526 



the apparatus under the air-pump, and measuring the electro- 

 lytic resistance at a pressure of 1.1 inches. This gives 



at64°.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 = 20 — 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 



