Natural-Philosophical Collections, 467 
filled with mercury. One of the thermometers was immersed to the bottom of 
the caldron, and gave the temperature of the water in its fluid state; the other, 
which was shorter, reached only to within a few inches of the surface of the wa- 
ter, and gave the temperature of the steam. 
Our knowledge of the elastic powers of steam at high temperatures was, as we 
have said, of hardly any amount when the commission began its labours. Be- 
yond eight atmospheres, we had in France but a single number communicated 
to M. Clement by M. Parkins ; but this number 215° has been found to be alto- 
gether erroneous. The elastic power of steam would be thirty-five atmospheres, 
while it is in fact only twenty. Steam to form an equipoise to thirty-five atmos- 
pheres, would require to be raised to abont 245°. 
Germany was more advanced than England. M. Arzberges, professor at the 
Polytechnic Institution of Vienna, had made experiments on the temperature of 
steam, which he had extended as far as twenty atmospheres. For determining the 
elasticity of steam, he had employed lever valves, a process very defective in it- 
self, but of which he has corrected the inaccuracies by very ingenious precau- 
tions. The most remarkable of these consisted in employing a spherical steel 
valve, resting upon the edge of a circular orifice formed in another piece of the 
same substance. 
The numbers which he obtained, however, are not correct, and their inaccuracy 
doubtless depends upon the circumstance of his having neglected, in the valua- 
tion of the temperature, two indispensable precautions, which we have already 
mentioned,—that of withdrawing the thermometer which he immersed in the cal- 
dron from the pressure of the steam, and that of making allowance for the cool- 
ing produced by the part of the thermometer remaining exposed to the action of 
the atmospheric air. 
The errors resulting from these two omissions would, it is true, affect the re- 
sults in opposite directions ; but their effects could not be perfectly compensated 
in high pressures. The second would greatly prevail over the first, and would 
make the temperatures be estimated above what they really were. Thus M. 
Arzberges found that the pressure of twenty atmospheres corresponds to 222°, 
whereas it is really furnished by a temperature of 215°. 
The law which would correctly express the elastic power of steam in function 
of the temperature is not known, and no more manifests itself in the new obser- 
vations of our academicians, than in those which we already possess on the lower 
part of the thermometric scale. In the mean time, a formula of interpolation has 
been sought, deduced from experiment alone, and calculated to make known the 
elastic powers for any given point of the thermometric scale. 
Numerous formule of this kind have been proposed to the commission by va~- 
rious authors; but none of them has borne the proof of the application to high 
temperatures. A single remarkable exception is to be made. M. Roche, pro- 
fessor at Strasburg, resting not upon experiment, but upon theoretical considera. 
tions peculiar to himself, has arrived at results which agree in a very remarkable 
manner with those furnished by the Observatory. MM. Roche’s theoretical opi- 
nions are, if we mistake not, submitted to the judgment of the Academy of Sci- 
ences, which will report concerning them. 
The formula of interpolation which the commissioners have chosen is the fol- 
lowing :— 
e = (1 + 0,71532) 5. 
é is the elasticity, ¢the temperature. The pressure of the atmosphere is taken 
as one. 
This formula pretty accurately represents all the results furnished by experi- 
ment up to 24 atmospheres. The greatest deviation to which its application 
leads, is observed at the pressure of eight atmospheres. It is then 9-10ths of a 
centigrade degree. As to the temperatures which correspond to the pressures 
higher than 24. atmospheres, the above formula gives them so much the more eas 
sily, that it has heen calculated upon the highest of the pressures observed. The 
