526 
the apparatus under the air-pump, and measuring the electro- 
lytic resistance at a pressure of 1.1 inches. This gives 
at 64°.6. . e= 589.6, 
and it is shown, that the chances are 3 to 2 that the unexplained 
difference is mere error of observation. The mere escape of 
the gas, therefore, does not change e. 
This change of temperature produces no alteration of me- 
tallic affinities, as is shown by the intensity of Daniell’s cell 
being the same at 64° and 163°. The expression of this is 
e=zo—2cu.o. That for a cell excited with dilute sulphu- 
ric acid = zo — cu.o—ho, and it is found to decrease 27.9 
for 100°. The mean of all gives 25.1; and, if we might sup- 
pose this rate to be uniform through the thermometric scale, 
it would give 2386°, midway between the melting points of 
gold and cast-iron, for the temperature at which this affinity 
would cease. 
The author concludes by expressing his doubts, that the 
combination of these gases is in any case produced by heat ; 
and suggests that light is more probably the agent when the 
combustion is rapid, and the capillary force of the surfaces in 
contact with them, at lower temperatures, aided by some actinic 
influence extricated by the heat. Finally, he points out as a 
promising subject of mathematical research, the application 
of the undulatory theory to the phenomena of conducted and 
latent heat. 
Sir William R. Hamilton read a paper by Professor Young, 
of Belfast, on an extension of a theorem of Euler. 
The object of the author is to extend and generalize the 
theorem of Euler,—that the sum of four squares, multiplied by 
the sum of four squares, produces the sum of four squares. He 
commences by examining into the construction of the four- 
square formula, with the view of ascertaining whether any 
thing like a definite law or principle connects its component 
ee 
