'i)’) c»»s Gi/)], 
(S,')' = T — 4' cos 4f/) 4" /3 I p 4 cos 2(f) — Pj cos G(f> \ 
+ ^"[•g(74)'=+ 7 b cos 44 — (7^0 + a (/-'lb) c"s S 4 J. 
