apparatus differ from that described herein in many important respects, the present design, described above, being especially adapted to the measurement of the normal component of the velocities of the slowest rays. His general conclusions are that these electrons may be called independent, that their properties are similar to those of the S-rays produced by a-rays, and that they are produced by the intermediary rapid B-rays. Two other factors that might enter must be considered. The first is the effect of the secondary X-rays from the gold. In a previous paper the writer has shown that this must be too small to produce a major effect, and the most frequent normal component of the speed, being in the neighbourhood of 0.48 volt, corresponds to ionization by rays in the visible region of the spectrum if we use the value 3 × 0.48 volts to calculate the mean resultant energy of these slow rays. The second effect is due to the thermal reaction accompanying the recoil of an atom emitting a rapid B-ray. Interest in this subject has been renewed recently by P. L. Kapitza †, who has shown that the slow electronic S-radiation arising from the impact of a-particles is due to thermal effects arising from localized points of impact, the intermediary being high-speed electrons. Richardson's thermionic equations are applied to the resultant distribution of S-radiation, and temperatures of the order 20,000° abs. are assigned to the centres yielding the observed most probable speed. 8. If the distribution of speeds is Maxwellian, the current received by the plate opposite the radiator, and therefore that leaving the radiator designed as described in paragraph 3, is governed by the equation ‡ where n is the number of molecules in 1 c.c. of a perfect gas at 0° C. and 760 mm. pressure, R is the gas constant for this quantity of gas, V1 is the retarding potential reducing the current from i。 to i, ne=43 e.m. unit, R=3·7×103 erg/deg. C. The curves show how far the distribution in speeds differs from the logarithmic distribution represented by the dotted lines in fig. 3. It should be pointed out here *Phil. Mag. xli. p. 130 (1921). Phil. Mag. xlv. p. 989 (1923). O. W. Richardson, 'The Emission of Electricity from Hot Bodies,' 1916, p. 144. that no special preparation of the surface to ensure cleanliness was possible, and the vacuum maintained was of the order '01 cm. of mercury. These two factors would probably account for the loss of a fraction of the very slowest electrons, indicated by a bending over of the curves to the current axis. Assuming that the curves are logarithmic over the major part of their length and that the process of emission can be compared with the thermionic process, we have from both curves using formula (iv) T=1·1 × 101 deg. abs. 9. That atomic recoil can scarcely account for this high temperature is shown as follows:-The velocity of recoil of a stationary atom of mass M yielding an electron of energy eV will be (2meV)/M. In the present case M=197 × 1·66 × 10-24 gm. for a gold atom, V=4'4 x 10 volts, being the peak potential supplied to the Coolidge tube, and hence the velocity of recoil =34 x 10 cm./sec. as compared with an average velocity of 1.89 x 104 cm./sec. due to the thermal motion of gold atoms at 15° C. A simple calculation shows that under the most favourable circumstances of recoil, i. e., when the direction of motion of the ejected electron is opposite to that of thermal motion of the atom, and therefore the above velocities will be added, the resulting energy of the atom cannot be greater than that corresponding to 2300° abs. The approximate average velocity corresponding to a temperature of 11 x 10 deg. abs. is 11.6 x 10 cm./sec., and consequently an atom would need a thermal velocity of (11·6-3·4) × 104 cm./sec. at least before recoil in order to acquire this temperature. Taking this velocity, viz. 8.2 x 10 cm./sec. and the average velocity at normal temperature as 1-89 x 10 cm./sec., the ratio is 43. The ratio of the number of atoms whose velocities lie between 4.3u and 4.3u+ du to those that lie between u and u+du, where u is the root mean square of the velocity of the atoms, from Maxwell's distribution law is then only of the order 10-10 to 1. This, together with the fact that very few of all the atoms present are influenced by the radiation, rules out the possibility of centres acquiring the extremely high temperature of 1.1 x 10' deg. abs. by recoil alone. 10. We are therefore left to account for the experimental observations in some such manner as follows. The original form of the energy is that of the fast-moving B-rays, the final form is energy of the same type but degraded. The primary B-ray of large energy yields a large number of slow B-rays all of similar origin-or d-rays, as they have been called,--energy corresponding to that of the ionization potential being taken from the parent store at each inelastic impact. Only the most loosely bound electrons are affected. The mechanism of the interchange of energy is difficult to conceive, but colour is lent to this view by the fact that C. T. R. Wilson's tracks of B-particles are unforked, i. e. a rapid B-ray only produces by impact with atoms other B-rays or ions whose energy is very small in comparison with that of the parent particle. Very rarely does a large change of energy by direct impact occur. The logarithmic distribution of the particles will be the subject of further investigation. Abstract. It is shown that the normal component of the velocity of over 85 per cent. of the electrons emitted from a gold film under the influence of a heterogeneous beam of X-rays is less than 2 volts. The distribution with velocity bears a relationship to that of the thermions from a hot body. It is argued that the mode of production of these slow electrons can scarcely be due to atomic recoil consequent on the ejection of a rapid B-ray nor to the action of the transformed X-ray energy into energy of longer wave-length. The analogy with the thermionic process probably arises from the fact that in both cases only the outermost system of electrons take part in the action, though the mechanism of the two processes must differ considerably, in the present case the intermediary being the rapid primary B-ray. The distribution with velocity of the electron atmosphere, from the point of view of thermionics in the case investigated, corresponds to a temperature of 11,000° abs. It becomes important, therefore, to investigate under all conditions the correspondence between the two processes. A "null" method of using an electroscope is described. My best thanks are due to Professor A. Griffiths for giving me the facilities of his laboratory, and to the Governors of Birkbeck College for a grant for the purposes of this research. Birkbeck College (University of London), E.C. 4. LII. Two Solutions of the Stress Equations, under Tractions only, expressed in general Orthogonal Coordinates, with two deductions therefrom. By R. F. GWYTHER, M.A.* THIS paper is in continuation with a portion of one entitled "An Analytical Discrimination of Elastic Stresses in an Isotropic Body "†, and I employ the same notation {P, Q, R, S, T, U} for stress and {e, f, g, a, b, c} for strain. There are two solutions, one giving the elements of stress in terms of three functions 0, and one in terms of three functions, each of them being general solutions. As there will be no transformation of coordinate axes, the two solutions will be considered separately. I now find that I should have attributed the e-solution in Cartesians to Maxwell, and the solution to Morera. Ultimately I combine the two solutions to derive the six equations of identity connecting the differential coefficients of the elements of strain in an orthogonal coordinate system. 1. I propose to find the solution, step by step, of the stressequations, under tractions only, which I shall consider in the form and I shall retain this notation throughout. Communicated by the Author. † Phil. Mag. July 1922, p. 274. Phil. Mag. S. 6. Vol. 46. No. 273. Sept. 1923. 2 I (1) which satisfy the equations in third differential coefficients of 1, and proceeding to satisfy the equations in the next lower degrees of differential coefficients, we find the expressions terminate. At this stage and in other stages throughout the paper we make use of the two triads of identities between the second differential coefficients of h's and squares and products of first differential coefficients, which I shall cite as Lamé's Identities. I quote one identity from each triad :— The final values for the elements of stress are: |