558 Mr. A. K. McLeod 



By means of these four formulae, we are enabled to get the 

 values of fa and m; for the eight parts of a ray corresponding 

 10 i = lj2, ... . .8. The values of wi 4 - for the rays already 

 considered are given in Table IV. From this table it is 

 seen that there is a considerable change in the curvature 

 when fa and hi vary. There is a slight irregularity in the 

 curvature of rays which pass very close to the horizon. The 

 errors due to the approximate character of (30)-(3oj, which 

 are most important here, do not account for this. Other 

 slight irregularities, especially for small values of fa, are 

 due to errors in the calculation caused chiefly bv errors 

 in the last figures of the logarithms used in determining 

 the refractions AC- 



TABLE IV. (Values of 



m n . m v ,n.. on-. in„. m~. m 6 



90° -182 -149 -142 -134 -126 -118 -109 -101 



89 30' -173 -155 146 137 '128 '119 '110 -101 



89 -169 -157 -147 138 -129 -120 111 -102 



88 -166 -156 -147 -138 -129 -120 111 -102 



87 '164 -156 -147 '138 -129 120 111 102 



86 -164 -155 -146 137 -128 -119 -111 102 



85 -164 -155 -147 137 '128 118 111 -102 



83 -162 -153 -145 -136 -127 118 -110 101 



80 161 153 144 135 126 118 409 100 



75 160 149 142 -133 124 115 107 "098 



70 155 145 138 130 120 112 105 -097 



HO 143 134 125 120 -111 102 -098 -088 



50 126 120 111 104 -098 -091 -U85 -080 



40 107 100 -092 -090 -081 -077 071 "066 



20 -056 -053 -050 -046 '046 -039 "037 '036 



-000 -000 -000 -000 -000 -000 -000 -000 



The dips corresponding to a given value of fa are given 

 by the formula 



D,= ^-4> (t=l,2,....8), . . - (34) 



The values of D t for the rays previously dealt with are given 

 in Table V. The advantage in specifying a particular ray 

 by fa rather than by D z lies in the fact that </> is fixed for 

 the ray, while D e varies with the height. 



