142 Mr. Dyke on the Determination of the Mean Spherical 



To compensate for both these disturbing influences, each 

 pair of mirrors was placed at such a distance from the photo- 

 meter that the illumination on the screen due to each was 

 the same as it would have been, had the cosine relation been 

 rigidly followed and the reflexion coefficients been all the 

 same as the coefficient for No. 1 pair of mirrors (the mirror 

 pairs being numbered as in fig. 2) . 



The following table shows the results of these investigations 

 and adjustments. 



No. of 

 mirror 



Illumina- 

 tion less 

 than cosine. 



Reflexion 

 coefficient. 



Illumi- 

 nation less 

 than No. 1. 



Distance 

 lessened. 



Total distance 



lamp to 

 photometer. 



Distance 



mirror to 



photometer 



pair. 



per cent. 



per cent. 



per cent. 



per cent. 



inches. 



inches. 



1 , 



00 



68-5 



o-o 



o-o 



73-75 



3250 



2 



o-i 



68-5 



o-i 



o-i 



73-68 



32-47 



3 



09 



714 



-2-0 



-10 



74-49 



32-87 



4 



21 



68-9 



1-7 



0-9 



73-10 



32-18 



5 



3-6 



69-1 



30 



1-5 



72-66 



31-96 



6 



6-1 



695 



51 



2-6 



71-84 



31*55 



7 



61 



(56-8 



7-8 



39 



70-88 



31-06 



8 



3-6 



673 



4-8 



2-4 



7199 



31-62 



9 



21 



69-2 



1-4 



07 



73-24 



32-25 



10 



09 



692 



0-2 



01 



73-68 



32-47 



11 



01 



65-1 



35 



1-8 



7244 



31-85 



12 



00 



70-5 



1 

 i 



(sliding 



pair) 





These adjustments having been made it will be sufficient 

 to insert in the formula 



K='685 and D= ^4^ =6-15 feet. 



12 



The formula given above was 



M.S.C.P. = -I?- . Vi 



IT 



x illumination of screen in C.F. 



K * 2(w + l) 

 But the illumination of the screen 



_ 7 M.H.C.P. 



where d = total distance in feet from source to screen by way 

 of the sliding pair, and k = reflexion coefficient of sliding pair 

 of mirrors. 



Hence 



M.S.C.P. = £(^) 77^-tt . M.H.C.P. 



kW/ 2(?i + l) 



