Mr Lees, Note on constant volume explosion experiments 289 



than T. From its nature, therefore, the curve must always slope 

 upwards from D to E. Referring to this diagram, it is easily seen 

 from the definition (3) of T„, , that the shaded areas ACD and CEB, 

 on opposite sides of the line AB, must be equal. 



In the absence of more accurate knowledge as to the shape of 

 the curve DCE, we may take it as approximately a straight line. 

 This will, at any rate, give some kind of approximation to the 

 truth. On this assumption, we shall apply our expressions to some 

 results obtained by the late Prof. B. Hopkinson. In one of his 

 explosion vessel experiments, Hopkinson* found for the instant of 



Fig. 2. 



maximum pressure (corresponding in this case to a mean tempera- 



- ture of 1600° C.) a maximum temperature at the centre of the 



' vessel of about 1900° C, whilst the temperature was probably as 



■ low as 1100° C. in the immediate neighbourhood of the walls. The 



difference between the maximum temperature and the mean being 



less than the difference between the minimum temperature and the 



j mean, the curve of temperature distribution has been arbitrarily 



assumed as DCE in fig. 2. In this diagram, DC and CB are taken 



as straight lines, whilst the point C on AB has been so chosen that 



' the area ADC equals the area CEB. It will readily be verified for 



the temperatures obtained by Hopkinson that AC = ^N/8, whilst 



' CE = 5Nj8. 



[ For continuously varying temperatures throughout the gas, 

 !; expression (14) must be replaced by 



# 



hB\t^dN, .. 



* Proc. Eo>j. Soc, 1906. 



.(15) 



