Dynamical Theory of Heat. 381 



Mayer's first paper does not contain the details of the calcu- 

 lation; but in his second paper, published in 1845, he formally 

 goes through it. In ray ' Lectures on Heat ' I have tried to put 

 this subject into its most elementary form ; and as many persons 

 may take an interest in this discussion who are not conversant 

 either with the details or history of the mechanical theory of heat, 

 I will ask permission to make a quotation from the work referred 

 to. In calculating the mechanical equivalent of heat, while using 

 my own language I strictly adhere to the method of Mayer. 



" Let C be a cylindrical vessel with a base one square foot in 

 area. Let P P mark the upper surface of a cubic p ,i 

 foot of air at a temperature of 32° Fahr. The 

 height AP will then be 1 foot. Let the air be heated 

 till its volume is doubled; to effect this it must, 

 as before explained, be raised 273° C. or 490° F. 

 in temperature; and when expanded, its upper 

 surface will stand at P' P', one foot above its initial 

 position. But in rising from P P to P' P' it has 

 forced back the atmosphere, which exerts a pres- 

 sure of 15 lbs. on every square inch of its upper 

 surface ; in other words, it has lifted a weight of 144 x 15 = 2160 

 lbs. to a height of 1 foot. 



"The l capacity 3 for heat of the air thus expanding is 0*24, 

 water being unity ; the weight of our cubic foot of air is 1*29 oz. ; 

 hence the quantity of heat required to raise 1*29 oz. of air 490° F. 

 would raise a little less than one-fourth of that weight of water 

 490°. The exact quantity of water equivalent to our 1*29 oz. of 

 air is 1'29 x 024 = 0*31 oz. 



"But 031 oz. of water heated 490° is equal to 152 ozs., or 

 9^ lbs. heated 1°. Thus the heat imparted to our cubic foot of 

 air, in order to double its volume and enable it to lift a weight 

 of 2160 lbs. 1 foot high, would be competent to raise 9| lbs. of 

 water one degree in temperature. 



" The air has here been heated under a constant pressure ; and we 

 have learned that the quantity of heat necessary to raise the 

 temperature of a gas under constant pressure a certain number 

 of degrees, is to that required to raise the gas to the same tem- 

 perature, when its volume is kept constant, in the proportion of 

 1*42 to 1 ; hence we have the statement, 



1-42: 1=9-5 lbs. : 6-7 lbs., 

 which shows that the quantity of heat necessary to augment the 

 temperature of our cubic foot of air at constant volume 490° 

 would heat 6'7 lbs. of water 1°. 



"Deducting 6*7 lbs. from 9*5lbs.,wefind that the excess of heat 

 imparted to the air, in the case where it is permitted to expand, 

 is competent to raise 2*8 lbs. of water 1° F. in temperature. 



