FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 49 
the theory of gases is the same fractional part of the specific heat of the solid. This 
is somewhat confirmatory of the theoretical interpretation of the law of volumes 
(§ 15). The vaporous molecule of mercury is indivisible. The vaporous molecule 
of arsenic is divisible into four parts : of sulphur into six parts ; of phosphorus into 
four parts; of hydrogen into two parts ; of oxygen into two parts ; of water (0 4 2H 4 ) 
into three parts; of alcohol (2(HC 4 ) + 2H 4 0 4 ) into five parts ; of sulphuric ether 
(4(HC 4 ) + 2ll 4 0 4 ) into seven parts ; sulphuric acid, anhydrous (30 4 + S.) into four 
parts ; etherine 4(HC 4 ) into four parts, &c. We may thus predict the specific heat of 
pyroxilic spirit to be 0‘83, and of pyroxilic ether 0’72. 
Note F. — M. Clapeyron’s Fundamental Position. 
The density and tension of a medium expanding according to Marriotte’s law, are 
represented linearly by the co-ordinates to the common hyperbola CMEL referred to 
its asymptote AG; the abscissa AB, &c., representing the volume, and the oi’dinates 
BC, &c., the tension. 
We have shown that each incremental expansion is made at the expense of the 
molecular vis viva of the medium, so that to maintain the expansion, according to 
Marriotte’s law, the loss of vis viva must be continually made up ; and the amount 
required to be supplied for any given expansion, as from B to D, is to the constant 
Fig. 4. 
original amount as the area CEDB is to 3 CB.AB, or to the original tension CB 
acting through three times the original volume AB (XIII.). 
Suppose the medium to expand from B to H (against pressure) without having its 
loss of vis viva supplied; then, according to § 22, its tension from CB, or unity, 
becomes KH = 
CB. 
Assuming the original volume and tension as unity and 
BIT = y, we have KH = x = 
the asymptotal area CKHB. 
1+3/ 
and x dy = dy j = the differential of 
To integrate this put — = 1 -f- y, and differentiating gives dy = — ; and since 
MDCCCXCII.—A 
H 
