TRANSACTIONS OF THE SECTIONS. 21 
On the Cohesion of Gases, and its relations to Carnot’s Function and to recent 
Experiments on the Thermal effects of Elastic Fluids in Motion, By James 
Crott, Glasgow. 
From the fact that those gases which are most easily liquefied by compression are 
those which are found to deviate most from the law of Mariotte, we are led to the 
conclusion that their deviations from this law are due to the mutual attraction of 
their particles. Deviations from Mariotte’s law after the manner of carbonic acid 
follow as necessary consequences from cohesion. Other phenomena are also ex- 
plainable on the same principle; such, for instance, as why the coefficient of expan- 
sion is greatest for the gases which deviate most from Mariotte’s law—why the 
coefficient of expansion increases with the density in gases which deviate from 
this law—why, when equal weights are employed to compress different gases under 
the same conditions, the greatest amount of work is performed on the gas which 
deviates most—why, in the expansion of gases by heat, least work is performed by 
heating the gases which present the greatest deviation. 
The influence of Cohesion in relation to the Experiments of Prof. W. Thomson and 
Dr. Joule on the Thermal effects of Elastic Fluids in Motion. 
In these experiments, air, carbonic acid, or hydrogen, under very high pressure, 
was made to expand by forcing itself through a porous plug, and it was found that 
the temperature of the gas after expansion was somewhat less than before it; in 
other terms, the heat of friction was found to fall short of compensating the cold 
of expansion. The expenditure of elastic force experienced by the gas, in forcing 
itself through the porous plug, tends in the first instance to lower its temperature ; 
but as this force is spent in friction, the heat produced from friction ought exactly 
to compensate the cold of expansion. This is only the case, however, when all the 
force of expansion has been spent in friction; ifa portion of this force be consumed 
in producing some other effect than heat, then the heat of friction will not com- 
pensate the cold produced by the waste of force in expansion, and a cooling effect 
will be the result. Now it is perfectly evident that if the atoms of a gas when 
compressed attract each other, the force of expansion cannot be all converted into 
heat, a portion of it must be consumed in overcoming attraction, hence the heat of 
friction will fall short of compensating the cold of expansion by an amount equal 
to the equivalent of the work against attraction. 
It is generally understood that in certain cases a heating instead of a cooling 
effect may take place. How this may occur is not so apparent. Prof. W. Thomson 
states, that when the temperature of air rises above a certain height, the heat of 
friction will exceed the cold of expansion, because P'V', the work which a pound 
of air must do in expanding through the plug, is rather less than P V, which is the 
work done on it in pushing it through the spiral up to the plug. It is by no means 
obyious how this can result in a heating effect. That which produces the cold of 
expansion is the expenditure of the elastic force in expanding through the plug; 
but as this force is not consumed on external work, but entirely spent in friction on 
the particles of the air itself, the force which it loses on the one hand is entirely 
restored to it on the other. But more force cannot be restored than was lost; for 
the force restored is just what was lost. : 
The only way whereby it is possible to account for a heating effect, is by supposing 
that a gas which exhibits the heating effect possesses a certain amount of elastici 
independent of heat, and that the expenditure of this force in the production of heat 
by friction, is an expenditure of elastic force, but not an expenditure of heat—a 
conclusion which is very improbable. 
The Influence of Cohesion in relation to Carnot’s Function, 
The following was suggested by Dr. Joule, in a letter to Prof. W. Thomson in 
1848, as the true expression of Carnot’s function, 
mG eT) 
ie a) Renee 
J denoting Joule’s equivalent, E the coefficient of expansion*, and ¢ the tempera- 
* In this formula Carnot’s function is equal to the mechanical equivalent of the thermal 
