“The molecule, as a whole, can only vibrate in virtue of the forces exerted between it and its neighbour molecules. The intensity of these forces, and consequently the rate of vibration, would, in this case, be a function of the distance between the molecules. Now the identical absorption of the liquid and of the vaporous nitrite of amyl indicates an identical vibrating period on the part of liquid and vapour, and this, to my mind, amounts to an experimental demonstration that the absorption occurs in the main within the molecule. For it can hardly be supposed, if the absorption were the act of the molecule as a whole, that it could continue to affect waves of the same period after the substance had passed from the vaporous to the liquid state.”—Proc. of Roy. Soc., No. 105. 1868.
Professor W. A. Norton, in his memoir on “Molecular Physics,”[325] has also arrived at results somewhat similar in reference to the nature of heat-vibrations. “It will be seen,” he says, “that these (Mr. Croll’s) ideas are in accordance with the conception of the constitution of a molecule adopted at the beginning of the present memoir (p. 193), and with the theory of heat-vibrations or heat-pulses deduced therefrom (p. 196).”[326]
III.
ON THE REASON WHY THE DIFFERENCE OF READING BETWEEN A THERMOMETER EXPOSED TO DIRECT SUNSHINE AND ONE SHADED DIMINISHES AS WE ASCEND IN THE ATMOSPHERE.[327]
From the Philosophical Magazine for March, 1867.
The remarkable fact was observed by Mr. Glaisher, that the difference of reading between a black-bulb thermometer exposed to the direct rays of the sun and one shaded diminishes as we ascend in the atmosphere. On viewing the matter under the light of Professor Tyndall’s important discovery regarding the influence of aqueous vapour on radiant heat, the fact stated by Mr. Glaisher appears to be in perfect harmony with theory. The following considerations will perhaps make this plain.
The shaded thermometer marks the temperature of the surrounding air; but the exposed thermometer marks not the temperature of the air, but that of the bulb heated by the direct rays of the sun. The temperature of the bulb depends upon two elements: (1) the rate at which it receives heat by direct radiation from the sun above, the earth beneath, and all surrounding objects, and by contact with the air; (2) the rate at which it loses heat by radiation and by contact with the air. As regards the heat gained and lost by contact with the surrounding air, both thermometers are under the same conditions, or nearly so. We therefore require only to consider the element of radiation.
We begin by comparing the two thermometers at the earth’s surface, and we find that they differ by a very considerable number of degrees. We now ascend some miles into the air, and on again comparing the thermometers we find that the difference between them has greatly diminished. It has been often proved, by direct observation, that the intensity of the sun’s rays increases as we rise in the atmosphere. How then does the exposed thermometer sink more rapidly than the shaded one as we ascend? The reason is obviously this. The temperature of the thermometers depends as much upon the rate at which they are losing their heat as upon the rate at which they are gaining it. The higher temperature of the exposed thermometer is the result of direct radiation from the sun. Now, although this thermometer receives by radiation more heat from the sun at the upper position than at the lower, it does not necessarily follow on this account that its temperature ought to be higher. Suppose that at the upper position it should receive one-fourth more heat from the sun than at the lower, yet if the rate at which it loses its heat by radiation into space be, say, one-third greater at the upper position than at the lower, the temperature of the bulb would sink to a considerable extent, notwithstanding the extra amount of heat received. Let us now reflect on how matters stand in this respect in regard to the actual case under our consideration. When the exposed thermometer is at the higher position, it receives more heat from the sun than at the lower, but it receives less from the earth; for a considerable part of the radiation from the earth is cut off by the screen of aqueous vapour intervening between the thermometer and the earth. But, on the whole, it is probable that the total quantity of radiant heat reaching the thermometer is greater in the higher position than in the lower. Compare now the two positions in regard to the rate at which the thermometer loses its heat by radiation. When the thermometer is at the lower position, it has the warm surface of the ground against which to radiate its heat downwards. The high temperature of the ground thus tends to diminish the rate of radiation. Above, there is a screen of aqueous vapour throwing back upon the thermometer a very considerable part of the heat which the instrument is radiating upwards. This, of course, tends greatly to diminish the loss from radiation. But at the upper position this very screen, which prevented the thermometer from throwing off its heat into the cold space above, now affects the instrument in an opposite manner; for the thermometer has now to radiate its heat downwards, not upon the warm surface of the ground as before, but upon the cold upper surface of the aqueous screen intervening between the instrument and the earth. This of course tends to lower the mercury. We are now in a great measure above the aqueous screen, with nothing to protect the thermometer from the influence of cold stellar space. It is true that the air above is at a temperature little below that of the thermometer itself; but then the air is dry, and, owing to its diathermancy, it does not absorb the heat radiated from the thermometer, and consequently the instrument radiates its heat directly into the cold stellar space above, some hundreds of degrees below zero, almost the same as it would do were the air entirely removed. The enormous loss of heat which the thermometer now sustains causes it to fall in temperature to a great extent. The molecules of the comparatively dry air at this elevation, being very bad radiators, do not throw off their heat into space so rapidly as the bulb of the exposed thermometer; consequently their temperature does not (for this reason) tend to sink so rapidly as that of the bulb. Hence the shaded thermometer, which indicates the temperature of those molecules, is not affected to such an extent as the exposed one. Hence also the difference of reading between the two instruments must diminish as we rise in the atmosphere.
This difference between the temperature of the two thermometers evidently does not go on diminishing to an indefinite extent. Were we able to continue our ascent in the atmosphere, we should certainly find that a point would be reached beyond which the difference of reading would begin to increase, and would continue to do so till the outer limits of the atmosphere were reached. The difference between the temperatures of the two thermometers beyond the limits of the atmosphere would certainly be enormous. The thermometer exposed to the direct rays of the sun would no doubt be much colder than it had been when at the earth’s surface; but the shaded thermometer would now indicate the temperature of space, which, according to Sir John Herschel and M. Pouillet, is more than 200° Fahrenheit below zero.