53.2 Royal Society : — 



14 The properties manifested by glass in general, and espe- 

 cially by flint-glass, show that in optical instruments this sub- 

 stance may act as a luminous source ; the rays emitted in virtue 

 of this action, although of small intensity, must mix themselves 

 with those transmitted through this substance. 



15. On passing electric discharges through tubes containing 

 phosphorescent substances in rarefied air, very remarkable lumi- 

 nous effects are produced, and that not only during, but after 

 the passage of the electricity ; in this manner we are enabled to 

 exhibit with great intensity the various phosphorescent phseno- 

 mena usually observed with solar light. Hence with this dis- 

 position we have effects analogous to those observed in the phos- 

 phoroscope, except that here the electric discharges replace the 

 intermittent flashes produced by the solar light on penetrating 

 the latter instrument. 



This mode of experimenting, too, is well suited to the exhi- 

 bition of the luminous properties of bodies which retain the im- 

 pression of light only for a short time ; for the observer here 

 sees the effects produced upon bodies immediately after the 

 passage of each discharge, and even when the luminous impression 

 of these discharges is retained for a time too short to be measured. 



These conclusions, which support the theory of undulation as 

 at present admitted, prove that luminous vibrations, when trans- 

 mitted to any body, or at least to a great many bodies, compel its 

 molecules to vibrate for a time and with an amplitude and wave- 

 length which depend not only on the chemical constitution of 

 the body, but also upon its physical condition. 



LXXX. Proceedings of Learned Societies. 



KOYAL SOCIETY. 



[Continued from p. 474.] 



May 5, 1859. — Sir Benjamin C. Brodie, Bart., President, in 

 the Chair. 



THE following communications were read : — 

 "Propositions upon Arithmetical Progressions." By F. Ele- 

 fanti, Esq. 



The author sketches the investigation of the way of throwing 

 various series of integer terms into arithmetical progressions, such as 

 the sums of squares, cubes, &c. of figurate numbers, of the powers 

 of a number, &c. He also gives the resolution of a given number, 

 in certain cases, into an arithmetical progression. Thus, having the 

 tlieorem that N can be resolved into an aritlimetical progression 

 when IG N+ 1 is a square, he is enabled to detect factors in N ; he 

 thus shows that 20/9519603 has 43 and 101 among its factors. 

 Among theorems which the method gives, may be noticed the 



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