506 



phous, pulverulent solid, which is reconverted into acetaraide by 

 contact with water. 



These reactions establish the fact, that by the action of zincethyl 

 one of the atoms of hydrogen, in ammonia and analogous nitrogen 

 compounds, combines with ethyl and becomes replaced by zinc. It 

 will be interesting to extend this reaction to the nitryles, especially 

 such as contain electro-negative radicals of the othyl family, since we 

 may thus expect to obtain a new series of double radicals, amongst 

 which the ketones will perhaps find a home. 1 hope soon to lay the 

 results of this extension of the investigation before the Royal Society. 



VIII. "On a Class of Dynamical Problems." By ARTHUR 

 CAYLEY, Esq., F.R.S. Received June 18, 1857. 



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 (z. 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 hanging 

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

 the system takes into connexion with itself, and sets in motion with 

 a finite velocity an infinitesimal length ds of the chain ; in fact, if v 

 be the velocity of the part which hangs over, then the length vdt is 

 set in motion with the finite velocity v. The general equation of 

 dynamics applied to the case in hand will be 



where the first line requires no explanation, in the second line , ?j, 



