of the Moon loiih a Sextant or Reflecting Circle. 33S 



a''*+y^=r^equ. of circle of fom/s w?«J>-^. y^4-(.r'— D)^ = 

 d'^ eqii. of circumf. of ]) refl. to 2d axes. 



y 



,2_ D) -I- =4 -j- ,//) _). 2DV5— 2D'(('^— ar'^d" 



D"- +»•->- f/'s 



SD 



4D- 



y^ = T2_.r'^ = 



_DI— T*— (/" fSD^T^ + aD'f/'-'+ST'fi" 



making 3^ =e we have 



4DV-D*-2Dt«-2DV'^= -T*-fZ'H2TV^ 

 D* + 2D-(2c^-T^-fZ'-0=-T*-rf'* + 2TV'' 

 D^= - {2c'-T^-d'')± \/ 4c* + r' + (i'-— 4-cV - ^cv/^ + 4^/' V 



= (t + c)(t-c)((Z' + c)(^'-c) 



A'=(t+c)(t-c), B'=(rf' + c)(<£'-c), D^=A' + B'+2^ A'B'" 

 D- = a'^ + /33 = (Ar + A,-)^H2(AA+XX;)/ + A2 + A3 

 whence (making — AA^— aa,=A A/ + a;- = B 



^*- 



2At 



"b" 



IT 



.A / A^ D^-A«-x^ 



' = ir±Vi^ + — ^ii — 



The time of the middle of the ecHpse is = T + 4- 



B 



'I'hc (our roots of the following tHjiiation 





