354 Aitronomical and Nautical Collections. 



And consequently 



fl- = 24" + a - ^ P. (A) 



For the corresponding observation in the afternoon, indicating 

 the quantities by the same letters, butwith accents to distinguish 

 them, and adding 24'" to H', that both observations may reckon 

 from the same time, we shall have 



24" + i/' = h' + a 



And therefore ^^ 



24" + H' = a' +-L P'. (B) 



The equations {A) and (JS) give 

 Ua + a')=.i{H+H')-ilEfin. (C) 



The quantity 4^ (a + «) 's what the chronometer is fast of the 

 precise middle time of the two observations, which is nearly the 

 time of apparent noon ; and the equation (C) shows that 

 what it is fast is equal to the half sum of the two times H and //', 

 plus a correction equal to half the difference of the two horary 

 angles reduced to time. 



The chronometer has been supposed fast of apparent time, 

 and this may always be considered as the case, for if sZow it can 

 easily be read fast by merely subtracting what it is slow 

 from 12''. 



Spherical Trigonometry gives 



i (P'-P) = ^_i-^-_. Tang.L. 

 sme ^ (P — P) 



-k X 



Tanff. D. 



tang.i(P'+P) 



X being the sun's declinatory movement towards the North 

 Pole in the interval betwixt the observations, L the latitude of 

 the place, supposed North, and D the declination of the sun, 

 also North, calculated for a time equidistant from both obser- 

 vations, which in the present case is the declination for ap- 

 parent noon. 



In this value of | (P' — P), the quantities of the third order 

 only have been neglected, being absolutely insensible, as has 

 been shown by Delambre in his Treatise on Astronomy. 



