DULONG AND PETIT’S LAW OF THE SPECIFIC HEAT OF SIMPLE BODIES. 121 
happen that during the experiment, the water 
in the exterior vessel is constantly giving off 
heat at the expense of the substance, which is 
the object of experiment, and conveying it to 
the vessel andsurroundingbodies. Avogrado, 
however, corrected this source of error by 
applying Newton’s law, according to which, 
the communication of heat is continually pro- 
portional to the actual difference to tempera- 
ture between the two bodies, a law which is 
exact for moderate temperatures. He found 
also a formula nearly accurate, in which the 
I excess of temperature of the exterior vessel, 
I and of the water contained in it, above that of 
I the surrounding air, as well as of the interior 
vessel, and the substance contained in it above 
that of the water, is regarded as being a mean 
during the experiment between the initial and 
final excess. . 
According to the law of Dulong and Petit, 
the specific heat of simple bodies, taking for 
unity that of an equal weight of water, mul- 
tiplied by their atomic weights, gives us the 
constant number ‘375, (or *376*) In other 
words, the specific heat of anatom of these 
bodies is -375, adopting as unity the specific 
heat of a body of water, equal in weight to 
that of an atom of oxygen. From which it 
follows that if the same law applies to oxygen, 
and if the relation adopted between the atoms 
of different bodies and that of oxygen, is really 
that which exists between the atoms, to which 
the law refers, and which may be called their 
thermic atoms, the specific heat of oxygen in 
the solid state, ought to be 0'375, taking as 
unity that of an equal weight of water. This, 
however, cannot be verified by experiment, 
because we are unacquainted with any me- 
thod of operating upon oxygen in the solid 
state. It is obvious, therefore, that to fix the 
atoms ofbodies relative to oxygen, is some- 
what arbitrary ; for the rule of the equality of 
the specific heat of atoms, would be verified 
by doubling all the atoms in relation to that of 
oxygen, or in taking a half or third, provided 
that we changed at the same time the constant 
number. 
Let us turn our attention to various bodies 
with this object in view. I. The specific heat 
of carbon appears to indicate that we may, 
reduce the atoms of sulphur, and the metals 
to one-half of the numbers attributed to them 
at present. The atom of carbon is really 
0 764 (or rather -75, as will be presently seen) 
of the atom of oxygen. The same relation 
ought then to subsist between the atoms of 
carbon and oxygen, both in the solid state., 
in order that the law of Dulong and Petit 
may be applicable. The specific heat of car- 
bon, according to the determination of Crawd- 
ford and Avogrado, is 2.5, or one fourth of 
that of water. Now, *75, the true atom of 
carbon (and not *764, the number adopted on 
the Continent) + .25 == *1875, or the half 
of *376, and exactly the half of .375, the 
co-efficient adopted by Avogrado. From this 
fact Avogrado argues that the co-efficient of the 
law of Dulong and Petit ought to be reduced 
to this half number, .1875, and for the 
same reason that the atoms of sulphur and the 
metals should be reduced to the half of the 
numbers which represent them at present. The 
specific heat of carbon would then be, accord- 
ing to this modified law g:i|75~o*25, or 
exactly the result of experiment. The num- 
ber deduced by Avagrado is, however, incor- 
rect, because he adopts *764 as the atomic 
weight of carbon, instead of *75, the number 
obtained by Dr. Thomson, and which is here 
substituted. 
In this view of the subject the specific heat 
of oxygen, in the solidstate, ought to be '1875, 
a number which Avogrado also finds to be 
nearly the specific heat of oxygen in the state 
of gas, by a calculation founded on the experi- 
ments of Berard and Delaroche, relating to 
the specific heat of the oxygen of the air com- 
pared to that of water; and it is probable that 
the specific heat of a body, which preserves 
the same atomic composition may not differ 
much in each state. This could not happen, 
however, if the numbers are preserved to 
which Dulong and Petit applied their law, 
because the specific heat of oxygen would 
then be *375, or the double of that which it 
possesses in the gaseous state. 
2. PHOSPHORUS. — The specific heat 
of this substance was determined by Avogrado, 
by observing how many degrees, phosphorus 
at several degrees below zero cooled the liquid 
(which was spirit of wine) in the exterior ves- 
sel. The mean of two experiments gave for 
the specific heat of phosphorus 0 385, taking 
that of water as unity. Now, that atomic 
weight of phosphorus being 2* we obtain an 
approximation to this number if we take the 
fourth of it, or -5, and divide the co-efficient 
*1875 by it. The quotient is *375, or the spe- 
cific heat of phosphorus in the solid state. 
Hence, according to the view laid down by 
Avogrado, the thermic atom of phosphorus 
will be ‘5. In the gaseous atom he considers 
that there would be 8 thermic atoms, 
3. ARSENIC. — The atom of this sub- 
stance is 4-75, the half of which is 2'375. To 
obtain the specific heat we have 
*79 or *80. The number obtained by the 
experiment was *81. Mitscherlich has found 
the density of the vapour of arsenic correspond 
to double the number at present received as 
the atom of arsenic. There would, therefore, 
be in the gaseous atom four thermic atoms. 
4. IODINE. — For the specific heat of 
this substance in the solid state, Avogrado 
obtained the number ‘089. 
Now, to procure an approximation to this 
number theoretically, we must divide the atom 
15*75 by *8, and we have T9G7. Now, 
-095. Hence arsenic is analogous to phos- 
phorus. 
We may, perhaps, extend the same analo- 
gies to bromine, and chlorine. Avogrado infers 
that the combining atom of azote is formed 
of 2 thermic atoms ; those of chlorine, iodine, 
bromine and phosphorus, of 8 thermic atoms, 
and that of arsenic of 4 true or thermic atom, 
each multiple atom requiring 5 atoms of oxy- 
gen to form nitric, chloric, iodic, bromic, 
phosphoric, and arsenic acids. 
Now, with regard to compound bodies, 
Avogrado considers that the law deduced from 
** Thomson on Heat and Electricity, 97. 
