A Mathematical Question. 53 
rated from their combination in the gaseous form. 2dly, Con- 
sidering water as an element, an undecompounded body, and 
that the radicles of oxygenous aud hydrogenous gas were com- 
municated by the positive and negative wires, and these com- 
bining with the water, probably in definite portions, constituted 
gaseous oxygen and hydrogen. This was the opinion of Ritter 
“of Jena, and I remarked that it. was in harmony with our best 
views of electrical phenomena. How'can we account for the elec- 
trical spark not only decomposing but recomposing water, on the 
latter supposition ?—two opposite effects resulting from the same 
cause ?—analysis and synthesis accomplished by similar means? 
—destruction and reunion, by one agent, under identical medi- 
fications? It is hard to be conceived. But a more satisfactory 
solution is obtained, if we admit that oxygen and hydrogen in the 
form of gas are elements (evolved by means of attrition in the 
electrical machine, or the action of acid and alkaliné menstrua 
on metallic bodies in the Veltaic trough,) united with water : 
then, these gases in definite proportions, by passing the spark 
through them, may be united, and the radicles furm a neutral 
effect ;—-when the power of holding the water in solution ceas- 
ing, the moisture is precipitated. 
There is much obscurity in Mr. Walker’s solution of the phz- 
nomena of combustion, arising from his using indiscriminately 
the terms heat (caloric) and combustion. Now calorie (the mat- 
ter of heat) and combustion (the act of ignition) are not iden- 
tical. What may be collected, however, from the general tenor 
of that paper, is merely the theory of Lavoisier in anew dress. 
Mr: Walker may please to be informed that combustion takes 
place where there is not the least evidence of the existence of 
oxygen, as that elicited from the union of sulphur and some of 
the metals, &c. 
~ I solicit your pardon for this digression, and am with much 
respect, 
Sirs, your humble servant, 
é Joun Murray. 
To Messrs. Nicholson and Tilloch. 
XV. A Mathematical Question. By Sir H. C. Eyeieriztp, 
Bart., F.R.S. F.4.8., Gc. Sc. 
Petersham, Jan-18, 1814 
Sirs, Tus very extraordinary powers of the American bo¥ 
[Zerah Colburn] in fitding the roots of numbers, among other 
wonderful effects of mental computation, led me lately to con- 
Sider the subject ; and in the course of what I may esil a meeha- 
ical dissection of numbers, I fell on the niethod which, if you 
be da 
