Section III, 1888. [ 25 I Trans. Roy. Soc. Canada. 



III. — Detei'mination of Time hij TraiisUs across /he Vertical of Polaris. 



By Edouard Deville. 



(Read May 23, 1888.) 



Every star iu its daily revolution tw^ice crosses the vertical ol' Polaris, once above 

 and ouce below the pole; and these transits may be used for the determination of time. 

 The second one may or may not be visible. 



Generally, it is not i)ossible to observe the transit of both stars across the same 

 vertical and at the same time ; the instrument has to be pointed first to one star, Polaris 

 for instance, and then, H seconds later, to the time star. But this case may be brought 

 back to that of simultaneous transits by assuming that instead of the time star actually 

 observed, another one vi'as employed haA'ing the same declination, but a right ascension 

 smaller by 6 seconds. 



Let P be the pole, Z the zenith, (S and S' the time star and Polaris, 



Pilf=p=perpeiidicular to >S'J'jr 0=Latitu(lo 



ZPS^=t ^,(5'=declinalions 



S'PS^A a,n'=^'R. ascensions 

 ^Ç)°—MPS=x 



In the triangle ZPM, we have : 



(1) Sin (f+;*;)^lan ^j tan tp 



and in SPM : 



(2) Sin x'^tan p tan ô 



Were p known, the values of/ + x and x could be deduced from the above formula 

 and / found by subtraction ; but considering that I, x, and p are small arcs, and that wh&n 

 no great precision is required, the powers of these arcs above the second may be neglected, 

 we may write : — 



f+x=p tan (j) 

 x^^p Ian Ô 

 from which we oVjtain 



(3) t=p (tan (l/—tim ô) 



This formula is easily calculated by means of a table of natural tangents, or it may 

 be put into the following form for logarithmic computation : — 



sin (i^ — Ô) 

 *> -' " cos ^ cos ô 



Sec. Ill, 1888. 4. 



