FOOTNOTES:
[A] As some of the readers of this volume may be interested to compare these values, we reproduce the "Table of Molecular Data" from Professor Clerk Maxwell's lecture on "Molecules," delivered before the British Association at Bradford, and published in "Nature," September 25, 1873.
Molecular Magnitudes at Standard Temperature and Pressure, 0° C. and 76 c. m.
| RANK ACCORDING TO ACCURACY OF KNOWLEDGE. | Hydrogen. | Oxygen. | Carbonic Oxide. | Carbonic Dioxide. |
|---|---|---|---|---|
Rank I. | ||||
| Relative mass | 1 | 16 | 14 | 22 |
| Velocity in metres per second | 1,859 | 465 | 497 | 396 |
Rank II. | ||||
| Mean path in ten billionths (10-10) of a metre | 965 | 560 | 482 | 379 |
| Collisions each second—number of millions | 17,750 | 7,646 | 9,489 | 9,720 |
Rank III. | ||||
| Diameter in hundred billionths (10-11) of a metre | 58 | 76 | 83 | 93 |
| Mass in ten million million million millionths (10-25) of a gramme | 46 | 736 | 644 | 1,012 |
Number of molecules in one cubic centimetre of every gas is nineteen million million million on 19 (1018).
Two million hydrogen molecules side by side measure a little over one millimetre.
[B] See Professor Maxwell's lecture, loc. cit.; also, Appletons' "Cyclopædia," article "Molecules."
[C] There is an obvious distinction between the free and the disturbed path of a molecule, and we can not overlook in our calculations the perturbations which the collisions necessarily entail. Such considerations greatly complicate the problem, which is far more difficult than would appear from the superficial view of the subject that can alone be given in a popular lecture.
[D] See notice of these investigations by the author of this article, in "American Journal of Science and Arts," September, 1877 (3), xiv, 231.
[E] The reader will, of course, distinguish between the differential action on the opposite faces of the vanes of the radiometer and the reaction between the vanes and the glass which are the heater and the cooler of the little engine. Nor will it be necessary to remind any student that a popular view of such a complex subject must be necessarily partial. In the present case we not only meet with the usual difficulties in this respect, but, moreover, the principles of molecular mechanics have not been so fully developed as to preclude important differences of opinion between equally competent authorities in regard to the details of the theory. To avoid misapprehension, we may here add that, in order to obtain in the radiometer a reaction between the heater and the cooler, it is not necessary that the space between them should actually be crossed by the moving molecules. It is only necessary that the momentum should be transferred across the space, and tide may take place along lines consisting of many molecules each. The theory, however, shows that such a transfer can only take place in a highly rarefied medium. In an atmosphere of ordinary density, the accession of heat which the vanes of a radiometer might receive from a radiant source would be diffused through the mass of the inclosed air. This amounts to saying that the momentum would be so diffused, and hence, under such circumstances, the molecular motion would not determine any reaction between the vanes and the glass envelope. Indeed, a dense mass of gas presents to the conduction of heat, which represents momentum, a wall far more impenetrable than the surrounding glass, and the diffusion of heat is almost wholly brought about by convection currents which rise from the heated surfaces. It will thus be seen that the great non-conducting power of air comes into play to prevent not only the transfer of momentum from the vanes to the glass, but also, almost entirely, any direct transfer to the surrounding mass of gas. Hence, as stated above, the heated molecules bound back and forth on the vanes without change of condition, and the mass of the air retains its uniform tension in all parts of the bulb, except in so far as this is slowly altered by the convection currents just referred to. As the atmosphere, however, becomes less dense, the diffusion of heat by convection diminishes, and that by molecular motion (conduction) increases until the last greatly predominates. When, now, the exhaustion reaches so great a degree that the heat, or momentum, is rapidly transferred from the heater to the cooler by an exaggeration, or, possibly, a modification, of the mode of action we call conduction, then we have the reaction on which the motion of the radiometer wheel depends.