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We have calculated the relative number of showers containing n mesons when a fast primary nucleon hits a compound nucleus on the assumption that in a single nucleon-nucleon collision only one meson is produced (pure plural production). The cross section for meson production is assumed to have the form Φ(/E)d /E, where E is the energy of the primary and the energy lost by it, but the absolute value of Φ and its dependence on /E are left open. The fluctuations of the shower size are duly taken into account. For comparison with experiments it is assumed that about half the number of fast shower particles are fast protons as suggested by the positive excess of penetrating shower particles. The theoretical results depend on two constants, the total cross section and some weighted average over the energy distribution Φ(/E). Choosing these suitably, the results are in good agreement with the relevant data within the experimental statistical errors, and the agreement extends also to the "large showers" with 20 or so thin tracks. The values of the constants thus determined are physically reasonable. It is concluded that the size-frequency distribution of penetrating showers can be fully understood on the basis of pure plural production, but some - small or large - contribution from multiple processes cannot be excluded.

Meson intensity has been recorded by using a triple-coincidence arrangement with a lead absorber 25 cm. thick between the counters. The comparison of daily mean values with the height of a number of pressure-levels has led us to take into consideration the temperature of the air layer between 200 and 100 mb. The results show that this temperature appears to be a factor closely controlling the meson intensity at the surface of the earth; the intensity increases with increasing temperature at the rate of 0.12% per °C.

Other factors in determining the intensity are the mass of air and the height of the 100 mb. level over the station. The corresponding coefficients of absorption and decay prove to be comparable with those obtained from other measurements for mesons of the same momentum. It has also been found that the coexistence of the three effects permits explanation of the variability exhibited by the barometric coefficient when evaluated from short periods of observations.

These results may therefore be taken as evidence that the bulk of mesons is produced at the height of 100 mb.

If the positive effect of temperature is interpreted as the result of processes of decay and interactions with air nuclei of π-mesons at the production level, then the coefficient 0.12% per °C. leads to a value of 4.9×10^-8 sec. for the upper limit of the mean life of π-mesons.

The production of τ-mesons (mass about 900 electron masses) by cosmic rays in rather thin layers of air in the upper atmosphere seems to indicate that the nucleon τ-meson coupling constant is not very small. The Berkeley experiments show that this is also true for the nucleon-π-meson coupling constant. Consequently the decay of a charged τ-meson into a photon and a charged π-meson by means of virtual creation and annihilation of nucleons ought to be fairly probable. In this paper this decay process, with the emission of one photon, is studied for the various types of τ-andπ-mesons. Unless both mesons have zero spin, the matrix elements, and therefore the lifetimes, are found to be of the same order of magnitude, and the τ-meson turns out to be too short-lived to be observed photographically.

If both mesons have zero spin the emission of only one photon is forbidden. The detailed discussion of higher order decay processes in this case is reserved for a later paper.

The electronic states of naphthalene are determined using antisymmetrized molecular orbitals, which are based on wave functions given by the simple molecular orbital theory. This method allows the electronic interaction term to be included explicitly in the Hamiltonian for the system. A clear distinction is made between electronic configurations determined with these wave functions and the actual states of the molecule: states arise from a superposition of configurations of the same symmetry. The ground state becomes considerably stabilized by this configurational interaction, to which even highly excited levels contribute. Calculated energy values for some of the lower transitions agree well with ultra-violet spectral data, as do the newly derived oscillator strengths. A tentative assignment is made regarding the polarization of the electronic transitions in the region of 30,000 - 55,000 cm^-1

Up to the present spectroscopic studies of flames supported on a tube have been limited by the geometry of the flame. Thus the important reaction zone presents a three-dimensional problem in which it is impossible to locate the emitters exactly. Moreover this zone is so thin in premixed gas flames that intermediate products cannot be determined from absorption studies. To overcome these difficulties the authors have constructed a burner with a two-dimensional diffusion flame in which the reaction zone at ordinary pressures is 5-10 mm. thick and has an optical depth of 5 cm. or more. With this flame many of the reacting molecules can be located through either their emission or absorption spectra or both. The value of the new technique in the elucidation of combustion processes is demonstrated with reference to NH₃-O₂ and H₂-O₂ flames, and mention is made of its application to hydrocarbon flames.

It is well known that some luminescent materials, notably zinc sulphide, show marked changes in dielectric constant and dielectric loss when excited. Recent work by the authors has established that the changes are due to the filling of electron traps, which have large effective diameter and high polarizability.

The present paper describes measurements of the dielectric changes in phosphors containing two or more luminescence activators. Assuming that the dielectric changes are due to electron trapping, it is possible to derive information regarding the nature of electron traps and in particular their apparent association with the luminescence centres. The results support the contention that the introduction of the activating impurity into phosphors produces trapping states for excited electrons and that each trap forms part of a complex which includes the luminescence centre.

The eigenfunctions following from Sommerfeld's polynomial method were determined in the general case. They are products of a convergence factor E and a polynomial P given by a hypergeometric series. The form of E depends upon whether P is expressible by the ordinary or the confluent hypergeometric series.

Corrections to 1949 Proc. Phys. Soc. A 62 537