1881.] 



597 



[Chase. 



I 



The extreme lines are phyllotactic, d being | of a- The greatest discrep- 

 ancy is 5^ of one per cent, which is unquestionably ■within the limits of 

 probable error. 



145. Application of ScJmster's Tests. 



The ratio between the hydrogen lines « and S is between f and |. 



d = a = 1.59997 

 5 = 5= 1.60000 

 3 -- 2 = c = 1.50000 

 i —G = d= .10000 

 i —a — e = .00003 

 e -^ d^= To^W' ^^ ^^^^ ^^^^'^ sV of one per cent, of the probable error. 

 The ratio between y and d is between || and ^f 

 J.H- 5 = «.i = 1.058227 

 18 -- 17 = 5i = 1.058824 

 91 -- 86 = Ci = 1.058140 

 b^ — Ci =di= .000684 

 ffj — ci = ^1 = .000087 

 e^-i- dj^ = ^^j, the probable error being ± g^^V- 

 The ratio between « and /? is between |^ and |^. 

 an- /3 — «2 = 1-350165 

 77 -4- 57 = &, = 1.350877 

 27-^20 = C2 = 1.350000 

 \ — c^ = (^2 = .000877 

 ^2 — C2 = 62 ==^ .000165 

 ^2 -7- (^2 ==^ Iff' tli6 probable error being ± fyf . If we were to stop here, 

 the test would be pronounced satisfactory, and the evidence of harmonic 

 influences in which all the lines are involved would be conclusive. But if 

 we try another mode of grouping the result will be different. 

 The ratio between ^3 and 8 is between |f and ||. 

 13— d =«3= 1.185009 

 77 -T- 65 = 53=1.184616 

 32 ---27 = 03 = 1.185185 

 C3 — 63 =(^3= .000565 

 C3 — a.j = 63 = .000166 

 (5j, -=- CZ3 = ^f f, the probable error being only ± iff. 

 fails in this case. 



The ratio between jS and y is between f f and |f . 



13-i-y =a4 = 1.119816 



28 -V- 25 = &4 = 1.120000 



75-f-67 = C4 =1.119403 



h — c^ =di= .000597 



J)^ — a^=e^= .000184 



e^-^ di^ iff, the probable error being only ± |ff . 



fails in this case also. 



Therefore the test 



Therefore the test 



