io6 



SCIENCK 



[Vol. XIX. No. 472 



dize the assumed AsHg developed by the cultures. The gas 

 so obtained, when burned by oxide of copper, furnishes an 

 abundance of COg ; but it is not possible, thus far, to reach 

 any positive conclusions on this point, nor even to exclude 

 the suspicion that the formation of the CO3 may depend on 

 the admixture of some other hydrocarbon gas. This point 

 ■will be made clearer by the special studies that I have un- 

 dertaken together with Dr. Gorini, for which I am making 

 use of a large culture material. 

 September, 1891. 



A PROBLEM IN PHYSICS. 



In Science for Nov. 28, 1890, there was a short note on the 

 experiment conducted by Joule, in which air compressed in 

 one cylinder was allowed to expand into an exhausted cylin- 

 der. It was shown that the only work done by the com- 

 pressed air was that of imparting a velocity to its own parti- 

 cles, i.e., it did not expand against a resistance, and hence 

 the chilling produced was slight. This experiment has not 

 received the attention it deserves, and, moreover, it seems to 

 have been entirely misinterpreted. It has been suggested 

 that, while at the first instant on opening communication be- 

 tween the two vessels, there is an expansion into a vacuum 

 and no work done, yet at the very next instant there is air 

 in the previously exhausted cylinder, and there is work done 

 in compressing that. This is a serious fallacy, and lies at 

 the bottom of the misinterpretation. It is very certain that 

 no work against a resistance is done at any moment during 

 the expansion This experiment is so far-reaching in its ap- 

 plication, and is so extremely important, that I desire to 

 discuss it a little farther, and I sincerely trust that some one 

 in a suitably-equipped laboratory may be induced to try a 

 few simple experiments in this line. 



Tyndall has shown that mere rarefaction is not a source of 

 cold, though this is somewhat of a popular fallacy. Let us 

 take a cylinder with a piston fitted air-tight and moving 

 without friction. Let us consider that there is no loss of 

 heat from the interior nor accession from the outside. Sup- 

 pose the piston is raised suddenly from bottom to top. A 

 perfect vacuum will be formed; but, as no work has been 

 done below the piston, there will be no cooling effect; all 

 the work and consequent healing would be at the engine, 

 which may communicate with the cylinder, though a hun- 

 dred feet away. Now, suppose a very thin film of air .001 

 of an inch thick were at the bottom of the cylinder. When 

 the vacuum was formed this thin film would impart a veloc- 

 ity to its particles in order that they might follow the piston, 

 but this air certainl.y would not expand against a resistance, 

 and hence the chilling would be exceedingly slight. Sup- 

 pose the piston should be at a point half-way from top to 

 bottom; when it was raised the air beneath would impart a 

 certain velocity to its particles in following the piston, but 

 here again there would be no expansion against a resistance, 

 and hence the chilling would be slight. 



Let us change the conditions slightly. Instead of having 

 the air at atmospheric pressure beneath the piston, as in the 

 last case, let it be at double that pressure. On lifting the 

 piston as before we have taken off the pressure and the air 

 beneath imparts a certain velocity to its particles in following 

 the piston. At the first instant that the piston starts there 

 may be a very slight expansion against a resistance, but that 

 would be momentary. The bulk of the cooling would, as 

 befol^e, be due to the fact that a velocity is imparted to the 

 narticles beneath the piston, and, in this case, this velocity 



would be given to a greater number of particles than before. 

 The cooling would he slightly greater, also, but it would not 

 be due to the loss of heat consequent upon the work of ex- 

 panding against a resistance. 



In order to compute the cooling in such cases as these, a 

 formula has been used which will be found in ihe American 

 Meteorological Journal for November, 1890, p. 339, as fol- 

 lows: 



T lp\ 



T 



In this T and T are the absolute temperatures corresponding 

 to p and p. It seems to me, however, that this formula is 

 not applicable in this case; for it gives a greater cooling, the 



P 

 less the work that is done. Suppose — = 4, the cooling by 



P 

 p 

 the formula would he 38° ; if — = ^ the cooling would he 

 P' 



134° ; and if — = 0, or the expansion was in a vacuum, the 



P 

 cooling would be 490°. Now, by the principles already 

 enunciated, if the expansion took place in a vacuum there 

 would be no e\pansion against a resistance, and hence there 

 would be no work done except in imparting a certain veloc- 

 ity to the particles. If the formula fails in the last case, it 

 must also fail in all the others. It seems to me that the for- 

 mula is only intended to be used in cases where there is an 

 expansion against a resistance, and not in the cases here 

 given. 



A question has come up recently which may he partly an- 

 swered by this discussion. It is this: What will be the cool- 

 ing due to the expansion of gas in a balloon if it should as- 

 cend very suddenly to several thousand feet above the earth? 

 Suppose the balloon were instantly put into a perfect vacu- 

 um, and the envelope had no resistance; there would be no 

 expansion whatever against a resistance, as we have just 

 seen, and the only work performed would be that of impart- 

 ing a certain velocity to the particles of gas. As a result 

 the gas would be slightly chilled, but vastly less than if it 

 had expanded against a resistance. Now, if the balloon had 

 been suddenly placed at a point where the pressure was ten 

 inches, or one-third that at the earth, the same principles 

 would apply; the only work done would be in imparting a 

 certain velocity to the particles of gas, and in consequence 

 there would be only a slight chilling. 



I should be very glad if some physicist would kindly solve 

 the following problems. 



1. Given an exhausted cylirider of certai a dimensions, 

 how much vrould the air be heated if allowed to enter with- 

 out noise, and until the pressure was the same as that out- 

 side? 



2. What would be the cooling of a perfect gas in a balloon 

 one-third full, if the pressure on the outside were suddenly 

 reduced from thirty inches to ten inches, the temperature of 

 the outside air remaining constant, the envelope of the bal- 

 loon being without weight and infinitely flexible? 



H. A. Hazen. 



Thomas Whittakee announces a volume by Frederick Saun- 

 ders (of the Astor Library), entitled " The Story of the Discovery 

 of the New World by Columbus," the same being an abridgment 

 from the latest authorities. It will be an illustrated quarto. 



