364 Mr. Herapath on new Demonstrations [May, 
mingled with an alkali and then with an acid. The same treat- 
ment does not form any prussic acid. ’ 
_In conclusion, I take the opportunity of recording a few 
observations which J have made on the action of iodine, of 
hydriodic acid, and of sulphuretted hydrogen, on prussic acid, on 
cyanuret of mercury, and on sulphuretted chyazate of copper. 
Iodine decomposes the aqueous solution of prussic acid, and 
becomes hydriodic acid, cyanogen being at the same time 
evolved. 
On the contrary, hydriodic acid is itself decomposed by 
cyanuret of mercury, red ioduret of mercury and prussic acid 
being formed. The affinity of mercury for iodine doubtless 
determines this decomposition. 
lodine, when put into a solution of cyanuret of mercury, sets — 
the cyanogen at liberty, and forms red 1oduret with the metal. 
Sulphuretted hydrogen gas, when quite dry, does not appear 
to act on sulphuretted chyazate of copper; but it instantly 
decomposes it when water is present, sulphuretted chyazic acid 
being separated, and sulphuret of copper fob 
Tower, April 3, 1819. R. Porrert, Jun. 
ARTICLE V, 
New Demonstrations of the Binomial Theorem. By Mr. Herapath. 
(To Dr. Thomson.) 
Amownc the many demonstrations that have been given of the 
binomial theorem, | do not remember to have seen one that is 
both elementary and complete. That in the Calcul des Fonc- 
tions is, perhaps, one of the most elegant and complete that has 
yet been given; but it has been objected to as not being element- 
ary. The same objection might, with a little modification, be 
made to one or two neat demonstrations that have appeared in 
some of the late volumes of the Philosophical Transactions, and 
to others that I have met with in different authors. It seems 
that mathematicians have considered the lower branches of 
algebra to be quite insufficient, without some assistance from 
the higher analysis, to effect a proof of this celebrated theorem. 
Whether Newton’s not attempting to demonstrate this, one of 
the most beautiful and valuable of his mathematical discoveries, 
and his resting satisfied of its general truth merely from trials 
in a few particular cases, may have had any influence, [| will 
not take upon me to determine ; but I hope the following demon- 
stration, drawn from common algebra, will show, that there is no 
necessity of having recourse to other pemeiples ta obtain a 
4 
