I’REE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 23 
§ 20. If a medium is not allowed to increase in volume while its vis viva is 
increasing, no force will of course be expended, and each increment of vis viva 
engenders a like increment of tension. Thus if ive compare the amount of vis viva 
required to produce an increment of molecular vis viva in the medium, in the two cases 
of constant pressure and constant volume; it is manifest that the ratio is 4 to 3, 
or 4/3".XIV. 
§ 21. If we suppose the heavy plane n instead of being raised by the medium to 
descend upon it through the same differential height 2 w 2 jgn 2 , it is obvious that the 
same differential vis viva that was formerly abstracted is now communicated to the 
molecules of the unit volume. Force is exerted by the descending weight upon the 
medium and is transferred to its molecules.! Thus it is evident that the conversion 
of mechanical force into molecular vis viva is subject to the same law as the conversion 
of molecular vis viva into mechanical force. This law is expressed in XII. and XIV. 
The following is another form of annunciation which refers to an experimental method 
of ascertaining it if such media were actual existents. The ratio of the increment of 
vis viva evolved by a small condensation of a medium to the diminution of molecular 
vis viva required to maintain the same condensation under a constant pressure 
is H .XV. 
§ 22. If a medium is compressed or dilated and the molecular vis viva evolved in it 
or given out from it by the act of condensation and dilatation be retained, let us 
enquire into the ratio of the density to the pressure. The preceding reasoning has 
shown that the increment or decrement of vis viva is equal to one-third of the 
• , c . dv 2 dA 3 , 2 dv dA , . . . . 
increment or decrement or density, or — = —hence which being 
integrated gives v° = A. But -y 3 A 3 = e, therefore A 4 = e, and v 2 = e. Thus we 
deduce that if a medium is compressed or dilated from a given condition of density 
and vis viva, the mean square molecular velocity varies as the fourth root of the 
tension or as the cube root of the density §.. XVI. [| 
§ 23. The tendency of media to have their vis viva augmented when being forced 
into smaller volume is very similar to the rise of temperature that appears in air 
when being condensed. Thus tinder may be inflamed by the sudden compression of 
a small quantity of air, and on charging an air gun the condenser and force pump 
become so hot as to be painful to touch. Again, mercury may be frozen if exposed to 
a jet of air escaping from a state of high compression and expanding against the 
* [The ratio of specific heats, commonly called 7, should be 5 : 3, not 4 : 3.—R.] 
t Note A (motion indestructible as matter). 
+ [This result also requires correction.—R.] 
§ Note B (vapours). 
|| [The corrected argument is—Since dr 2 /?; 2 = dA 3 /A 3 , we get dvjv — 4A/A, or v == A. Accordingly 
v 2 = A 2 = (A 3 )§. But v 2 A 3 = e; therefore, A 5 = e, and v 2 = eh Also e = (A 3 )h o v p =■ pV, where 
7 - 4--R-] 
