Prof. Thomson on the Dynamical Theory of Heat. 115 



37. Explanation of the Tables. 

 Column I. in each table shows the assumed ranges. 

 Column II. shows ranges deduced by means of Table II. of 



the former paper, so that the value of / fj,dt for each may be 



kJ t 

 the same as for the corresponding range shown in column I. 



Column III. shoM^s what would be the duty of a unit of heat 

 if Carnot's theory required no modification (or the actual duty 

 of a unit of heat witli additions through the range, to compen- 

 sate for the quantities converted into mechanical effect). 



Column IV. shows the trae duty of a unit of heat, and a com- 

 parison of the numbers in it with the corresponding numbers in 

 column III. shows how much the true duty falls short of Carnot's 

 theoretical duty in each case. 



Column VI. is calculated by the formula 



where € = Si'71828, and for / fjidt the successive values shown in 

 column III. are used. ^"^ 



Column IV. is calculated by the formula 

 W = 1390(1 -R) 

 frpm the values of 1 — R shown in column V. 



12 



