742 SIR W. THOMSON ON THERMODYNAMIC MOTIVITY. 
scale, founded on the values of Carnot’s function, and expressed by the follow- 
ing equation :— 
ie > 
where ais a constant which may have any value, but ought to have for its value 
the reciprocal of the expansibility of air, in order that the system of measuring 
temperature here adopted may agree approximately with that of the air thermo- 
meter. Then we have 
e tfe eat an! | 
tt+a 
It was only to obtain agreement with the zero of the ordinary centigrade 
scale of the air thermometer that the a was needed, and in the joint paper by 
JOULE and myself, published in the Transactions of the Royal Society 
(London) for June 1854, we agreed to drop it, and to define temperature 
simply as the reciprocal of Carnot’s function, with a constant co-efficient 
proper to the unit or degree of temperature adopted. Thus definitively, in 
equation (6) of § V. of that paper, we took t= , and have used this expression 
ever since as the expression for temperature on the arbitrarily assumed thermo- 
dynamic scale. ‘With it we have 
i i 
and by substitution (1) becomes 
W=I fifdadyd fodt(i—7) ..... 
Suppose now B to be surrounded by other matter all at a common tem- 
perature T. The work obtainable from the given distribution of temperature 
in B by means of perfect thermodynamic engines is expressed by the formula. 
(4). If, then, there be no circumstances connected with the gravity, or 
elasticity, or capillary attraction, or electricity, or magnetism of B in virtue 
of which work can be obtained, that expressed by (4) is what I propose to 
call the whole Motivity of B in its actual circumstances. If, on the other 

