As the origin is approached, it is seen that the maxima fall nearer and nearer together, until finally they become indistinguishable, due to diffusion and other causes. In fig. 3, for example, this occurs after the maximum corresponding to seven half cycles.

5. The velocities W of the ions may be found from the points of maximum current on the curves, the electric force being V/d. With With hydrogen at 94 mm. pressure, the velocities W and the corresponding electric forces X obtained from the curve, fig. 2, are:

With hydrogen at 181 mm. pressure, the values of W and X obtained from the curve fig. 3 are :—

If the mobility Wo be defined as the velocity of the ions under an electric force of one volt per cm. in the gas at 760 mm. pressure, the velocity at the pressure p is

Using this relation, the values found for the mobility from the values of Wo obtained with the two largest forces are 5.66 and 5.78 where the pressure was 94 mm., and 5.93 and 5.95 where the pressure was 181 mm. The mean of the above values gives W。=5.8 cm. per second for positive ions in hydrogen.

The values obtained by different observers for the mobility of the positive ion in hydrogen vary, but most of these values lie between that of 534, obtained by Lattey and Tizard*, and that of 6.70 obtained by Zeleny +.

*R. T. Lattey & H. T. Tizard, Proc. Roy. Soc. A, lxxxvi. p. 349 (1912).

+ J. Zeleny, Phil. Trans. A, cxcv. p. 193 (1900).

6. The method of determining mobilities described in this paper shows the presence of ions of a given velocity by a curve characterized by a series of maxima, whose sharpness and relative positions give a measure of the accuracy and reliability of the results. The accuracy of the experiments is not appreciably affected by diffusion and space-charge, as these tend not to shift the positions of the maxima, but merely to make them less sharp. The method is adapted to the investigation of cases where there may be present in the gas different kinds of ions having different velocities. Each kind of ion would then be shown by a separate series of maxima whose abscissæ would show the velocity and whose ordinates would show the relative number of ions of that kind.

The alternating-current generator used in the present experiments can be replaced by a valve oscillator capable of supplying potentials of higher frequency, which could be used to extend this method of investigation to the determination of the large velocities of free electrons, or of positive ions in gases at low pressures.

7. In conclusion, I have much pleasure in expressing my gratitude to Professor Townsend for his constant advice and inspiration throughout the course of this research.

XVII. On the Magnetic Susceptibilities of Electronic Isomers. -Part II. By Professor S. S. BHATNAGAR, D.Sc.(Lond.), and R. N. MATHUR, M.Sc.*

Na previous paper in this Journal †, S. S. Bhatnagar

was found to give remarkably satisfactory results for the diamagnetic susceptibilities of some twenty electronic isomers. According to this equation

where

m=−285×10 x (KR),

=molecular diamagnetic susceptibility.

(1)

R=radius of the molecule calculated on the assumption of closest packing of the atoms constituting the molecule, by using Bragg's data for the diameter of atoms ‡. (A complete account is given in the paper referred to above.)

Communicated by the Authors.
Phil. Mag. [7] v. p. 536 (1928).

+ W. L. Bragg, Phil. Mag. xl. p. 169 (1920).

And Kan arbitrary constant, but which in a series of

isomers is found to exhibit variations with the number of atoms in the isomers. (Its significance was considered in the paper referred to above, and has again been considered later on in this paper.)

According to Langevin's theory of atomic diamagnetism

the summation being extended over the n electrons in the atom, and 72 being the mean square of the radius of the projected orbit in a plane perpendicular to the field. Multiplying (2) by Avagadro's number, we get

And on substituting the values of constants in the equation, we get

x=-2·85 × 1010 Σn2.

A

(3)

The resemblance between our empirical equation (1) and (3) is remarkable, but while (R2) in (1) gives the square of the radius of the molecule, (2) in (3) is the mean square of the radius of the projected orbit in a plane perpendicular to the field. In order to make the resemblance closer, we take in (3) the mean square of the radius of the orbit itself, instead of the mean square of the radius of the projected orbit. If r (components 1, 1, 1) is the distance of an electron from the nucleus, then for an atom symmetrical in the sense that

and equation (3) then becomes

x2.85 x 1010 x 3Σr12,

and equation (1) can be written as

(4)

(5)*

The resemblance between Langevin's equation (4) and our empirical equation (5) is now closer than that between

* Equation (3) employed in the previous paper to this Journal has been modified to equation (5) in order to facilitate the theoretical interpretation of the values of K on the Langevin's concept of the theory of diamagnetism.

equations (1) and (4), and shows the significant fact that instead of extending the summation over all the electrons in the isomer, it has to be extended only over a fraction of them, given by the value of the constant K. It has been noted by several workers that, in order to make the equation of Langevin applicable to all atoms, an effective value of n may have to be taken, and hence the constant K in our equation (whose value is different from n, and in the case of isomers of high values of n, much less than n) assumes particular significance. In this investigation the values of the diamagnetic susceptibilities of over twenty electronic isomers have been experimentally determined, and equation (5) is found to be applicable in all cases.

The apparatus used to determine the diamagnetic susceptibilities is Wilson's modification of Curie's Balance. The substance contained in a small glass tube, attached to a light aluminium system, is suspended in a non-homogeneous magnetic field by a thin silver ribbon. The force exerted by the field is balanced by the torsion of the supension, and read off from a graduated torion-head. A complete description of the experimental arrangement is given in a paper shortly to be communicated. The susceptibilities of the substances are calculated by the formulat

where susceptibility of the specimen.

=

M=mass of the specimen in grams.

specific susceptibility of air (210 x 10-7). M1=the mass of air filling the same volume as the specimen.

the specific susceptibility of water (-7.25 x 10-7). me=mass of water filling the same volume as the specimen.

ma=mass of air filling the same volume as water.

D torsion due to specimen-tube -+ specimen.

=

D, torsion due to specimen-tube alone.

D=torsion due to specimen-tube + water.

Before determining the susceptibilities of the substances given in this investigation, substances of known susceptibility were used, and the results obtained were within the limit of the experimental error.

The radii of the isomers used in this communication, calculated according to the method given in the previous * Stoner's 'Magnetism and Atomic Structures,' Chap. 14. + Oxley, Proc. Roy. Soc. A, ci. pp. 264–279.

paper to this Journal, are given in Table I. and the remaining results in Tables II. and III. :

* In the case of substances marked with the radii have been obtained by summation of the radii of the atoms. This is as it should be.

In Table II. the results obtained by calculation from equation (5) are tabulated against the experimental values, some of which are taken from the Physico-Chemical Tables of Landolt and Börnstein, and some determined experimentally.