viscosity. Values were also assigned to the effects of the iso-grouping of atoms, the double linkage of carbon atoms, and the ring grouping. The values thus obtained are given in the following table : : Fundamental Viscosity Constants (molecular viscosity at the boiling point, in dynes x 10). As regards the meaning to be attached to fundamental viscosity constants in general, the following points may be noted. Viscosity may be taken as a measure of the attractive forces in play between molecules, i.e., of intermolecular attraction. From the fact that an increment of CH, in chemical composition, or the substitution of an atom of chlorine, bromine, or iodine for an atom of hydrogen, brings about a definite change in the viscosity, it is evident that intermolecular attraction is really a property of the atoms forming molecules. But, besides change in molecular weight, change in the mode of grouping of the same atoms also affects the magnitude of the viscosity. The observations show that iso-compounds have values differing from those of isomeric normal compounds; ring compounds have not the values which, by the study of straight chain compounds, they might be expected to have. Compounds containing hydroxyl oxygen give values of the viscosity differing widely from those of compounds containing carbonyl oxygen. The same atoms must, therefore, exert different effects when differently linked together. That the effects of all the atoms in the molecule are not altered by change in the mode of linkage is proved by the fact that the effect of CH2, of iodine, of bromine, &c., is the same in normal and in iso-compounds. In the present state of the question it is impossible to say what particular atoms are affected by change in the mode of linkage. Hence the method adopted in deducing fundamental constants is to assume that certain atoms retain the same values under all conditions, whilst the change in the values of those atoms which are affected by the mode of linkage is, when possible, expressed either by a new constant-the value of an iso-linkage, a double linkage, &c., or by saying that a particular atom has assumed a new value, e.g., carbonyl oxygen, hydroxyl oxygen, &c. In some cases the method of calculation may lead to the result that a negative constant is ascribed to a particular atom. In deducing the values of carbon and hydrogen, for example, it is implied that in a CH, group and in the molecule of a paraffin the individual effect of each atom of carbon or of hydrogen is the same. The above facts, and the reasoning based upon them, show that this is not the case, and although the absolute effect exerted by each atom upon the viscosity is positive, the fundamental constant of an atom may be negative, as it may involve a constitutive effect, which at present cannot be localised in a particular region of the molecule. For these reasons fundamental constants are to be regarded as empirically ascertained magnitudes, which are merely intended to indicate how far the observed results may be represented as the sum of partial values which are the same for all substances. They have no reference to the possible behaviour of the elements when in the free state; they simply show how far definite changes in chemical nature correspond with definite changes in viscosity. Tables are given which show the concordance between the observed molecular viscosity and those calculated by means of these constants. In the case of forty-five liquids the difference between the observed and calculated values rarely exceeds 5 per cent. In the case of the isomerie ketones and aromatic hydrocarbons, the differences are in part due to constitutive influences, which cannot at present be allowed for in obtaining the calculated values. In a second table are given those substances for which the differences exceed this 5 per cent. limit. These may be roughly classed as unsaturated hydrocarbons, polyhalogen compounds, formic and acetic acids, benzene, water, and the alcohols. Similar fundamental constants for molecular viscosity work at the boiling point have also been deduced. These are given in the table on p. 155. Tables are also given showing the comparison between the observed and calculated numbers, the substances being classified into two groups, as in the case of molecular viscosity, according as the differences are less or greater than about 5 per cent. On taking a general survey of the comparisons at the boiling point, it is evident that for the majority of the substances examined-the paraffins and their monohalogen derivatives, the sulphides, the ketones, the oxides, and most of the acids and the aromatic hydrocarbons-molecular viscosity and molecular viscosity work may be Fundamental Viscosity Constants (molecular viscosity work at the boiling point, in ergs × 103). quantitatively connected with chemical nature. The remaining substances-unsaturated hydrocarbons, d- and poly-halogen compounds, formic acid, benzene, water, and the alcohols-present marked exceptions to the foregoing regularities. As regards the comparison of the viscosity magnitudes at the corresponding temperature, it is found that, although the critical data are too unsatisfactory to warrant us in laying any particular stress on the relationships obtained under this condition of comparison, these relationships are similar to, even if less definite than, those of ined at the boiling point. For a property like viscosity, which alters so rapidly with temperature, a corresponding temperature is no better as a condition of comparison than the boiling point. On comparing the viscosity curves of those substances which give the best physicochemical relationships at the boiling point, it was at once seen that the general shape of the curves towards the boiling point was practically the same. If tangents were drawn to the curves at points corresponding with the boiling points of the liquids, the inclinations of the tangents to the axes, that is, the slopes of the curves, varied but little. On the other hand, the curves for liquids such as the alcohols, or the lowest members of homologous series, which gave little indication of physicochemical relationships, had invariably a different shape; the inclinations of tangents drawn at the boiling point were markedly different from those of the majority of substances. It seemed probable, therefore, that the discrepancies were related to this difference in the value of the slopes, and that, if the temperature of comparison was chosen so as to eliminate this difference, better relationships ought to be obtained. This idea led to the adoption of temperatures of equal slope as comparable temperatures, and, indeed, apart altogether from considerations such as the above, which refer to the particular case of viscosity, much may be said, from a theoretical point of view, in favour of employing such temperatures for physicochemical comparisons in general. To begin with, at the temperature of equal slope, the effect of temperature upon the property examined is the same for different substances. In the case of viscosity, for instance, dy/dt, or the rate at which viscosity is being altered by the temperature, has the same value for all liquids, and this equality might be taken as sufficient justification for supposing that at temperatures of equal slope the substances, so far as viscosity is concerned, are in comparable states. Another argument which may be advanced in favour of such a method of treatment is that the comparable temperatures are chosen by means of a study of the effect of temperature on the property actually examined. The main objection which can be urged against the boiling point as a comparable temperature, even when, as in the case of such a property as density, it gives comparatively definite stoichiometric relationships, is that these relationships may not be general. If, however, comparable temperatures be chosen, as in the case of slope by a study of the property considered, the generality of the relationships obtained can be ascertained without the study of other properties of the substances. Comparisons were made, therefore, at temperatures at which dŋ/dt is the same for the different liquids. Or, graphically, the temperatures may be defined as those corresponding with points on the viscosity curves at which tangents are equally inclined to the axes of coordinates. The temperatures are therefore those at which temperature is exercising the same effect on viscosity, and for shortness may be termed temperatures of equal slope. The temperatures were obtained by means of Slotte's formula. It was apparent from the shape of the curves that all the liquids could not be compared at any one value of the slope, because the effect of temperature on the slope varied so much from substance to substance. In some cases-the whole of the alcohols for examplethe slope at the boiling-point was considerably greater than that at 0° in the case of some of the less viscous liquids. A slope was, therefore, selected at which as many liquids as possible could be compared. Another slope was then obtained at which the outstanding liquids could be compared with as many as possible of the liquids used at the original value of the slope. The relationships between the magnitudes of the viscosities of these liquids which could be compared at the two slopes were then found to be the same at either slope, so that general conclusions regarding the behaviour of all the liquids could be deduced. These are as follows: 1. Temperatures of equal slope tend to reveal much more definite relationships between the values of viscosity coefficients and the chemical nature of the substances than are obtained at the boiling point. 2. In all homologous series, with the exception of those of the alcohols, acids, and dichlorides, the effect of CH, on the value of the coefficient is positive, and tends to diminish as the series is ascended. 3. Of corresponding compounds the one of highest molecular weight has the highest coefficient. 4. Normal propyl compounds have slightly larger coefficients than the corresponding allyl compounds. 5. An iso-compound has invariably a larger coefficient than a normal compound. 6. In the case of other isomers the orientation of the molecule and branching of the atomic chain influence the magnitudes of the coefficients. Similar effects of constitution are also exhibited on comparing saturated and unsaturated hydrocarbons, and the variable effects produced by successive substitution of halogen for hydrogen. 7. The alcohols, and to some extent the acids, still give results which are peculiar when compared with other substances. As regards molecular viscosity at equal slope the following conclusions may be drawn: 1. For the great majority of the substances molecular viscosity at equal slope can be calculated from fundamental constants which express not only the partial effects of the atoms existing in the molecule, but also those due to different atomic arrangements. These are given in the accompanying table: Fundamental Viscosity Constants (molecular viscosity at |