MOLECULAR ATTRACTION. VI11 PAPER BY J. E. MILLS
I have occasionally seen and heard my previous papers upon the subject of molecular attraction’ designated as “highly theoretical” papers. Such a statement, when it is applied t o the papers as a whole, it seems t o me, rests either upon an entire misconception of the relationship between fact and theory, or upon a very erroneous idea as t o the content of the papers themselves. For the error involved in such a statement I feel myself largely responsible. I have failed t o make sufficiently clear the boundary between the facts presented and the theory used, and I have moreover repeatedly referred t o the theory of attraction ” presented, and thus unintentionally aided in the misconception. Moreover, the papers have been written as the work was completed and subsequent papers, while containing in themselves new material, contain also many additions and changes applicable t o the papers that went before. I realize keenly t h a t the entire set of papers should be revised. This revision is now made absolutely necessary by the fact t h a t Dr. Sydney Young has just completed a revision of the volumes of the saturated vapor a t the lower temperatures for the substances investigated by him, and this revision makes extensive, though usually small, alterations necessary in twenty-five of the substances examined. Dr. Young has also revised the Biot formulae used in eight of the substances examined. Dieterici’ has also recently proposed an equation which throws much light upon, and is very similar in form to, the equation of Crompton which was studied in the previous papers of this series. For these reasons I am a t present engaged upon a full and complete revision of the entire series of papers. But owing t o the amount of work in\-olved, (1905);
*
Jour, Phys. Chem., 6 , 209 i 1 9 0 2 ) ; 8, 3 8 3 (1904); 8, j 9 3 (1904);9, I (1906); 11, 132 (190;); 11, j 9 4 (1907). Drude’s Ann., 2 5 , 569 (1908).
IO,
402
Moleculas Attraction
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and t o my wish t o extend the work somemhat, the final republication cannot be attempted for a year or two. I see no reason for delaying publication of the new results obtained until t h a t time. The object of this paper is therefore threefold : First, t o call particular attention t o the boundary between fact and theory so far as these papers are concerned; Second, t o give a summary of the changes caused by the revisions made by Dr. Young in the data previously used; Third, to present the underlying fundamental equation in a new form-a form more simple and far more significant. First.-Distinction between the Theory of Molecular Attraetion and t h e Law Discovered by Means of the Theory The work was based upon the belief that the total energy pes s e of a molecule must be the same in the liquid as in the gaseous state, the temperature being the same. If a t a gil-en temperature a giren weight of gas represents more energy than the same weight of the substance as a liquid, the extra energy of the gas must be energy of position only (assuming no intramolecular change). l y e have made no effort in any of our papers to prove this belief. It is not, however, a purely gratuitous assumption and the reasons leading t o this belief were briefly outlined at the beginning of the sixth paper.’ Expressing the above belief in a different form, n-e may say that the energy necessarl; to change a liquid into a gas must, then, be spent solely in overcoming the external pressure and in altering the distance apart of the molecules. (Cnless the molecule breaks apart also or nears the point of disruption.) Denoting the heat of vaporization by I,, and the energy necessary to overcome the external pressure during the change from liquid to gas by E,, I, - E, must equal the energy spent in overcoming the molecular attraction. S o w is this amount of energy actually spent in overcoming the molecular attraction? In order to answer this question directlj- and definitely i t xx-ould be necessary t o 1
J o u r Phys Cheni ,
11,
15:
I
190;)
J . E . Mills
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know the amount of the molecular attraction and the way in which this attraction varied with the distance apart of the molecules. Neither of these factors were known. But in this particular case the difficulty did not appear insurmountable. For we could assume the law of the attraction and obtain the amount of the attraction in a given case, and then find if the assumed law and the amount of the attraction found, were in accord Tvith the facts under all other conditions. This is exactll- what we proceeded to do. lye assumed that the molecular attraction varied inverselj- as the square of the distance apart of the molecules and was a mutual property of each pair of molecules. Then from the internal heat of vaporization at one temperature and the assumed law i r e calculated the aniount of the attraction. Having once fourid the aniount of the attraction for the suhstance in question x e proceeded to calculate the internal heat of vaporization a t other temperatures and compare the calculated result n i t h the observed in order to determine t o what extent our supposition was in accord with the facts. After publishing the first paper we recognized that the test of the assumed law of the attraction could be more easily made, and more readily interpreted, if the quantities involved were combined into an equation having the form, I
I,
-
42-
I?, - = constant = p’ QD
The derivation of this equation is given in the sixth papei above cited. I, denotes the heat of vaporization a t a certain temperature, E, is the amount of energy spent in pushing back the external pressurr as the liquid vaporizes. I, -- E, denotes, therefore, the internal heat of vaporization. d and D are the densities of liquid and saturated vapor respectively at the temperature in question. The constant we have called p’. The above equation I * is, therefore, theoretically derived from the assumptions we have stated and in the manner detailed in the sixth paper above cited. -\nd had we stopped
Molecular i l t t ~ a c t i o ~
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with the mere derivation of this equation our work would have deserved the criticism of being theoretical. But we proceeded t o test the truth of the equation by reference t o the facts. -qssuming for the present (we review the proof below) that the facts were sufficient to establish the truth of the equation beyond reasonable doubt, then it is surely evident that the above equation represents a )act absolutely independently of the theory by which it was deril-ed. The aboTe equation, i] 111 nccoid uitlz the jacts, 9,epresents n lncu., +tot a tlieoiy. If the equation is true it does not necessarily follow that the assumptions b!- which it was derived are true. The truth of the asiumptions upon n-hich the equation is based is rendered far more probable bJ- the proof that the equation is true, but the assumptions are not therehh- proved. l y e must distinguish, therefore, betn een the theory of molecular attraction advanced in these papers, and the law which n-as discovered by means of that theorj- Son- 99 percent of the work detailed in the papers under discussion, if not 99 percent of the words, had t o do with the p ? o o ) o j the laki. I am willing for any critic to attack the proof of the law as presented, but I am not willing for critics longer t o class the law as theoretical merely because the law was theoretically derived, when it was afterwards established by direct reference t o the facts. It is as if a hunter concluded from certain tracks t h a t there was a bear in a certain canebrake. So long as he does not go t o the canebrake and look for the bear the existence of the bear in that canebrake is only a more or less probable theor!-. But if he goes to the canebrake and finds the bear, the existence of the bear a t that point is a fact quite independent of the prex-ious theory of the hunter upon the subject. The existence of the bear does not prove that he made the tracks which started the hunter upon his search. The tracks wzzght have been made by some other bear. If, however, the hunter follows the tracks carefully t o the canebrake and then finds the bear, and only one bear, and the bear’s feet fit the tracks observed, the hunter is justified
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in supposing t h a t his first conclusion with regard t o the tracks was correct. It is for that reason that I am justified in examining the tracks as well as the bear-the theory as well as the law. L-Ee Second.-Proof of t h e Law, __ = Constant.
