56 



REPORTS ON THE STATE OF SCIENCE. — 1919. 



cliL= ^ , ,., , r^— , =cos 74°8, 



a/ 



v^l+V5 + -^-^+l' 



n/5 + 1 



■ + 



cl L= 



V 2 ^^ 



n/5 + 1 



+ 



v/ 



v/5 + 1 



=cos 40* 75. 



fV5 



2 "^ V 2 

 Legendre, F. E. II. p. 283, has calculated 



,^(9) = 10° . 59286766=10° 35' 34" . 3235850 

 which can be used in a numerical test. 



N^imeriral Calculation 



sin 5l=al 1-89050 25944 

 sin 69= 1-97015 17377 

 sin 54= i-90795 76446 



sin 63= 

 sin 81= 



i-94988 08840 

 i -99461 99270 



D=al i-94450 08110 



For c. 



sin 39=al i-79887 18039 

 sin 21= i-55432 91617 

 sin 54= f-90795 76446 

 sin 63= i-94988 08840 

 sin 81= i-99461 99270 

 2= 0-30102 99957 



sin^51 



sin-'69 



sin^54 



2 



N 

 D 



forc\ 



=al 1-67150 

 = i-91045 

 = i-81591 

 = 0-80102 



77832 

 52131 

 52892 

 99957 



=al 1-69890 

 =al i-94450 



c'"=^ 



=V2 



C(86) = 



v/k 



D(18) = 



sin»39 

 sin321 

 sin254 

 sin 63 

 sin 81 

 2^ 



1 



C2 



=al 1-75440 

 =al i-97544 



=al 0-07525 



=al 005069 

 = 1-12382 



=al 1-39661 

 2-66298 

 i-81591 

 i-94988 

 1-99461 

 1-50514 



=al i-32516 

 =al i-98251 



82812 

 08110 



74702 

 07470 

 74990 



82460 

 38587 



54117 

 74851 

 52892 

 08840 

 99270 

 99785 

 89755 

 68975 



=al 0-07525 74990 



n/k 



c(36)D(18)=^^'^=^!'' 

 ^ ' ^ ' K sin 



=al 0-00777 



= 1.01806 

 54 



45 



43965 

 23966 



