108 M. A. F. Sundell on Absolute 



sufficient to give a quantitative representation of all the phe- 

 nomena of physics; but we are obliged sometimes to introduce 

 arbitrary units. Among these may be reckoned the unit 

 angle, which is very useful in considering circular motion, for 

 which purpose it replaces the unit of length. From the unit 

 angle and the unit of time we derive the units of angular velo- 

 city and angular acceleration; since, further, moment of inertia 

 corresponds to mass, and moment of rotation to force, we obtain 

 a complete analogy with motion in a straight line, and equa- 

 tions analogous to the equations (2), (3), and (6). This ana- 

 logy is lost by regarding the angle as an abstract number. 

 The conceptions derived from the phenomena of heat. — A 

 quantity of heat w is proportional to the elevation of tempera- 

 ture T which it can cause in a mass m. We obtain thus the 

 equation of definition, 



w = cmT, 



where c is a factor depending on the material nature of the 

 body, which we will call the capacity for heat. The dimen- 

 sions of the unit of heat are determined by the equation 



[>] = [>iT]. 



We have here three new units, of which we may choose two 

 as fundamental units. Of the three possible combinations, we 

 have determined upon one, and choose units for capacity [c] 

 and temperature [T] at pleasure, so that the unit of heat [_io] 

 becomes a derived unit : it is the quantity of heat required to 

 raise by one unit the temperature of the unit mass of a sub- 

 stance having unit capacity. The units of temperature in use 

 are well known ; for unit of capacity we take the capacity 

 of water ; the capacity of a body is therefore expressed by the 

 same number as its so-called specific heat. As examples fur- 

 nished by the science of heat we may take the following : — 



The heat necessary to raise 10 kilogr. mercury (capacity 

 = 0-033 capacity of water) from 0° 0. to 100° C. = 0'033 x 

 10xl00( = 33) kilogr. x Centigrade degree x capacity of 

 water. 



Coefficient of linear expansion of iron = 0*000012 -= -^ 



1 degree 0. 



1 



= 0-000012 -t-t— ^ =£ x 0-000012 



f degree R. 4 degree K. 



= £x 0-000012 , * „ • 

 degree c . 



Latent heat of ice =79'25 degrees C. x capacity of water. 



We obtain the work A which is equivalent to a quantity of heat 

 w by multiplying this quantity by the mechanical equivalent 



