452 Prof. Potter on the Definition of the Temperature of Bodies, 



The discrepancies which were found between the scales led to 

 the conclusion that the divisions into equal intervals could not 

 apply accurately to all, though it has been taken to involve 

 uniform expansion. Thus if V is the volume of a body at any 

 given temperature, and SV the increase of volume for each degree 

 of temperature, then SV = constant was supposed to im r olve 

 uniform expansion. This is undoubtedly incorrect ; for the 

 expansion of a body of volume V is the ratio of the incre- 

 ment of V to V; or putting SV for the increment, then the 



. BY . ' . . 



expansion is ■=■ ; and if the expansion is constant or uniform, 



SV v . . 



then -T7- = constant for all temperatures. This not being 



hitherto recognized, we have had inadequate discussions in the 

 search for a normal thermometer. 



As to the probability of gases, spirit, mercury, or any other 

 fluids being subject to uniform expansion, it is desirable to con- 

 sider the physical state of each in the first instance. In the 

 liquids under the pressure of their vapours only at their surfaces, 

 their volume is that at which the repulsive force due to their 

 inherent caloric balances the attraction of aggregation of their 

 atoms. At certain temperatures peculiar to each substance, the 

 attraction of aggregation is overbalanced by the repulsion due 

 to the caloric of the body, and it ceases to be of two kinds, 

 liquid and vapour, and consists of vapour only. We see that 

 the law of the expansion of liquids depends on the increase of 

 the repulsive force due to the caloric of the body and the dimi- 

 nution of the attractive force of aggregation. We cannot see 

 a priori that the law of expansion for increase of temperature 

 should be very simple. 



With respect to gases under constant or uniform pressures, 

 the consideration of their volumes involves the law of their 

 elastic force with respect to their density (or reciprocal of their 

 volume) at different temperatures. Then, if the elastic force of 

 the gas is constant, the repulsive force due to the combined 

 caloric determines the volume and density of a given mass. We 

 cannot here, again, from a priori reasoning, see the law of 

 expansion for increase of temperature. It has been generally 

 called uniform expansion ; but, with the exception of Dalton, 

 uniformity of expansion has been universally taken to mean 

 expansion by equal increments of volume for equal increments 

 of temperature, as expressed in the law of Gay-Lussac for 

 the relation of the volumes and temperatures of gases under 

 constant pressures, or V=V (1 +at°), where V is the volume 

 of the gas at the freezing-point of water, and V its volume at 

 f above that point. If this were a physical law, the absolute 



