DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 463 



In comparing these values it must be remembered that and p l enter in both. 

 Equating the two, disappears and 



3 = 



This is easily satisfied by possible observation errors e.g., />, = p 2 = p n = 1'4 say, 



A, = 267713-'0126-01 



(3) WATSON'S Separations. When the strong lines giving these separations are 

 taken, the exactness of the equality of the separations obtained from them is most 

 remarkable. Using the interferentially measured lines by PRIEST, MEISSNER, and 

 MEGGERS, with 9-figure logarithms the following values are found in LA. for the 



means 



1429'4292 8 '0065 '0048 



417'4533 7 '0120 '0064 



1070-075 1 



The last enters as a component of 1429, viz., 1429 = 1070 + 359. 



The second column gives the number of the observations used, the third the 

 maximum deviation of a single observation from the mean, and the last the root mean 

 square of all the deviations. Using these the mantissas of the following numbers 

 have to be found with +di> added 



31852-1816 1429-4290 33281T,10<> 417'453 33700'0153G, 1070'075 32922'2530 



They are 



855630 > 30-29'130 



40286 '52 -l-857+27fZi., 



81534378 -27'273 (+(&>,) 



11278-99- -505^+27^ 



80406479-26768 



825224-33-27721 (g+dv a ) 9980'55-'448f-27 (dv a - 



In this particular case, F, = 17082, and F, + 1429 have both been observed 

 interferentially and the separation is 17082'0240-185ir4499 = 1429'4259, or 

 d Vl = -'0031. The 417 separation is altered by some displacement to 422'52'17 

 and is therefore not directly applicable. The calculations have been carried out on the 

 basis of the values obtained on the averages. It must be remembered, however, that 

 when displacements enter in a sequent they frequently occur on values of the sequent 

 which have already received a small displacement, in which case the separations 

 themselves receive small changes. Too much weight must therefore not be given to 

 the 417 case here, in which its actual value for the particular set is not obtainable. 

 The dv-i, however, is certainly very small. 

 VOL. coxx. A. 3 R 



