XXIV INTRODUCTION. 



ml--t~^. In thermometric units by substituting /^ for m the factor becomes //~^, 

 and in dynamical units mt~^d~-. 



5. Thermal Capacity. — This is the product of the number for mass and 

 the specific heat, and hence the dimensional formula and conversion factor are 

 simply M and w. 



6. Latent Heat. — Latent heat is the ratio of the number representing the 

 quantity of heat required to change the state of a body to the number represent- 

 ing the quantity of matter in the body. The dimensional formula is therefore 

 M0/M or 0, and hence the conversion factor is simply the ratio of the tempera- 

 ture units or 0. In dynamical units the factor is /V~^,* 



7. Joule's Equivalent. — Joule's dynamical equivalent is connected with 

 quantity of heat by the equation 



ML2T-2=JH or JM©. 



This gives for the dimensional formula of J the expression L'^T"^©. The conver- 

 sion factor is thus represented by Pi~W. ^^'hen heat is measured in dynamical 

 units J is a simple number. 



8. Entropy. — The entropy of a body is directly proportional to the quantity 

 of heat it contains and inversely proportional to its temperature. The dimen- 

 sional formula is thus M©/0 or M, and the conversion factor is w. When heat is 

 measured in dynamical units the factor is ml-t~'^6~^. 



Examples, (a) Find the relation between the British thermal unit, the calorie, 

 and the therm. 



Neglecting the variation of the specific heat of water with temperature, or de- 

 fining all the units for the same temperature of the standard substance, we have 

 the following definitions. The British thermal unit is the quantity of heat required 

 to raise the temperature of one pound of water i° F. The calorie is the quan- 

 tity of heat required to raise the temperature of one kilogramme of water t° C. 

 The therin is the quantity of heat required to raise the temperature of one gramme 

 of water 1° C. Hence : — 



(i) To find the number of calories in one British thermal unit, we have 

 ;« = .45399 and ^ = §; .'. m^=. 45399 X 5/9 = -25i99' 



(2) To find the number of therms in one calorie, ;;/=iooo and ^=1; 

 .-. 7}i6 =^ 1000. 



It follows at once that the number of therms in one British thermal unit is 

 1000 X -25199 = 251.99. 



{b) What is the relation between the foot grain second Fahrenheit-degree and 

 the centimetre gramme second Centigrade-degree units of conductivity ? 



The number of the latter units in one of the former is given by the for- 



* It will be noticed that when is given the dimension formula L^T-^ the formulae in thermal 

 and dynamical units are always identical. The thermometric units practically suppress mass. 



