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As has already been pointed out, the numbers for Cl are rough, so that no importance attaches to the discrepance between the ratio 9 for Cl and 14 for Cl2, which numbers ought to be identical. All that the table shows is that the relation found to hold between MB and (M2) in the gaseous non-metals does not extend to the other non-metals. The transition cases from metal to non-metal will have to be worked out before the principle ruling in the values of (M2) for the non-metals becomes clear.
4. General Summary and Analysis of Molecular into
The chief result of the present inquiry has been the demonstration that M2l, which occurs in the treatment of the attractions of like molecules, and which represents Am2 in the expression 3Am2/4 for the attraction between two molecules of mass m, can be analysed into two factors (M2) which are the sum of numbers characteristic of the atoms composing the molecule whose mass referred to the atom of hydrogen is M. This is the logical outcome of the proof given in the papers on "The Attraction of Unlike Molecules," that the attraction of two unlike molecules is expressed by the product of two parameters characteristic of each and equal to the square roots of the corresponding attractions for a pair of each of the molecules. The values of (M2) studied in this paper are therefore relative values of Am. But as we have found no evidence of a direct connexion between m and Am, it is desirable to remove all implication of such a connexion, which was originally adopted for the sake of analogy with the Newtonian law of gravitation. Accordingly A'm would be better denoted by a single symbol a, so that the attraction between two molecules of mass m, at distance r apart is 3a,2/r1, and of two molecules of masses mi, m, is 3a1 a/r1, and so on.
The fact that a for a molecule is the sum of parts due to the atoms in it enables us to analyse molecular into atomic attraction; for if two molecules of composition Bb, Ce, Da...
are at a distance r apart, and if the force between the atom or radical B in one molecule and C in the other is kẞyf(r), and between C in one and D in another is kydf(r), and so on, then the attraction between the two molecules is
k(b2 B2 + c2y2+...+2cdys+2dbdẞ+2bcßy + ...)
the parameter for the whole molecule, is given by a=ks (bB+cy+dd + ...),
which is the symbolical statement of our result for the carbon series of compounds that the parameter a for a molecule is the sum of parts due to the separate atoms and radicals in it, and shows that in these compounds the atoms and radicals attract one another with a force proportional to the product of parameters characteristic of each. This does not imply that the parameter belonging to an atom is invariable, for the atoms in a free element have different parameters from those they possess in a compound: by chemical combination both the volumes and force-parameters of many atoms are altered, and the amount of alteration depends on the chemical function of the atom in the molecule; while the chemical function of an atom or radical in an organic compound is constant, its force-parameter is constant. This influence of chemical function on the parameter of molecular force becomes manifest in the typical inorganic compounds, especially of the metals. If the compound is of the type RS,, where R is an atom of valency n combined with n monad atoms S, then the expression for a takes the form
(p and a being parameters belonging to R and S); or perhaps a more suggestive form in which to put it is
which means that the mutual energy of two molecules of this type divided by the number of equivalents in each can be obtained by regarding each equivalent as a separate attracting entity. The equations just given hold true not only when R is a metal and S a non-metal, but also when R is an acid radical of any basicity and S a monad metal. The law for the more general case of a compound RS, has not been investigated in this paper because of the want of suitable
data; nor have the transition cases between the simple typical compounds and the organic series been worked out. It is interesting to find in molecular force a new clue towards the realization of the desire of chemists to trace out the transition from the dualistic to the unitary type of compound.
The atomic parameters B, y, ... p, ..., relative values of which have been given under the symbol F, which is the part contributed by an atom to (M2), have been shown to be related to the volumes of the atoms; in the organic compounds many atoms and radicals have F closely proportional to the volume of the atom, and in the case of the halogens this holds good also in the inorganic compounds. Denoting the volume of an atom by B, the approximate relation is B=10 F or 9 F, but for a compound acid radical of basicity higher than one the relation becomes B=9F/2; here again is evidence of chemical influence on molecular force. In the case of metallic atoms in their compounds, it has been shown that F is not proportional to the volume of the atom, and on passing on to the uncombined metals it is found that F, which represents the atomic parameter, is in the main families of metals approximately proportional both to the square root of the volume of the atom and the square root of the valency, and in the subfamilies is a simple multiple of a number which is so proportional. On returning to the metal atoms in the combined state, it was found that the relation is F2=aB+b in each family, a and b being constants characteristic of the family. The profound influence of valency in the uncombined metals is again of deep chemical interest, as is also the great difference in the law connecting atomic parameter and volume from that holding amongst the extreme non-metals. These are the main results; amongst subsidiary results may be mentioned a certain amount of confirmation given to the Kinetic Theory of Solids by its successful application to the calculation of force parameters, successful insomuch as its results are in harmony with those obtained by a perfectly independent method. This confirmation is the more useful because it applies to the extension of the theory to compound solids, whereas in the original paper the metals only were treated of.
Melbourne, August 1894.
II. The Influence of Temperature on the Specific Heat of Aniline. By E. H. GRIFFITHS, M.A.*
[Plates I. & II.]
UR knowledge of the effect of changes of temperature upon the specific heat of substances is limited. The reason of this is evident, for, in addition to the difficulties of thermometry, the experimental methods usually adopted are based on comparisons in which water is used as a standard, and our knowledge of its capacity for heat at different temperatures is far from satisfactory. The conclusions of Rowland (1879), of Bartoli and Stracciati (1893), and my own investigation completed in 1892, all point to the fact that the specific heat of water diminishes as the temperature rises to 20° C., at which temperature Bartoli and Stracciati find it is a minimum. My observations did not extend beyond 27° C., up to which temperature I found no signs of a minimum, which Rowland places at about 34° C. When such discrepancies exist with regard to the standard, it is not surprising that the conclusions arrived at regarding other substances are unsatisfactory.
For other reasons water is by no means an ideal standard for calorimetry. Its capacity for heat is so great that the changes in temperature caused by the immersion in it of bodies whose specific heats are small are too minute to be measured with exactness under ordinary circumstances. The difficulty is surmounted in practice by causing the immersed body to cool through a considerable range. Other errors are, however, introduced by this method, for the transference of the hot body into the cool water can rarely be conducted without loss of heat. What we require is a liquid of small capacity for heat whose temperature-coefficient of specific heat is accurately known. It should also, if possible, be a liquid easily obtainable in a fairly pure state and should have a low vapour-pressure at ordinary temperatures. I believe that in Aniline we possess such a liquid, and I hope to be able to adduce sufficient evidence to lead to the conclusion that its specific heat is now known with considerable accuracy over a range of 15° to 52° C.
The method I have adopted is an old one, viz. a supply of heat to the interior of the calorimeter by means of an immersed conductor whose ends are kept at a constant potentialdifference. I admit that there are difficulties inseparable from
* Communicated by the Physical Society: read October 26, 1894.
the method (such as doubts as to the actual resistance of the conductor when its temperature is raised by the current, &c.), but when once these difficulties are overcome, there is no such accurate means of determining the quantity of heat passed into a calorimeter in a given time.
The limits of this paper forbid any detailed account of the somewhat complicated apparatus used in this investigation, and I do not contend that it is of the form which I should have selected had my object simply been to determine the specific heat of aniline. I am at present engaged in a determination of the latent heat of evaporation of water and other liquids at different temperatures, consequently the apparatus has been designed and put together in anticipation only of that investigation, and many portions of it are unnecessary and in fact detrimental to the inquiry I am now describing. Hence I have been compelled to adopt methods of observation which may not, at first sight, seem the most advantageous.
I have in my possession an apparatus for maintaining the walls of a chamber at a constant temperature. The arrangement has been fully described in a communication entitled "The Mechanical Equivalent of Heat," Phil. Trans. clxxxiv. A (1893), and as I shall somewhat frequently have to refer to this paper, I will now label it with the letter "J." Briefly, the apparatus as there described consists of a tank containing about 20 gallons of water within which is a steel chamber shaped somewhat like a hat-box with vertical sides, the space between the double walls and floor containing rather more than 70 lbs. of mercury, which communicates by a narrow tube with a gasregulator differing but little from the ordinary pattern. Thus a row of about 50 tiny gas-jets (placed under a tube through which water is always flowing) are so controlled as to be distinctly affected by a change of 46° C. in the temperature of the steel chamber. An addition has been made to the apparatus since the publication of the description in paper J, where it is stated that tap-water continually passed into the tank through a silver tube placed above the gas-jets: this plan answered admirably from the temperature of the tap-water (10° to 12° C.) to about 30° C. Last year, however, Prof. Callendar and I wished to use the tank for purposes of comparison of platinum and air thermometers up to 50° or 60° C., when it was found that alterations in temperature presented themselves, occasionally amounting to as much as C.,--the lag in the temperature of the large mass of mercury being so great that when the gas was lowered by the action of the regulator, the resulting inflow of cold water tended to lower the temperature of the tank before the reaction of the regu