In addition, if the values of 7 and p1 are obtained, E and n can be separately calculated. Some observations were taken upon different lengths of one of Salter's steel springs (r=1494 cm.), using as the vibrating body one whose moment of inertia could be varied by known amounts from an arbitrary value K by moving two equal masses in and out along a bar. The following is a specimen of the numbers obtained, in C.G.S. measure :— Exp. 1.-4-300π, l=1408, x=78, m=130.5, M=267. And as a verification we can deduce K+3mr2=886, 892, 903, 884; mean 891, which gives for K the value 794. The results of the experiments are exhibited in the following table : The last experiment of the above series was made by attaching an additional mass to the vibrating body, so that a was increased to 125, and of course K was changed. Thus we see that the method furnishes consistent results and we deduce for this specimen of steel, Also, since for our wire p is about 0617 centim., we obtain as approximate values, E=2.00 x 1012, n =7·79 × 1011. An experiment with a spring of hard-drawn copper wire gave XLV. On the Velocities of the Ions and the Relative Ionization-Power of Solvents. By W. C. DAMPIER WHETHAM, M.A., Fellow of Trinity College, Cambridge*. FROM ROM a knowledge of the electrical conductivity and migration-constant of a solution, Prof. F. Kohlrausch has shown us how to calculate the velocity with which its ions must travel in order that, in accordance with Faraday's law, a given current should be carried (Wied. Ann. xxvi.). Prof. O. Lodge experimentally determined the velocity of the hydrogen ion as it travelled through a jelly solution of sodium chloride and so formed hydrochloric acid, the presence of which was indicated by the decolorization of phenolphthalein. When the ion was driven by a potential gradient of one volt per centimetre the speed came out 0·0029 centimetre per second, a number agreeing in a most remarkable manner with Kohlrausch's theoretical value 0.0030 for a decinormal solution (B.A. Report, 1886). The author of this paper has observed the specific ionic velocity of other ions, such as copper and the bichromic-acid group (Cr2O7), by tracing the motion of the junction of two salt-solutions (one of which is of different colour from the other) under the influence of an electric current (Trans. Roy. Soc. 1893 A.). The results agree with Kohlrausch's numbers even in the case of alcoholic solutions, the conductivities of which are much less than those of the corresponding aqueous solutions. Certain substances, e. g. ammonia and acetic acid, have been regarded as exceptions to the application of the theory. From a knowledge of the conductivity and migrationconstants of acids such as nitric and hydrochloric, we can * Communicated by the Author, calculate the velocity of the hydrogen ion; and from the same constants for a solution of (say) sodium or potassium acetate, we can get the velocity of the acetic-acid group C2H3O2. If we calculate what conductivity these velocities would give to a solution of acetic acid (whose ions are H and C2H2O2) of strength 0.1 gram equivalent per litre, we obtain a number greater than the observed result in the ratio of 3168 to 46. In order to observe whether the velocity of the ions was reduced in the same proportion as the conductivity, the velocity of the hydrogen ion through a solution of sodium acetate was determined by Lodge's method. The apparatus used is represented in the figure, and was the same as that employed in the earlier investigation above mentioned. Ordinary aqueous solutions were at first set up; but the junction did not travel uniformly, and agar jelly solutions were found to be much better for this purpose. A preliminary investigation was made to examine the influence of the jelly. The velocity of the bichromic-acid group when driven by a potential gradient of one volt per centimetre was determined by filling the longer limb of the tube with a solution of potassium bichromate in agar jelly just strong enough to set, and the shorter with a similar solution of potassium chloride. A current was then passed across the junction by connecting the electrodes with a battery of storage-cells giving an electromotive force of about 50 volts. The bichromic-acid group travels in a direction opposite to that of the current and displaces the chlorine, so that the colour-boundary moves. If v represents the observed velocity, A the area of cross section of the tube at the point of junction of the solutions, r the specific resistance of the solution, and y the strength of current as shown by a galvanometer empirically graduated by means of a Daniell's cell and box of resistance-coils, it is easy to prove that the specific ionic velocity of the ion causing the change of colour is vA v1= γη when the potential gradient along the tube is unity. In the case of the Cr2O, group travelling through an agar-jelly solution of decinormal strength v1=00044 centim. per second. In the earlier investigation the same group travelled through an aqueous solution of corresponding strength with a velocity of 00047 centim. per second. The effect of the jelly is thus to slightly retard the motion, but the alteration appears to be not more than about 10 per cent. The use of jelly having been thus justified, a solution of sodium acetate (whose strength was afterwards found to be about 0.07 grm. equiv. per litre) in agar jelly was prepared and coloured red with phenolphthalein, just enough caustic soda being added to bring out the full colour. Half of this was decolorized by means of a few drops of dilute acetic acid, and placed in the longer limb of the tube. When it had cooled and become solid, the alkaline red portion was poured into the other limb and also allowed to solidify. A glass scale was fixed behind the junction-tube, and the whole placed in front of a window. The position of the boundary was then read off on the scale by means of a telescope. An electromotive force of about 40 volts was applied, and the velocity with which the boundary between the coloured and colourless solutions travelled observed, readings being taken at intervals of half an hour. The details of the first set of observations are:— Similar sets of observations were then inade at intervals of 10 minutes, the following being the space traversed in centimetres during that time : •10 ⚫09 ⚫09 ⚫09 ·09 ⚫09 ⚫08 ⚫07 The final mean velocity deduced from these figures, by allowing weight to each in proportion to the time-interval used in obtaining it, comes out 0.48 centim. per hour, and the mean galvanometer reading 41°.0. The specific resistance of the solution was measured by using a Wheatstone's bridge with alternating currents, and gave 246-2 legal ohms per cubic centimetre when reduced. to 18° C. The area of cross section was determined by weighing the water required to fill an observed length of the glass tube, and found to be 0.430 square centim. The strength of the current was shown by the galvano· meter-reading to be ampere. Substituting these values in our equation, we get for the hydrogen ion travelling through a solution of sodium acetate in agar jelly whose concentration is 0.07 gram equivalent per litre, when urged by a potential gradient of 1 volt per centimetre, a velocity of 0.000065 centimetre per second. The value given by Kohlrausch for the same ion is 0.0030 centim. per second, so that in acetates its speed is reduced in the ratio of 1 to 46. The ratio of the conductivity of a solution of acetic acid of the strength used above to that of a decinormal solution of hydrochloric acid is 1 to 59. Thus the velocities of the ions are reduced in about the same proportion as the conductivity, and even in such cases as these the conductivity can be calculated from a knowledge of the opposite ionic velocities. It appears that all the factors determining the conductivity of a solution primarily act by exerting an influence on the ionic velocities. These factors may be (first) the "ionization," i. e. the average fractional time during which an ion is on the whole active (in whatever its activity may really consist); and (secondly) the resistance offered by the solution to its motion by reason of viscosity. It seems probable that the "ionization " power of different solvents is largely dependent on their specific inductive capacities. Prof. J. J. Thomson has pointed out that the effect of immersing a molecule held together by electric forces in a medium of high specific inductive capacity is to greatly reduce the forces between the atoms. In this manner they may acquire the freedom necessary for electrolytic activity, which would, for any one salt, be proportional to the specific inductive capacity of the solvent in which it was dissolved. If we assume that the resistance of a liquid to the passage of an ion through it depends on its ordinary viscosity, we ought to be able to calculate the relative conductivities of a |