638 Mr. R. D. Kleemau on Different Kinds of y Rays 
The reversed series necessarily involves the quotients, 
powers, and products o£ the differences, and for this reason is 
difficult o£ computation. This difficulty is largely overcome 
in the above formulas by taking advantage of the homo- 
geneity of the reverted series, and expressing certain factors, 
the /'s, as functions of the same quantities. If the values of 
the fs, or preferably their logarithms, were tabulated, the 
labour involved in inverse interpolation would be not much 
greater than that of direct interpolation ; for each of the 
terms in (4), (5), or (6) would then be given in the form 
of simple product expressions suitable for logarithmic com- 
putation. This method has the further advantage of being 
straightforward ; and in so far as the reversion of the series 
is concerned, a check is provided without the introduction of 
any new quantities by the substitution of n in equation (1). 
The possibility of using the reversed series as a formula 
for inverse interpolation was suggested to me by Dr. George 
F. Becker of the U.S. Geological Survey, with whom 
I have cooperated in preparing a volume of mathematical 
tables * entitled ' Tables of Hyperbolic Functions/ and now 
in course of publication by the Smithsonian Institution of 
Washington, D.C. The formulas here suggested have been 
used to a certain extent in the preparation of these tables. 
Washington, D.C., 
February 1908. 
LIX. On the Different Kinds of y Rays of Radium, and the 
Secondary y Rays which they produce. By R. D. 
Kleeman, B.A., B.Sc, 1851 Exhibition Research Scholar 
of the University of Adelaide, and Research Student of 
Emmanuel College-, Emmanuel College, Cambridge^. 
IN a paper published in the Philosophical Magazine \ the 
writer showed that part of the y radiation of radium 
could be approximately divided into three groups of rays. 
Each of these groups of rays is selectively absorbed by one 
* In this volume are tabulated the natural and logarithmic hyperbolic 
sines, cosines, tangents, and cotangents to five places ; the natural and 
logarithmic circular sines and cosines to five places ; the ascending and 
descending exponential to seven significant figures with log 10 ev to seven 
places ; the natural logarithms of the integral numbers from 1 to 1000 to 
five places ; the gudermannian to seven places and the corresponding- 
angular equivalents ; the anti-gudermannian to hundredths of a second ; 
and other tables of minor importance. The arguments for the most part 
advance by ten-thousandths fromOtoO'l, by thousandths from 01 to 3*0, 
and bv hundredths from 3*0 to 6-0. 
t Communicated bv Prof. J. J. Thomson, F.R.S. 
X Phil. Mag. Nov. 1907, p. 618. 
