seeds, which consist chiefly of legumine and soluble albumen, contain for the same quantity of phosphoric acid one and a half to twice as much nitrogen as the seeds of cereals, which consist principally of gluten. 9. The relation of phosphoric acid to nitrogen is modified when one of these albuminous substances is replaced by another in seeds of the same kind and variety, as has been shown by Millon. 10. The ash of most kinds of corn contains large quantities of magnesia, which is partially present as ammonio-phosphate of magnesia. And hence the proportion of nitrogen in a seed does not exactly give the quantity of albumen. 1. XI. On the Nature of the Motion which we call Heat. BEFORE writing my first memoir on heat, which was published in 1850, and in which heat is assumed to be a motion, I had already formed for myself a distinct conception of the nature of this motion, and had even employed the same in several investigations and calculations. In my former memoirs I intentionally avoided mentioning this conception, because I wished to separate the conclusions which are deducible from certain general principles from those which presuppose a particular kind of motion, and because I hoped to be able at some future time to devote a separate memoir to my notion of this motion and to the special conclusions which flow therefrom. The execution of this project, however, has been retarded longer than I at first expected, inasmuch as the difficulties of the subject, as well as other occupations, have hitherto prevented me from giving to its development that degree of completeness which I deemed necessary for publication. A memoir has lately been published by Krönig, under the title Grundzüge einer Theorie der Gaset, in which I have recognized some of my own views. Seeing that Krönig has arrived at these views just as independently as I have, and has published them before me, all claim to priority on my part is of course out of the question; nevertheless, the subject having once been mooted in this memoir, I feel myself induced to publish those parts of my own views which I have not yet found in it. For the present, I shall confine myself to a brief indication of a *From Poggendorff's Annalen, vol. c. t This was first printed separately by A. W. Hayn in Berlin, and afterwards appeared in Poggendorff's Annalen, vol. xcix. p. 315. few principal points, and reserve a more complete analysis for another time*. 2. Krönig assumes that the molecules of gas do not oscillate about definite positions of equilibrium, but that they move with constant velocity in right lines until they strike against other molecules, or against some surface which is to them impermeable. I share this view completely, and I also believe that the expansive force of the gas arises from this motion. On the other hand, I am of opinion that this is not the only motion present. In the first place, the hypothesis of a rotatory as well as a progressive motion of the molecules at once suggests itself; for at every impact of two bodies, unless the same happens to be central and rectilineal, a rotatory as well as a translatory motion ensues. I am also of opinion that vibrations take place within the several masses in a state of progressive motion. Such vibrations are conceivable in several ways. Even if we limit ourselves to the consideration of the atomic masses solely, and regard these as absolutely rigid, it is still possible that a molecule, which consists of several atoms, may not also constitute an absolutely rigid mass, but that within it the several atoms are to a certain extent moveable, and thus capable of oscillating with respect to each other. I may also remark, that by thus ascribing a movement to the atomic masses themselves, we do not exclude the hypothesis that each atomic mass may be provided with a quantity of finer matter, which, without separating from the atom, may still be moveable in its vicinity. By means of a mathematical investigation given at the end of the present memoir, it may be proved that the vis viva of the translatory motion alone is too small to represent the whole heat present in the gas; so that without entering into the probability of the same, we are thus compelled to assume one or more motions of another kind. According to this calculation, the excess of the whole vis viva over that of the translatory motion alone is particularly important in gases of a complicated chemical constitution, in which each molecule consists of a great number of atoms. * I must not omit to mention here, that some time ago Mr. William Siemens of London, when on a visit in Berlin, informed me that Joule had also expressed similar ideas in the Memoirs of the Literary and Philosophical Society of Manchester. My views being consequently no longer completely new, this was an additional reason why I should hasten their publication less than I otherwise probably should have done. Hitherto I have not been able to procure the memoir of Joule in question, and therefore I am ignorant how far he has pursued the subject, and whether his views coincide with mine in all points. It is to be regretted that Joule did not publish his memoir in a more widely circulated periodical. 3. In one and the same gas the translatory motion of the whole molecules will always have a constant relation to the several motions which, in addition to the above, the constituents of the molecules likewise possess. For brevity I will call the latter the motions of the constituents. Conceive a number of molecules whose constituents are in active motion, but which have no translatory motion. It is evident the latter will commence as soon as two molecules in contact strike against each other in consequence of the motion of their constituents. The translatory motion thus originated will of course occasion a corresponding loss of vis viva in the motion of the constituents. On the other hand, if the constituents of a number of molecules in a state of translatory motion were motionless, they could not long remain so, in consequence of the collisions between the molecules themselves, and between them and fixed sides or walls. It is only when all possible motions have reached a certain relation towards one another, which relation will depend upon the constitution of the molecules, that they will cease mutually to increase or diminish each other. When two molecules whose constituents are in motion come into collision they will not rebound, like two elastic balls, according to the ordinary laws of elasticity; for their velocities and directions after collision will depend, not only upon the motion which the whole molecules had before impact, but also upon the motion of those constituents which are nearest each other at the moment of collision. After the equalization of the several motions, however, when the translatory motion is, on the whole, neither increased nor diminished by the motions of the constituents, we may, in our investigation of the total action of a great number of molecules, neglect the irregularities occurring at the several collisions, and assume that, in reference to the translatory motion, the molecules follow the common laws of elasticity. 4. The explanation of the expansive force of gases and its dependence upon volume and temperature, as given by Krönig, suffers no essential modification through the introduction of other motions. The pressure of the gas against a fixed surface is caused by the molecules in great number continually striking against and rebounding from the same. The force which must thence arise is, in the first place, by equal velocity of motion inversely proportional to the volume of the given quantity of gas; and secondly, by equal volume proportional to the vis viva of the translatory motion: the other motions do not here immediately come into consideration. On the other hand, from Gay-Lussac's law we know that, under constant volume, the pressure of a perfect gas increases in the same ratio as the temperature calculated from -273° C., which we call the absolute temperature. Hence, according to the above, it follows that the absolute temperature is proportional to the vis viva of the translatory motion of the molecules. But as, according to a former remark, the several motions in one and the same gas bear a constant relation to each other, it is evident that the vis viva of the translatory motion forms an aliquot part of the total vis viva, so that the absolute temperature is also proportional to the whole vis viva in the gas. These considerations, together with others connected therewith to be given hereafter, induced me, in my memoir "On the Moving Force of Heat," to express the opinion that the specific heat of gases was constant; which opinion was in opposition to the experiments then known*. The quantity of heat which must be imparted to a gas, under constant volume, in order to raise its temperature is to be considered as the increase of the vis viva in the gas, inasmuch as in this case no work is done whereby heat could be consumed. The specific heat under constant volume, therefore, is in a perfect gas the magnitude which Rankine calls the true specific heat. Now the assertion that the true specific heat of a gas is constant, is simply equivalent to the assertion that the total vis viva in the gas has a constant ratio to the vis viva of the translatory motion which serves us as a measure of the temperature. With respect to the specific heat under constant pressure, I have proved in the memoir before cited, and by means of a hypothesis proceeding from the same considerations, that it differs only by a constant magnitude from the true specific heat. 5. The foregoing is true for permanent gases only, and even for these only approximatively. In general, the small deviations which present themselves can be easily accounted for. In order that Mariotte's and Gay-Lussac's laws, as well as others in connexion with the same, may be strictly fulfilled, the gas must satisfy the following conditions with respect to its molecular condition :: (1) The space actually filled by the molecules of the gas must be infinitesimal in comparison to the whole space occupied by the gas itself. (2) The duration of an impact, that is to say, the time required to produce the actually occurring change in the motion of a molecule when it strikes another molecule or a fixed surface, must be infinitesimal in comparison to the interval of time between two successive collisions. (3) The influence of the molecular forces must be infinitesimal. Two conditions are herein involved. In the first place, it is requisite that the force with which all the molecules at their ** Poggendorff's Annalen, vol. lxxix. p. 393. Phil. Mag. vol. ii. pp. 1, 102, mean distances attract each other, vanish when compared with the expansive force due to the motion. But the molecules are not always at their mean distances asunder; on the contrary, during their motion a molecule is often brought into close proximity to another, or to a fixed surface consisting of active molecules, and in such moments the molecular forces will of course commence their activity. The second condition requires, therefore, that those parts of the path described by a molecule under the influence of the molecular forces, when the latter are capable of altering appreciably the direction or velocity of the molecule's motion, should vanish when compared with those parts of its path with respect to which the influence of these forces may be regarded as zero. If these conditions are not fulfilled, deviations in several ways from the simple laws of gases necessarily arise; and these deviations become more important the less the molecular condition of the gas fulfils the conditions in question. On becoming acquainted with the celebrated investigations of Regnault on the deviations of gases from Mariotte's and GayLussac's laws, I attempted, by means of the principles above intimated, to deduce some conclusions with respect to the molecular condition of several gases from the nature of the deviations which Regnault detected in the same. A description of this method, however, would be too prolix; and even the results, in consequence of the many difficulties encountered in actual calculation, are too uncertain to merit being here adduced. Whenever, therefore, in the sequel a gas is spoken of, we shall, as before, conceive it to be one which perfectly fulfils the above conditions, and which Regnault calls an ideal gas, inasmuch as all known gases present but an approximation to this condition. 6. After these considerations on the gaseous condition, the question at once arises in what manner the solid and liquid conditions differ from the gaseous. Although a definition of these states of aggregation, in order to be satisfactory in all its details, would require a more complete knowledge than we at present possess of the condition of the individual molecules, yet it appears to me that several fundamental distinctions may be advanced with tolerable probability. A motion of the molecules takes place in all three states of aggregation. In the solid state, the motion is such that the molecules move about certain positions of equilibrium without ever forsaking the same, unless acted upon by foreign forces. In solid bodies, therefore, the motion may be characterized as a vibrating one, which may, however, be of a very complicated kind. In the first place, the constituents of a molecule may vibrate among them |