OP ARTS AND SCIENCES. 177 



where 



a is the adopted right ascension of the star. 

 T is the observed time of transit. 



T is an approximate correction to the time-piece employed, 

 /i^ T is the correction to t. 

 8 T is the hourly rate of the time-piece. 

 T — Tg is the interval in liours between the time of observation and 

 the mean of the times of observation of all the stars com- 

 bined in one group. 

 ^ a is the correction for error of azimuth, when the Circle is East. 

 A a' is the correction for error of azimuth, when the Circle is West. 

 Bb is the correction for error of level. 



Oc is the correction for error of coUimatiou, positive when the 

 Circle is East. 

 0'.021 cos (f sec 8 is the correction for diurnal aberration. 



Where the hourly rate is extremely small, and the error of the time- 

 piece is determined at the same instant at both stations, we may write 



a — {T-\~Bb-{-r — 0^021 cos cp sec 8) = /I r -\- A a (or A' a') + 



Oc; 



and, putting for the first member the known term y, the equation be- 

 comes 



= — j' + Jr + ^a (or A' a') -{- C c 



for each star observed. 



In the case of a fixed instrument, we should have 



= — j'-fz/T + ^a+ Cc. 



The normal equations for the first case are, — 



= — ^7 +^Jt -]-2:Aa -\-Z A' a' ^Z Gc, 

 = — ZAy-\-2:AJr^i:A'a -^ ZAA' a' -\- Z A G c, 

 = — 2A'y-\-ZA'/iT-\-i:A'Aa-\-ZA'^a'-\-i:A'Gc, 

 () = — ZCy ^Z G Ar -\- Z G A a -\- Z GA' a' -\- Z G •' c; 

 and for the second case, 



= — ^•j' -}-ZzJr -\-ZAa-}-ZGc, 

 = ~Z A y-^ZAzir-^ZA^a-{-ZA G c, 

 = — ZGy-[-ZG/it-\- ZGA aJf-ZG^c. 



VOL. XIII. (n. S. V.) 12 



