198 



PROCEEDINGS OP THE AMERICAN ACADEMY 



difference will generally be so slight that either value may be em- 

 ployed for both bodies. 



The effect of parallax in azimuth in displacing Venus relatively to 

 the sun's centre can never exceed 0".08, and will usually be much 

 less; but, if it is thought desirable to correct the equations (26) on 

 that account, the mode of doing so will be obvious wiien it is remem- 

 bered that it will be sufficiently accurate to consider the parallax in 

 azimuth as acting perpendicularly to the parallax in altitude. 



From the zenith distances and azimuths given by the equations 

 (26), the corresponding; polar distances and hour angles must next be 

 found. The rigorous fbrmuliB for this purpose are 



tan m = tan ^ cos A' 



tan A' sin m 



tan t =. 



cos \(f> — m) 



cotan A = tan (g) — in) cos t . 



(27) 



but A' will generally be so small that its cosine may be taken as 

 unity, and then we may write 



' tan t = 



tan A' sin ^' 



cos (<p — C) 

 cotan A = tan (g) — ^') cos t 



(28) 



In the spherical triangle PS'V, Fig. 4, we have the relations 



tan m = tan A 'v cos (t's — f V) 



cos aV . , , . 



sm o cos /, = sm (As — m) 



^ cos »« ^ * ^ 



sin (» sin A = sin A V sin {t's ~ t'y) . 



Usually it will be sufficiently accurate to put cos {t's 

 and then m = a'v, and these equations become 



sin Q cos X = sin {a's — A V) 

 sin p sin A = sin A 'v sin (t's ~ t'^) 



(29) 



t'.) = 1, 



(30) 



from which q and X are obtained. As a check, q may be computed 

 directly from the zenith distances and azimuths furnished by the 

 equations (26), the requisite formulae being 



