the Latitude of' an Observatory. 329 



ments of refraction and the star's altitude ; but^his success in that 

 attempt is only ideal. The north polar distances of the stars 

 were extracted from astronomical tables; and thus, though his 

 determination was freed from the errors of his own instrument 

 of altitude, and from a knowledge of refraction at the instant of 

 his observations, it yet involved the errors of other instruments, 

 and the knowledge of refraction at other places. His method, 

 in fact, can only be adopted at secondary observatories. Where- 

 ever the normal instrument exists, a method entirely indepen- 

 dent of the labours of other astronomers must be followed, 

 since, to adopt any determination made by means of instruments 

 of inferior delicacy, would be to reject all the advantages which 

 the possession of the superior instrument confers. 



I submit the following method to those astronomers who are 

 possessed of good altitude and azimuth circles, as a means of 

 rectifying the determination of their altitudes, and of ascertain- 

 ing, by a direct procedure, the actual amount of refraction. 

 ■ Using merely the azimuthal part of the instrument, let the 

 azimuths a, a, &c. and the corresponding hour-angle ^, A, &c. 



12 12 



of a star be observed : Denote by O the N. P. D. of the observa- 

 tory, by S that of the star, then have we 



cot a. sin h = cot S. sin — cos K cos O 



1 2 1 



cot a. sin h = cot S. sin O — cos h. cos O. 



2 2 2 



Whence 



(cG% h — cos h\ cos O = cot a. sin h — cot a sin h. 



^2 l/ 11 2 2 



Or 



2 sin. a, sin a, cos = sin (a + a\ cot. f "'' J gin (^ — "V 



12 ^12^ 2 ^ *^ 



cot X a; 



2 



cot a. sin h 



If we put — — ' — -. — ^ = cos <p*, we obtain the easy calculation, 

 ^ cot a.smh ' -^ * 



1 1 



cos O = i cot a. sin h. cse , a cse . ^ tan <p*. 

 a « 2 2 



The latitude of the observatory being thus determined, it is 

 easy thence to compute the declination of the star ; and, if the 

 passage of the star across the horizontal wires had also been 



