Measurement of Time and oilier Magnitudes, 101 



theory, the radiation from a Bohr model, consisting of a 

 single nucleus and two electrons. But none of the calculated 

 lines agree with any of the observed secondary lines. 



I tried to calculate the radiation from a system consisting 

 of two fixed positive centres*, and one electron, on the lines 

 of Sommer£eld J s generalization of Bohr's theory. It would 

 give, it was expected, the radiation from a positively charged 

 I [-atom. The complete mathematical solution of this problem 

 has already been given by Jacobi |. The quanta-integrals 

 come out in terms of elliptic integrals of the first, second, 

 and third kind, but it has not yet been found possible to 

 extricate the energy out of these functions, and express it in 

 terms of the quanta-numbers. 



XV. On the Measurement of Time and other Magnitudes. 



To the Editors of the Pldlosopliical Magazine. 



Sirs — 



OAVIXG to illness I have only just seen Dr. Silbersteiir's 

 criticisms of my remarks (Phil. Mag. xxxix. p. 366, 

 March 1920). Since my statements were very much con- 

 densed, perhaps you will allow me a few words in reply. 



(1) I do not deny that many instruments for measuring 

 time employ the assumption that some motion is uniform. 

 But it should be remembered that such instruments do not 

 include the pendulum-clock and the tuning-fork; the intro- 

 duction of the former, replacing methods involving an 

 assumption of uniform motion, is probably the most im- 

 portant advance that has ever been made in the measurement 

 of time. 



(2) AVhat I deny is that there is any experimental ground 

 for the assumption made, except that the results of making- 

 it are in accordance with measurements of time as a funda- 

 mental magnitude, in the manner sketched in my paper. 



There may be theoretical grounds for the assumption ; that 



* This incomplete paper was communicated to the Indian Science 

 Oonerress held at Bombay in January 1919. I find in the January No. 

 of the Phil. Mag. that Dr. Silberstein has traversed the same "•round 

 and arrived at identical mathematical results, but this paper likewise 

 contains no reduction of the ener<ry-expression to quanta numbers. 



t Jacobi, Vorleswiyen liber Mathematik, Article 28-30. Appel, Traite 

 de Mecanique llationelle, Tome ii. p. 407 et seq. 



Phil. Mag. S. 6. Vol. 40. No. 235. Jul// 1920. M 



