312 Prof. Miller on the Composition of Wolfram. 



dently very small compared with it, being less than the angle 

 at the moon, subtended by a tangent to the ray drawn from 

 the eye and bounded by the atmosphere. 



Moreover, w vanishes and changes sign at the same time 

 with the parallax p, and is therefore of the form kp + Ip^, 

 &c., where k, I, &c. are constants : for an approximation we 

 may reject the higher powers of j^ and find w = kp, where 

 ^ is a small fraction. 



§ 9. — By comparing sections 5 and 6 with this result, the 

 law of atmospheric refraction would be given by the two 

 equations, 



fsin {z — r + (1 + k).p} = a' sin (l+k) p 



Lsin {z + p) = a sin p. 

 The elimination of p between these equations, and the deter- 

 mination of the constants by observation, would give the ap- 

 proximate formula for the relation between the refraction and 

 true zenith distance, which of course would apply to light 

 coming from any heavenly body, though originally deduced 

 from but one of them. 



§ 10. — The equations of section 9 may be written in terms 

 of the apparent zenith distance z', 



{sin z' = c a sin (1 + k) p 

 sin (c' + r — kp) = a sin js, 



where c is an absolute constant = ; a is arbitrary, but 



had better be large, and Ic is a small constant and a function 

 of a. The elimination of p gives the relation between ;:;' 

 and r. 



§11. — Approximation by rejecting k-p^^ a p^, &.C., and 

 eliminating 



a sin (z' + r) 



sm z' = 23 ' 



l_lir.cos(;j' + ;-) 

 « 



or sin z' = u sin {z' +r) + /3 sin 2 (2' + r), 



a differing but little from unity, and /3 being a small fraction. 



R.M. 



XLVII. On the Composition of Wolfram. By W. H. 



Miller, -Es^., Professor of Mineralogy in the University of 



Cambridge* . 



nnHE analyses of wolfram from a number of different lo- 



-■- calities by Count Francis SchafFgotsch, show (1.) That 



the sum of the bases is always found to be larger than in a 



* From Poggendorff's Annalen, Band lii. 



