306 Royal Society : — 



in photography, and myself to be of considerably greater inten- 

 sity than that procured during the eclipse, was obtained in two 

 seconds. 



The ratio of luminous influence, as measured by the camera, 

 was therefore at the greatest 1 to 150. But the average exposed 

 area during the five minutes preceding the central effect, compared 

 with that of the entire disc, will be nearly as 1 to 24. I there- 

 fore infer that the circumference of the sun's disc gives out a 

 very weak luminous radiation (at least as measured by a sensitive 

 plate) in compai'ison with the central part. This observation is 

 quite in accordance with the experience of Mr. Dancer, who 

 finds that in the photography of the sun, the central part is 

 always much more rapidlv depicted than the circumference; so 

 much so, that he finds it impossible to obtain in the same image 

 a satisfactory delineation of both parts. 



On the eclipse becoming central, the darkness became sud- 

 denly increased, remained for a few seconds apparently constant, 

 and then as, or even more, suddenly cleared up. The light at 

 the darkest was evidently enormously greater than that of the 

 full moon, but from my experience in photogi'aphy, I have no 

 doubt that with it, two hours at the very least would have been 

 necessary to produce an effect equal to that attainable by one 

 second's exposure had the sun been vmeclipsed. 



I remain, Gentlemen, 



Yours respectfully, 



James P. Joule. 



XL. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 233.] 



June 18, 1857. — The Lord Wrottesley, President, in the Ciiair. 



I'^HE following communications were read : — 

 "On a (/lass of Dynamical Problems." By Arthur Cayley, 

 Esq., F.R.S. 



There are a class of dynamical problems which, so far as I am 

 aware, have not been considered in a general manner. The problems 

 referred to (which might be designated as continuous-impact pro- 

 blems) are those in which the system is continually taking into con- 

 nexion with itself particles of infinitesimal mass {i. e. of a mass 

 containing the increment of time dt as a factor), so as not itself to 

 undergo any abrupt change of velocity, but to subject to abrupt 

 changes of velocity the particles so taken into connexion. For 

 instance, a problem of the sort arises when a portion of a heavy chain 

 hangs over the edge of a table, the remainder of the chain being 

 coiled or heaped up close to the edge of the table ; the part banging 

 over constitutes the moving system, and in each element of time dt, 



