I50 



SCIENCE 



[Vol. XIX. No. 475 



with tlie number of observations made, — when the observer is 

 quite untrained; while good previous mental training in things 

 more or less analogous to those tested by the experiment might 

 enable the observer to utilize promptly the practice being got in 

 the experiment itself, and so might for a time overbalance the 

 effect of fatigue ? Thus, in the present case, the deviation in- 

 creased most with the child A. L. B. and one other person, and 

 decreased most with the artist L. F. and one other, but the data 

 are too few to be more than suggestive. It would seem that fur- 

 ther experiments upon the relation of fatigue, and of the effective 

 practice got during each experiment, to previous training, etc., 

 miglit be quite varied in direction and have some educational in- 

 terest; the best training, cceteris paribus, being presumably that 

 which best enables the trained to utilize fresh opportunities for 

 training of a kind somewhat new to him. 



2. Tho probable error of an estimated distance is, of course, 

 some function of the distance and of other data; but what func- 

 tion of the distance, when the other data remain, as far as may 

 be, constant? May.it not be commonly taken as some low power 

 of the distance whose exponent increases slowly with the dis- 

 tance ? In the present case the ratio of the two distances tried is 

 4.37 : 1 ; and the average odserver's mean deviation in inches 

 from the truth, and from his own average estimate, respectively, 

 are 2.69 and 2 .56 times greater for the long distance than for the 

 short; so that the exponent here would not he far from |. 



J. E. Oliver. 



Itbaea, N.T., March 5. 



Work and its Relation to Gaseous Compression and Ex- 

 pansion. 



It is quite well known that the fundamental, and perhaps the 

 most important hypothesis in theoretical meteorology is this, that 

 work is done by air in expanding, and that heat is evolved when- 

 ever aii' is compressed. See " Recent Advances in Meteorology," 

 p. 41. There is a most serious fallacy in this theory, however, in 

 that it ignores the resistance against which the air expands, and 

 considers that the mere diminution of the distance of the mole- 

 cules of a gas, without the direct expenditure of external enei-gy 

 in changing this distance, can evolve heat. 



An illustration will serve to make this clear. Take a cylinder 

 one square foot in area and two feet high with a piston at the top 

 and the air beneath it at atmospheric pressure. Place weights, 

 pound by pound upon the piston, allowing all the heat developed 

 to escape into the outside air. When we have added 3, 160 pounds, 

 the air beneath will be compressed to two atmospheres. Fasten 

 the piston and its load, and connect the cylinder with another 

 holding one cubic foot and containing air at normal pressure. An 

 equilibrium will be quickly established and the pressure will be 

 at 1.5 atmospheres in each cylinder. The potential energy re- 

 mains the same as before; no work has been done and therefore 

 thei-e has been no change in temperature, except a slight chilling 

 and heating due to the rush of the air from one into the other. 



Return to the cylinder with the air compressed to two atmos- 

 pheres and having the same temperature as the outside air. Take 

 off the weight from the piston pound by pound, and the air will 

 gradual y expand, and in doing so will lift a weight, thereby 

 doing work whfch cools the air very greatly, about 50° F. if the 

 initial temperature was 60°. Instead of taking off the weight 

 pound by pound, however, suppose the whole 2,160 pounds had 

 been removed instantly. The only resistance which kept the air 

 compressed has been entirely removed, and it is very evident that 

 the air would expand without doing any work, if we consider that 

 the piston moves back slowly ; or, in other words, if we neglect the 

 resistance of the air to the rapid motion of the piston, and hence 

 there would be onlj a very slight chilling, owing to the work of im- 

 parling a certain velocity to the particles rushing out. The same 

 result would have been attained if we had fastened the piston and 

 its load, and then had turned a stop-cock, allowing the air to es- 

 cape into the atmosphere without making a noise. 



I am well aware that the ordinary interpretation of this illus- 

 tration is very different; for example, Tyndall, in his "Heat as a 

 Mode of Motion," p. 64, in a somewhat similar discussion, says: 



"The gas. in this experiment, executes work. In expanding it 

 has to overcome the downward pressure of the atmosphere, which 

 amounts to 15 pounds on every square inch, and also the weight 

 on the piston itself. It is just the same as what it would accom- 

 plish if the air in the upper part of the cylinder were entirely 

 abolished, and the piston had a weight of 4,320 pounds." I do not 

 see that this changes the aspect of the case at all. Suppose that 

 the air were compressed to two atmospheres beneath the piston, 

 anJ that that was loaded with 4,320 pounds, while a perfect vac- 

 uum Existed in the upper part of the cylinder, suppose that we 

 suddenly remove 2,160 pounds from the piston. The piston, still 

 having a load of 2,160 pounds, would fly to the top of the cylinder. 

 How much work has the air done in expanding from two atmos- 

 pheres to one ? None at all. It looks very much as though the 

 compressed air must have lifted that weight, but a little reflection 

 will show that this is not the case. The best way to understand it, 

 perhaps, would be to think of the weight after it reached within 

 .001 of an inch of the top of the cylinder. Here is a weight of 2,160 

 pounds with the air under it at atmospheric pressure ; in one sense 

 the air sustains the weight, but if the air at atmospheric pressure 

 sustains the weight at this point (the top of the cylinder), then the 

 air at the same pressure would have sustained it at the middle of 

 the cylinder. In other words, if we had allowed the compressed 

 air to escape when the piston was at the centre of the cylinder, 

 still with its load of 2,160 pounds and with a perfect vacuum 

 above, there would have been an equilibrium, and we could have 

 pushed the weight up and down, allowing it to stand at any point 

 so long as the outside air had a communication with the lower 

 side of the piston. Does not all this show that the compressed 

 air, considered by itself, did not support any part of the weight at 

 the middle of ttie cylinder, but was free to expand without lifting 

 any weight or doing any work? 



We are strictly taught that the old idea, "nature abhors a 

 vacuum," is not at all tenable; but if we lay aside strict analysis 

 for a moment and resort to this view, I think it will make the 

 situation plainer to us. To all intents and purposes, when our 

 piston loaded with 2,160 pounds had a perfect vacuum above it, 

 we may say that it was sustained by that vacuum, or, at least, that 

 the compressed air had noi hing to do in supporting it or in moving 

 it to the top of the vacuum. This seems to be quite an intricate 

 problem, but a little reflection will show that the piston loaded to 

 2,160 pounds, and having a perfect vacuum above it, with air 

 having free access to its under side, is in precisely the condition 

 it would be in if both ends of the cylinder were open to the air 

 and the piston without weight were located at any point in the 

 cylinder. In this case the piston may be pushed up and down 

 without meeting any resistance except that to the flow of the 

 air. 



Consider now the question of heated air rising in the atmos- 

 phere. We may simplify the problem slightly by taking a bal- 

 loon, having an infinitely flexible envelope and without weight. 

 Empty the balloon, and tie the neck so that no air can enter. It 

 would require a pull of 15 pounds to the square inch to separate 

 the sides of the balloon, owing to the pressure of the air. Incredi- 

 ble as it may seem, this is the force which theoretical meteorology 

 has introduced into every discussion of the dynamical heating and 

 cooling of the air, and of the cooling and heating of masses of air 

 as they ascend or descend in the atmosphere, — a force which it is 

 no exaggeration to say is at least 25,000 times as great as that 

 really exerted or developed. Inflate the balloon one-third full 

 with hydrogen gas. The work required to do this is that needed 

 to displace a volume of air equal to the volume of gas which enters 

 the balloon, or it would be that of lifting a weight equal to 1.3 

 ounces per cubic foot half the height of the balloon. It will 

 probably be said that the outside air helps in this inflation, and I 

 grant that for argument's sake. 



Let the neck of the balloon remain open to the outside air, and 

 suppose that the gae can just lift a weight attached to the balloon.' 

 The balloon will rise in the atmosphere to a point where the 

 pressure is 10'', or until the gas has expanded to fill the whole 

 envelope. Since the work of the balloon is open to the air, the 

 pressure inside will continue exactly the same as that outside. A 

 little leflection will show, however, that the conditions would be 



