• PROBLEM IN THE DOCTRINE OF PERMUTATIONS. Oqj 



of fresh alcohol at 40°* were introduced drop by drop, re- 

 gulating the quantity as nearly as possible by what passed 

 over into the receiver. The process was continued so as to 

 obtain fifteen kilogrammes of a white limpid product, of 

 the most agreeable ethereal smell and taste, containing no 

 traces of sulphurous acid or oleum duke, and yielding, 

 when rectified on a water-bath, eight kilogrammes of pure 

 ether, with some alcohol of an ethereal smell well adapted 

 for future processes. 



The liquid remaining in the retort was of the colour of The residuum, 

 beer, and very clear. It consisted of nearly the whole of 

 the sulphuric acid employed, some alcohol, water, and no 

 doubt a certain quantity of ether completely formed. 



This residuum, heated afresh, quickly assumed a black Purposes to 



colour, and became sulphurous and oily. In this state it which ' l * m *y 



. be applied. 



may enter into the composition of Hoffmann's mineral 



anodyne liquor. The residuum might also be turned to 



account, by using it as sulphuric acid where the alcohol 



could do no harm, as for instance, in forming different 



salts. 



VIII. 



Investigation of a Problem in the Doctrine of Permutations. 

 By Mr. Peter Barlow. 



To Mr. NICHOLSON. 

 SIR, 



N the course of a mathematical investigation, in which Problem in th« 

 I was lately engaged, it was necessary for me to determine doctrine of per- 

 — -How many combinations could be formed out of a given ipU a 10n * 

 number of things, in which there were several things of one 



* I have observed, that alcohol at 36° is best adapted for the com- 

 mon preparation of sulphuric ether; and that the mixture is less co- 

 loured when it is at this strength, than if it contain less water. But at 

 the second addition, as the#cid is already weakened, it is better to em- 

 ploy it at 40°. 



tort, 



