Pendulum swinging through an Arc of Finite Magnitude. K51 



difference between A + B together and A and B separately 

 varied only from 2 to 1 per cent. Such a small difference 

 could not of itself have produced the initial abnormal decay. 

 Besides, two of the preparations whose intensities lay wholly 

 within the strictly additive portion of the range showed the 

 abnormal effect. 



Both the ft- and the 7-rays decay to zero. There is now 

 no detectable residual j3- or 7-radiation in the first active set 

 of preparations separated in November, 1908. The /3-rays 

 of the main preparation of Feb. 1909 have now (April 1 909) 

 just passed beyond the range of measurement, the decay, so far 

 as could be seen, having been quite normal right up to the end. 

 In this period of 14 months, the radiation decays in the ratio 

 of 100,000 to 1. All samples of crystals of uranyl nitrate of 

 third, fourth, and fifth separation tested against an equal 

 weight of standard untouched crystals have regained their 

 equilibrium content of uranium X quite normally. There is 

 not the slightest evidence that in the numerous chemical 

 operations to which the crystals have been at various times 

 subjected, any concentration or impoverishment of a body, 

 intermediate between uranium and uranium X, and acting as 

 the direct parent of the latter, has taken place *. 



Physical Chemistry Laboratory 

 University of Glasgow. 



\M 



LXXXIX. On the Motion oj aPendumm mmying through an 

 Arc of Finite Magnitude. By J. Rose-Innes, M.A., B.ScA 



IN the following paper it is proposed to investigate by 

 comparatively simple methods the motion of a pendulum 

 uhen the swing is not treated as infinitesimal. 



The Elliptic Integral of the First Kind. 



The Jacobian theory of elliptic functions is developed 

 primarily from an examination of the properties of the 

 integral 



*• dx 



Jo 



v 1 — kt sin- x 

 Tn tin 4 present section a new geometrical interpretation will 



* M. J. Danne ha? described the separation of such a body (Le JRadhnn, 

 1909, vi. p. 42 s ). but it is -desirable to await further confirmation of his 

 reMilts before basing any conclusion upon them. 



t Communicated by Prof. l\ T. Trouton, F.R.S 



