The Rev. Dr. Robinson on the Constant 0/ Refraction. 187 



If the barometer become h -j- A, Instead of h, the normal pressure, the terms 



H 4- A 

 a, /3, 7, &c., are to be multiplied by ; q', a , /3', &c., by its square, and 



H 



q" by its cube ; we find the barometric change of c, 



E = - X [c + q' + 2q" - a' + ^ &c.]. 



If h be one inch, the value of e at 85° = — 2".34, so that these corrections can 

 be worked by mental computation.* 



* This form of the refraction has the advantage of being easily applicable to the equatorial. In 

 a memoir on this instrument, (Trans. R. L A. vol. xv.,) I have shewn that most of its corrections 

 depend on an arc of the hour circle passing through the star intercepted between the pole and a 

 perpendicular from the zenith. It is also equal to the intercept between the horizon and equator, 

 whence I call it the horizontal declination. Denoting it by the symbol ?, the polar distance by d ; 

 and being satisfied with the approximation, Refr. in P. Dist.z= Refr. in Zen. Dist. X cosine of angle 

 of position, we have, 



(H) = ,Xtang(x>-0-cX^-^^^g^. 

 c may be put in the form, 



^.9 Iq' sin«a —a + b tang* 9 — c tang^fl &c.], 



cos' 

 and its resultant in declination. 



(c) = 

 tang /■ ..x cos* ^ 



|- [q' sin' (D — ?) — a + 6 tang' (d — ?) - c tang* (d — ?)] 



The first of these three terms is obviously the value of c taken with the argument (d — ?) instead 



cos' ^ 

 of 0, and multiplied by . ^ , of which latter a table for each hour is sufficient. The second is 

 Sin 13,L 



never =r 0".01 ; and the third, which is insensible above 80°, is computed by the formula 



^^ ,. _ ,)^ X (^- i)[iog-' (6.28162) - iog-'^!:!^<i^t!))} 



cos* sin'lat ^sm'lat / \- ° ^ ' ° cos'(d — ?) '-" 



which at 85° zenith distance and 6 hours from the meridian, is only 1"58, and (if it be thought 



2b 2 



