145 



00 



Ia {e- ("+^)) F (e-^) e-^ da = B («-") 



or, assuming 



e-^ F (e-^) = K (x) 

 A (e-(«+^)) = ff iu-\-x) 

 B{e-^)=f{u) 



cc 



ƒ 



K{x) ff {u -{- x) dx = f{u). 

 b 



Now ScHWARZscHiLD multiplies this equation by e^^^^'* du and inte- 

 grates between the limits — go and -j- oo, thus 



CO 00 CO 



if{u)e -'"^ " dii— Ik {x) dx I r/) (m -f- x) e-^'^ da 



— 00 — 00 — oo . 



00 00 



= I K {x) e'^^ dx I fp (v) e—^^" dv 



00 00 



and puts 



f{u) = \F{).) e'^" du thus F {X) — — j/(?<) e-^'^« du 



00 00 



00 00 



K {x) — XL {X) é'^^ dx „ L{l) — —\K {x) e-^'^ dx 



■» ■ 00 



00 ^ ^ 



cp{v)= (<P {X) é'^" dv „ *P{X)= —- I (f {v) e-i''" dv 



— 00 00 



therefore 



F(l)zzz2jtL{-A)<P{).) 



or 



1 Fi-X) 



Multiplying again by é'^'^ dX and integrating between — oo and 

 -j- 00 this relation, he obtains 



1 rFi—X) ., 

 K{x) = — — -e'^dX. 



— 00 



If now we compare this result with the preceding, we have ..'., 



