1874.] 



115 



[Marsh. 



1863, p. 83), says : "Let C be a cylindrical vessel, with a base one square 

 foot in area. Let P P mark the upper surface of 

 a cubic foot of air at a temperature of 32° P, 

 The height A P will then be a foot. Let the air 

 be heated till the volume is doubled. To effect 

 this it must, as before explained, be raised 490° F, 

 in temperature, and, when expanded, its upper 

 surface will stand at pi P^, one foot above its 

 initial position. But in rising from P P to Pi F\ 

 it has forced back the atmosphere, which exerts 

 a pressure of 15 lbs. on every square inch of its 

 upper surface ; in other words, it has lifted a 

 weight of 144 X 15 = 3,160 lbs. to a height of 

 one foot. 



The capacity 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 

 0.24 = 0.31 oz. But 0.31 oz. of water heated to 

 490O is equal to 152 oz., 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 2,160 lbs. 

 one foot high, would be competent to raise 9^ lbs. of water one degree in 

 temperature. 



The air has been heated itnder 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 temperatui-e loJien its volitme is kept constant, 

 in proportion of 1.42 :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 one cubic foot of air, at a constant volume, 490°, would 

 heat 6.7 lbs. of water one degree. 



Deducting 6.7 lbs. from 9.5 lbs., we find that the excess of beat im- 

 parted to the air, in the case when it is permitted to expand, is com- 

 petent to raise 2.8 lbs. of water one degree in temperature. 



As explained already, this excess is employed to lift the weight of 

 2,160 lbs. one foot high. Dividing 2,160 lbs. by 2.8, we find that a 

 quantity of heat sufficient to raise one pound of water one degree F. in 

 temperature, is competent to raise a weight of 771.4 lbs. a foo£ high. 



This method of calculating the mechanical equivalent of heat was 

 followed by Dr. Mayer, a physician of Heilbron, Germany, in the spring 

 of 1842." 

 Now, since equal additions of heat make equal additions of volume, this 



