550 
STEAM ENGINE. 
density, we must suppose that if steam of the elasticity 60, 
that is, supporting 90 inches of mercury, were subjected to 
a pressure of 30 inches, it would expand into twice its 
present bulk. The augmentation of elasticity therefore is 
the measure of the bulk into which it would expand in order 
to acquire its former elasticity. Taking the increase of 
elasticity therefore as a measure of the bulk into which it 
would expand under one constant pressure, we see that equal 
increments of temperature produce nearly equal multipli¬ 
cations of bulk. Thus if a certain diminution of temperature 
diminishes its bulk ^th, another equal diminution of tem¬ 
perature will diminish this new bulk ^th very nearly. Thus, 
in our experiments, the temperatures 110% 140°, 170°, 200°, 
230% are in arithmetical progression, having equal dif¬ 
ferences , and we see that the corresponding elasticities 2.25, 
5.15, 11.05, 22.62, 44.7, are very nearly in the continued 
proportion of 1 to 2. The elasticity corresponding to the 
temperature 260 deviates considerably from this law, which 
would give 88 or 89 instead of 80 ; and the deviation 
increases in the higher temperatures. But still we see that 
there is a considerable approximation to this law, and it 
will frequently assist us to recollect, that whatever be the 
present temperature, an increase of 30 degrees doubles the 
elasticity and the bulk of watery vapour. 
That 4° will increase the elasticity from 1 to l T *g 
8 - - 1 to H 
10 - - 1 to 
12} - - 1 to U 
18 - - 1 to H 
22 - - 1 to If 
24 - - 1 to If 
26 - - 1 to 11 
This is sufficiently exact for most practical purposes. Thus 
an engineer finds that the injection cools the cylinder of a 
steam engine to 192°. It therefore leaves a steam whose 
elasticity is three-fifths of its full elasticity, = 18 inches . 
But it is better at all times to have recourse to a table framed 
from actual experiment. Observe, too, that in the lower 
temperatures, i. e. below ] 10 °, this increment of temperature 
does more than double the elasticity. 
This law obtains more remarkably in the incoercible 
vapours; such as vital air, atmospheric air, fixed air, &c., all 
of which have also their elasticity proportional to their bulk 
inversely: and perhaps the deviation from the law in steams 
is connected with their chemical difference of constitution. 
If the bulk were always augmented in the same proportion 
by equal augmentations of temperature, the elasticities would 
be accurately represented by the ordinates of a logarithmic 
curve, of which the temperatures are the corresponding 
abscissae; and we might contrive such a scale for our ther¬ 
mometer, that the temperatures would be the common 
logarithms of the elasticities, or of the bulks having equal 
elasticity; or, with our present scale, we may find such a 
multiplier m for the number x of degrees of our thermometer 
(above that temperature where the elasticity is equal to 
unity), that this multiple shall be the common logarithm of 
the elasticity y; so that m x = log. y. 
But our experiments are not sufficiently accurate for 
determining the temperature where the elasticity is measured 
by 1 inch; because in these temperatures the elasticities vary 
by exceedingly small quantities. But if we take 11.04 for 
the unit of elasticity, and number our temperature from 
170°, and make m = 0.010035, we shall find the product 
m x to be very nearly the logarithm of the elasticity. The 
deviations, however, from this law, are too great to make 
this equation of any use. But it is very practicable to 
frame an equation which shall correspond with the ex¬ 
periments to any degree of accuracy; and it has been done 
in French by Mr. Prony. It is as follows: Let x be 
the degrees of Reaumur’s thermometer; let y be the 
expansion of 10,000 parts of air; let e be = 10 , m — 
2.7979, n = 0.01768; then y= k^+jut— 627.5, Now e 
being = 10 , it is plain that e^+n* is the number, of which 
m + nx is the common logarithm. This formula is very exact 
as far as the temperature 60°, but beyond this it needs a 
correction; because air, like the vapour of water, does not 
expand in the exact proportion of its bulk. 
We observe this law considerably approximated to in the 
augmentation of the bulk or elasticity of elastic vapours; 
that is, it is a fact that a given increment of temperature 
makes very nearly the same proportional augmentation of 
bulk and elasticity. This gives us some notion of the 
manner in which the supposed expanding cause produces 
the effect. When vapour of the bulk 4 is expanded into a 
bulk 5 by an addition of 10 degrees of sensible heat, a 
certain quantity of fire goes into" it, and is accumulated 
round each particle, in such a manner that the temperature 
of each, which formerly was m, is now m + 10. Let it now 
receive another equal augmentation of temperature. This 
is now m + 20 , and the bulk is ^ x ._ or 6 $, and the arith- 
4 
metical increase of bulk is li. The absolute quantity of 
fire which has entered it is greater than the former, both on 
account of the greater augmentation of space and the greater 
temperature. Consequently if this vapour be compressed 
into the bulk 5, there must be heat or fire in it which is not 
necessary for the temperature ?n + 20 , far less for the tem¬ 
perature in +10. It must therefore emerge, and be disposed 
to enter a thermometer which has already the temperature 
m + 20 : that is, the vapour must grow hotter by compres¬ 
sion ; not by squeezing out the heat, like water out of a 
sponge, but because the law of attraction for heat is de¬ 
ranged. 
In the experiments of Robison, a main source of error had 
been, that he had neglected to keep the digester and the 
vacant part of the tube of the barometer of the same tempera¬ 
ture as the digester. Mr. Dalton ingeniously obviated this 
inconvenience by a very simple contrivance. He procured 
a perfectly dry barometer tube of the usual size, and having 
introduced some mercury, which had been previously freed 
from air by boiling, marked the place where it became sta¬ 
tionary. Then, dividing the space occupied by the mercurial 
column into inches and tenths, he poured out the mercury, 
and introduced some water to moisten the inside of the tube. 
On reversing the operation, that is, pouring out the water, 
and reintroducing the mercury, the water which adhered to 
the sides of the tube rose to the top of the mercurial column, 
where it formed a stratum from one-eighth to one-tenth of an 
inch in depth. The air was carefully excluded. Having 
thus satisfied himself as to the probable accuracy of the results 
to be obtained, he took an open cylindrical glass tube, two 
inches diameter and 14 inches long, in each end of which 
he fixed a cork. The corks were perforated in the middle, 
to admit the upper or vacant part of the barometer tube. 
The upper cork was fixed two or three inches below the top 
of the tube, and a small portion of it was cut away to allow 
water to be poured into the space between it and the lower 
cork. By this means, the upper or vacant part of the baro¬ 
meter tube was exposed to the several degree's of temperature 
from 32° to 155° inclusively; and the effect of heat, in the 
production of vapour within, was observed by the depression 
of the mercurial column. In experimenting on the higher 
temperatures, Mr. Dalton used a nearly similar apparatus, 
made of tin, with a syphon barometer, and thus obtained the 
remaining results up to 212 degrees. 
The results of these experiments, from 32° to 212° inclu¬ 
sively, agree very closely with the results of experiments 
made by Dr. Ure. 
Watt made experiments at a very early date, prior indeed 
to Robison’s. Watt conducted his experiments with a tin 
pan, 5 inches diameter, and 4 inches deep, having an in¬ 
verted barometer tube, 3 feet long, firmly fixed into a conical 
socket at the bottom, through which it passes. At one extre¬ 
mity of this tube was a bulb, an inch and a half in diameter, 
the capacity of which was nearly equal to the capacity of the 
tube. The bulb was filled with water, and the stem with 
mercury, and the lower end of the latter was immersed in a 
cistern 
