DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
463 
Ill comparing these values it must be remembered that ^ and enter in both. 
Equating the two, ^ disappears and 
•030--006^1+ 009|u-'003^3 = 0 
This is easily satisfied by possible observation errors— -e.gr., = —p^ = P;, = I‘4 say, 
A,, = 267‘713--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 Peiest, Meissnee, and 
Meggees, with 9-figure logarithms the following values are found in I. A. 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 mantissae of the following numbers 
have to lie found with ^-\-dv added— 
31852-1816 1429-4290 33281-6106 417-453 33700-0636, 1070075 32922-2530 
They are 
855630-30-29-130^^ 
815343-78-27-273 
804064-79-26-768 [i+dv^ + dv.,] 
825224-33-27-721 (f+cAg) 
40286-52-l-857f+27chj 
11278-99--505^^+27dj/. 
9980-55--448^-27 [dv^-dv,) 
In this particular case, = 17082, and Fj + 1429 have both been observed 
interferentially and the separation is 17082-0240-18511-4499 = 1429^4259, or 
dv^— —-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 2 , however, is certainly very small. 
VOL. ccxx.—A. 3 R 
