810 Royal Society: — 



term here ^=0, but H=cs, and thence -^ = s'. Moreover, d^ = 



s'dt, and thence finally the second term is s'-, which is of the form 

 dK .f 



dl'' K=is'.s'"-, 



the bar having the same signification as before, but after the differ- 

 entiation «'=«'. The resulting equation is 



\dt- '' J \dt) 



which may be written in the form 



ds J ( I 



s— d\ s- 



dt \ I 



and the first intes'ral is therefore 



ds J ( ds\ « , 



-v/fi'-a' V 3 

 where a is the length hanging over at the commencement of the 

 motion. If a=:0, then the equation is 



-/« V 3 ^ 

 and integrating from ^=0, 2\^s=\/ -^t, or finally s = --fft-, so 

 that the motion is the same as that of a body falling under the 

 influence of a constant force -ff. It is perhaps worth noticing that 



the differential equation may be obtained as follows : — We have, in 



the first instance, a mass s moving with a velocity «', and after the 



particle ds (=s'df) has been set in motion, a mass s-\-s'di monng 



say with a velocity s' + ls', whence neglecting for the moment the 



effect of gravity on the mass s, the momentum of the mass in motion 



will be constant, or we shall have 



ss' =(s + s'df) («' + cs') = ss' + s'-dt + sis', 



and therefore 52*'=— s'y/^ Hence, adding on the right-hand side 



d's 

 the term ffsdt arising from gravity, and substituting -— , dt for h', 



we have the equation « — ^^ns— ( —] as before. 

 ^ dt- ^ \dtj 



"On the Causes and Phsenomena of the Repulsion of Water from 

 the Feathers of Water-Fowl and the Leaves of Plants." By George 

 Buist, D.C.L., of Bombay, F.R.S. 



" Experimental Researches on the Conductive Powers of various 

 Substances, with the application of the Results to the Problem of 

 Terrestrial Temperature." By WiUiam Ho])kins, Esq., M.A., F.R.S. 



1 . The author remarks, that in giving ;ui account of these experi- 

 mental researches, it is first necessary to define strictly the manner in 



