90 
PHYSICS: H. S. UHLER 
This equation results from adding the correction function a' h' N -\- 
C (Z) + N)~'^ to Moseley's formula. From the mathematical point of 
view the correction terms mean that the residuals (5) of Moseley's 
law conform to the hyperbola Nb + Cib + + c^N + cj^^ = 0, which 
differs from the general conic solely in the omission of the term that 
would involve the square of the residuals. In the case of the 
series — for which the linear law shows the greatest departures from the 
experimental data — the deviations of the more complicated formula 
were only + 0.15%, -0.13%, and + 0.23%^ for As, Nd, and U, re- 
spectively. In all cases examined B was positive while A, C, and D 
were negative. D was always an integer and, although the mathe- 
matical analysis does not preclude the possibility of fractional values, 
this peculiarity may be accidental and not may have physical significance. 
Evidence in favor of the opinion that the wave-lengths of the K- 
series fall in the unexplored region between 600 A and 12 A will now be 
adduced. Substitution of unity for N in Moseley's formula leads to 
the infra-red wave-length 138.7^1, in the case of the mean K-a series. 
When the members of this formula are squared a parabolic equation 
with related coefficients is obtained. When N is replaced by 1 in the 
more general parabolic expression = a^ -\- aiN -\- a2N^ it is found 
that Xi = 366 A. Under the same conditions the cubic = bo -\- bi N 
-f- 62 ^ bz gives Xi = 130 A. The last equation fits the known 
wave-lengths better than either of the preceding parabolic formulae, 
especially for the longest wave-lengths (smallest values of N). The 
probable error of one residual is =±= 0.183% for Moseley's formula 
(squared) and ±0.102% for the cubic, that is, nearly twice as good on 
the whole. Since the extrapolated wave-length becomes shorter as 
the equation is made to conform more closely to the experimental data 
and since the values obtained from the power expansions with inde- 
pendent coefficients are both less than 400A it seems plausible to con- 
clude that the experimental wave-lengths when found will fall in the 
ultra-Lyman region. Extrapolation for the Z-series would be pre- 
mature for the reasons that the interval from N = 30 to N = 1 is too 
great and the law of nature is not yet known. 
In conclusion, I desire to express the hope that the present paper, 
which is tentative and by no means final, may stimulate experimental 
research in the difficult but very important region of the spectrum 
lying between the shortest wave-length (600 A) published by Lyman 
and the longest determined by Friman. 
