INTRODUCTION XXXvii 



Specific Heat is the relative amount of heat, compared with water as standard 

 substance, required to raise unit mass of different substances one degree in tem- 

 perature and is a simple number. 



Coefficient of Thermal Expansion of a substance is the ratio of the change of 

 length per unit length (linear), or change of volume per unit volume (voluminal), 

 to the change of temperature. These ratios are simple numbers, and the change 

 of temperature varies inversely as the magnitude of the unit of temperature. 

 The dimensional formula is (J) -1 } 



Thermal Conductivity, or Specific Conductance, is the quantity of heat, H, 

 transmitted per unit of time per unit of surface per unit of temperature gradient. 

 The equation for conductivity is therefore K = H/L 2 TQ/L, and the dimen- 

 sional formula [_H/QLT~\ = \_M Lr l T~ l ~\ in thermal units. In thermometric 

 units the formula becomes [L 2 r~'], which properly represents diffusivity, and 

 in dynamical units [_M LT~ 3 Q~ 1 ']. 



Thermal Capacity is mass times the specific heat. The dimensional formula 

 is [Af]. 



Latent Heat is the quantity of heat required to change the state of a body 



divided by the quantity of matter. The dimensional formula is [_MQ/M~\ or 



[_Q~\\ in dynamical units it is \_L 2 T~ 2 ~\. 



Note. — When is given the dimensional formula [UT~*\, the formulae in thermal and 

 dynamical units are identical. 



Joule's Equivalent, /, is connected with the quantity of heat by the equation 

 ML 2 T- 2 = JH orJMQ. The dimensional formula of / is [L*T*Qr*\ In 

 dynamical units / is a simple number. 



Entropy of a body is directly proportional to the quantity of heat it contains 

 and inversely proportional to its temperature. The dimensional formula is 

 [M0/0] or [M]. In dynamical units the formula is [_M L 2 ^ 2 ©" 1 ]. 



Exs. — Find the relation between the British thermal unit, the large or kilogram-calorie 

 and the small or gram-calorie, sometimes called the "therm." Referring all the units to the 

 same temperature of the standard substance, the British thermal unit is the amount of heat 

 required to warm one pound of water i° F., the large calorie, i kilogram of water, i° C, the 

 small calorie or therm, i gram, i° C. (i) To find the number of kg-cals. in one British thermal 

 unit, m = .45359, Q = 5/9; md = .45359 X 5/9 = .25199. (2) To find the number therms in one 

 kg-cal. m = 1000, and d = 1; md = 1000. (3) Hence the number of small calories or therms in 

 one British thermal unit is 1000 x -25199 = 251.99. 



ELECTRIC AND MAGNETIC UNITS 



A system of units of electric and magnetic quantities requires four funda- 

 mental quantities. A system in which length, mass, and time constitute three 

 of the fundamental quantities is known as an "absolute" system. There are 

 two absolute systems of electric and magnetic units. One is called the electro- 

 static, in which the fourth fundamental quantity is the dielectric constant, and 

 one is called the electromagnetic, in which the fourth fundamental quantity is 

 magnetic permeability. Besides these two systems there will be described a 

 third in common use called the "international" system. 



