511 



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

 motion. If a=0, then the equation is 



and integrating from t=0, 2v / '*=A/^, or finally s = -gt?, so 

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



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

 3 



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'dt) has been set in motion, a mass s+s'dt moving 

 say with a velocity s' + Ss', 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 



'= (s + s'dt) (s' + &') = ss' + s' 2 dt + &', 



and therefore s<is'=s' 2 dt. Hence, adding on the right-hand side 

 the term gsdt arising from gravity, and substituting * dt for Ss', 



we have the equation s=gs (} as before. 

 dt \dtj 



IX. "Remarks on a New Class of Alcohols." (Second Note.) 

 By A. W. HOPMANN, LL.D., F.R.S., and AUGUSTE 

 CAHOURS, F.C.S. Received May 15, 1857. 



(Abstract.) 



In a communication addressed to the Royal Society some time ago 

 (Proceedings, vol. viii. No. 1 9), we endeavoured to delineate the cha- 

 racters of a new alcohol the Allylic alcohol, which is the prototype 

 of a new class of alcohols. We have since continued these researches 

 in order to complete the history of this remarkable compound. 



In submitting to the Royal Society the full account of our expe- 

 riments upon the subject, we beg leave to mention in this abstract 

 briefly some additional compounds which we have examined since 

 our last communication. 



