TRANSACTIONS OF SECTION A. 415 
To perform a differentiation, that is to say, to find the measure of the slope 
of a curve at a given point, the templet, kept in a vertical position by means of 
a T-square, is adjusted so that the exponential curve touches the given curve at 
the given point. The ordinate of the exponential curve is then the measure of 
the ‘slope. 
Integration is performed somewhat similarly. The templet is fitted to 
sections of the curve whose area is to be measured in such a way that the two 
curves are in as good coincidence as possible. The area under the given curve is 
then equal to the difference of the extreme ordinates, corrected by a certain 
number of rectangles. 
The practical value of the method rests on :— 
(1) Its simplicity and rapidity. 
(2) The fact that all the operations may be made purely graphical, the 
result being expressed as a length, and no calculation intervening. 
(3) Its relative accuracy. 
With regard to the last point, it may be added that of the test operations 
carried out by the author, the error for operations 1, 2, 3, and 5 never exceeded 
1 per cent. For operation 4 the error was, of course, considerably greater, 
reaching as much as 15 per cent. in one test for a steep curve. 
6. Report on the Further Tabulation of Bessel and other Functions. 
See Reports, p. 39. 
Joint Discussion with Section M on the Connection between 
Agriculture and Meteorology.—See p. 738. 
TUESDAY, SEPTEMBER 10. 
_ Discussion on Series in Spectra. 
Opened by Dr. J. W. NicHouson, M.A. 
Dr. Nicholson gave a general account of the work which has been done in 
the representation of spectra by formule, with a detailed account of Rydberg’s 
work on hydrogen, in which the principal series is deduced from a knowledge of 
the nebular series, given by Balmer’s formula 
n* 
ata aay 
and the sharp series 
ay eee 
A= Nea —4 
discovered by Pickering in certain stars. 
This was followed by a review of the attempts made to obtain these formule 
from model atoms, with a more detailed account of that of Ritz, whose formula 
has been modified with such success by Hicks. It was concluded that the theory 
given by Ritz cannot actually represent the actual phenomena, and that Hicks’ 
modification is difficult to interpret physically—a remark which applies also to 
that of Whittaker. 
A modern theory must apparently build up the atom from electrons and 
positive electricity—the latter, from work on radioactivity alone, being dénsely 
concentrated at the centre of the atom. The electrons must be arranged in 
rings to avoid excessive radiation (Schott), and the atom is Saturnian. The 
necessary permanence of structure can be secured by allowing expansion of 
electrons,'as Schott supposes, or by a quantum theory, which is preferable. 
It has been shown that it is possible to explain the coronal and nebular 
spectra by simple ring-systems, with a quantum theory which implies a definite 
