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the motion of heat-energy, but we are unable to say why one of the two possible directions of change is invariably selected.
6. It may be well to point out that the problem here discussed bears distinct analogy to the problem of our former paper, where the Dissipation Function F represented what may now be called the interior" variation of molar fluidenergy and was seen to depend on the effect of molecular interaction on the values of qu=p2-p and 8=pris,
(37) and similar quantities, in analogy to the present proposition concerning the fifth term of (32), right-hand side. Put
8t and let My, Hz, Vy, v: be defined by similar equations. Suppose the Kinematical Theory of the Viscosity-problem to be given ; then what we have to do in order to complete the solution is simply to prove that the u's and the v's have constant and equal values : the results indeed given at the end of 2 of the former paper, and likewise the well-known equations of motion of viscous fluids, can then be easily deduced. The common value of the u's and the v's is the coefficient of viscosity and is positive if the mutual action between molecules is such as to tend always to dissipate the disturbances q and s. Again, put
ot and let ky and kz be defined by similar equations. It follows from (12) and (39) that
32 +52 д de
(40) From (17) therefore we obtain, calling }(E? +m2 +52)=0, dᎾ d a
дг. the equation of conduction, as usually given, following from this for a fluid at rest, if it is conceded that @ means the temperature at (xyz). The value of the last term of equation (32) is now 5 ku + ky
dx dz. · (42) dy
In order to complete our solution we have to prove that the k's have constant and equal values. It will be observed that the role of the expression
in Conduction is much the same as that played by Lord Rayleigh's Dissipation Function F in Viscosity; and we therefore propose to call this expression “ the Dissipation Function of Conduction."
In his great paper “On the Dynamical Theory of Gases," Maxwell practically confined himself to the case of a force between molecules varying inversely as the fifth power of their distance. It may, wo think, be legitimately assumed that the Theory of Matter will progress in the future without the aid of any such hypothesis. Whatever may be the law of molecular force, whatever may even be the opinion we hold as to the existence of molecules, we shall be justified in seeking to find a general law of subsidence of disturbances in fluids or possibly in all bodies—a general Law of Relaxation in Maxwell's sense of the term. Let a, ß, y denote constants, being the reciprocals of time-periods ; we have
and it does not seem unlikely that these equations should be special and no doubt approximate expressions of some general relation.
The subsidence of disturbances, to which we alluded, forms a characteristic feature of pbenomena which are going on in matter, as contrasted with those of which the æther is the seat. Now this property of gradually calming every kind of disturbance (which seems to be a fundamental property of matter) is in formal contrast with another property attributed to matter, i.e. with inertia. It seems therefore legitimate to suppose that it is with the properties of the æther that we are ultimately concerned in ordinary dynamics ; and if we adopt the well-known doctrine which asserts that matter may consist in some kind of disturbance in the æther, we shall find nothing to surprise us in such an assumption.
Phil. Mag. S. 5. Vol. 39. No. 241. June 1895.
L. The Heat of Combination of Substances in the Liquid
and Solid Condition. By SPENCER UMFREVILLE PICKERING F.R.S.* F it were found that the heat of formation of a solid
hydrate, or analogous compound, from its solid constituents were the same as that evolved when these constituents were mixed in the liquid condition, we should have a strong argument in favour of the view that the same substance was formed in the two cases—that the liquid mixture, just as much as the solid hydrate, consisted of a definite compound. The only instance in which sufficient data exist for the calculation of the heat of formation in the two conditions gives results indicating that this may be the case : taking the author's values for the monohydrate of sulphuric acid, it is found that solid water and solid sulphuric acid in combining to form the solid monohydrate evolve 6533 cal. at 17°.9, whereas the liquid constituents in combining to form the liquid hydrated acid at the same temperature evolve 6667 cal., practically the same amount of heat.
The present determinations were made in order to see whether a similar equality held good in other cases.
The results obtained, however, have been of an entirely negative character, and show that the equality found in the case of sulphuric acid is, probably, accidental.
Negative results, however, do not in any way prove that the mixed liquids do not contain, or consist of, the compound known in the solid condition, for the actions concerned are complex, and the quantity which is measured as the heat of combination represents, in reality, the difference between this quantity and several others.
Thus, suppose, for the sake of argument, that the same amount of combination occurs when the substances are brought together in either of the two conditions : and let C represent the heat of combination of the molecules a and b to form ab. Then we have, when the substances are all liquids, the splitting up of the liquid aggregates into the molecules a and b, la and 16, and the aggregation of the molecules of the compound into the liquid condition, so that the heat measured on mixing the liquids will be
H=C-02-03 + Vab. When the substances are in the solid condition, we shall have similarly the heats of conversion of the solids into the molecular condition, or, since the action may be regarded as taking place in the two stages, we shall have, first, the conversion of the solids into the liquids (heat of fusion = f), and subsequently the conversion of these liquids into the molecular condition ; the heat measured in this case will be
* Communicated by the Author.
H'=(-V4—26+ l'ab-fa-fo +fab. I will be equal to H' only if fa+fo=fab; i. e. if the heat of fusion of the compound is equal to the sum of those of its constituents.
The fact that with hydrates and analogous compounds the chemical combination is of a comparatively feeble character rendered it not improbable that this might be the case ; but there is no reason why it should necessarily be so, and the question can only be settled by direct experiment.
The present determinations show that it is not so. The above argument, as has been said, applies to a case where the amount of combination is supposed to be as great in the liquid as in the solid condition, that is, where the heat of fusion of the compound, fab, represents nothing but the mere change from the solid to the liquid condition (true heat of fusion). If, however, the compound undergoes partial dissociation on fusion, this dissociation will (generally) involve absorption of heat, and its apparent heat of fusion will be greater than its true heat of fusion. The present determinations, however, show that the observed heat of fusion of the compound is generally smaller than the sum of those of its constituents, and, a fortiori, the true heat of fusion of the compound must be smaller still ; therefore, the assumption that fu+fo=fab is untenable, and no conclusions can be drawn as to the amount of dissociation occurring on melting the compound from the measurement of H and H'.
The heat of combination of two substances in the liquid condition was determined by dissolving each of them, and also the compound, separately in a solvent. D being the heat
, . of dissolution, the heat of combination is
De+Do-Dabo When, as was generally the case, one of the constituents (say a) was identical with the solvent, Da=0.
With solids similar determinations were made ; and where the solvent is identical with one of the reagents, D, is the heat of fusion of the substance a.
As it was not possible to make the determinations in both conditions directly with each substance, the heat of dissolution in the one condition had to be calculated from that observed in the other by means of the heat of fusion. The heats of fusion of the substances had therefore to be determined, and to reduce these to the temperature used in the heats of dissolution determinations, the heat-capacity both in the liquid and solid conditions had also to be determined. A description of the method used and of the calculations will be found in the Proc. Roy. Soc. xlix. p. 11: it will be sufficient to state here that the substance is heated in a platinum bottle containing a thermometer to the required temperature, and then plunged into the calorimeter.
Table I. of the present communication gives the experimental details and Table II. the results. Table III. gives the values for the heat of dissolution-firstly, those obtained by direct experiment on the substance in the one condition, and, secondly, those calculated for it in the other condition, as deduced from the former by means of the heat of fusion. The heat-capacity is calculated from the equation
C= (t' – t)W-(1-t')w
(T-t'ju and the molecular heat of dissolution from the equation
where t' and t are the final and initial temperatures of the calorimeter, W the water-equivalent of the calorimeter and its contents, 7 the initial temperature of the substance when introduced into the calorimeter, w its weight, and M its molecular weight, w being the water-equivalent of the platinum bottle containing it.
Considerable difficulty was experienced in finding substances suitable for the present investigation. In order that the heat of fusion may be satisfactorily determined, it is necessary that the compound and both of its constituents should melt between temperatures of 0° and not much above 100°. Several substances other than those here mentioned were examined and found unsuitable.
Monohydrate of Sulphuric Acid.—The necessary data have already been given in the Trans. Chem. Soc. 1890, p. 112, and the Proo. Roy. Soc. xlix. p. 18: a very slight alteration in them has been made in consequence of round values for the atomic weights having been used in the present work.
Hexhydrate of Pinacone.—To prepare the anhydrous from the hydrated pinacone supplied by Messrs. Kahlbaum, fractional distillation was found to be unsatisfactory, and dehydration by treatment of the ethereal solution with potassium carbonate was adopted. The hydrated substance does not appear to be by any means insoluble in ether, as is stated, and