Mean amplitudes of vibration: Some pyramidal XY3 and tetrahedral XY4 molecules

The theory of the determination of the mean amplitudes of vibration in molecules using the symmetry co-ordinates has been applied to the cases of arsenic halides belonging to the pyramidal XY₃ type and a few silicon and stannic halides of the tetrahedral XY₄ type. The mean square amplitudes and mean amplitudes of vibration have been evaluated at 298° K.     

Refinement of the function for the evaluation of the N-H…O hydrogen bond potential energy

The parameters of the hydrogen bond potential energy function proposed earlier have been refined using the increased data available on N-H…O hydrogen bonds. The full-matrix least-square refinement procedure has been used and the discrepancy index has dropped down to a final value of 0 · 176. A linear interpolation has been proposed for the border regions where the hydrogen bonds are weak and the results are discussed.     

Hydrogen bonding and solvolysis of alkyl sulphonate esters and related compounds

Hydrogen bonding between alkyl sulphonyl compounds andp-chlorophenol in carbon tetrachloride solution has been investigated by infra-red spectrometry. Analysis of the intensity of the bonded O-H stretching absorption indicates that, under the conditions employed, only 1:1 complexes are formed in significant concentration. Equilibrium constants for the complex formation have been determined at 15, 25, 35 and 45° C., and the corresponding enthalpy values derived. The strengths of the hydrogen bonds have been estimated from the positions of the bonded O-H stretching bands, and these frequencies correlate with the normal electronic effect of substitution in aryl and alkyl groups attached to the sulphonyl group. The rate of solvolysis of the methyl sulphonates in water is shown to vary inversely as the strength of the hydrogen bond formed. The possible bearing of these observations on certain aspects of the detailed mechanism of solvolysis is discussed.     

Heats of combustion of some symmetrical dialkyl ureas and their corresponding alkyl carbamates

The standard heats of combustion of the disubstituted ureas, N, N′-diheptyl urea, N, N′-dioctyl urea and N, N′-didecyl urea and the carbamates,n-heptyl ammoniumn-heptyl carbamate,n-octylammoniumn-octyl carbamate andn-decyl ammoniumn-decyl carbamate have been determined. The values found are 2353±1·3, 2658·4±1·1, 3268·5±1·7, 2349·8±1·6, 2654·4±1·2, 3264·6±1·8, K.cals. mole^?1 respectively. The heats of formation of these compounds have been calculated.     

Rigidity spectrum of cosmic ray helium nuclei

An experiment has been carried out using an oriented stack of nuclear emulsions to determine the rigidity spectrum of cosmic ray helium nuclei between 12 and 40 GV, by taking advantage of the variation of the geomagnetic cut-off rigidity in the east-west plane over Hyderabad, India. Altotal of 2433 identified helium nuclei recorded in the stack, has been divided into 8 angular intervals in the east-west plane corresponding to 8 different cut-off rigidities. From this the integral fluxes of helium nuclei at the top of the atmosphere have been obtained for all the 8 rigidity intervals. The vertical flux above an effective threshold rigidity of 16·73 GV has been determined with high statistical accuracy and has a value of 15·0±0·5 helium nuclei (m².sr.sec.)^?1. The rigidity spectrum of these nuclei between 12 and 40 GV can be well represented by a power law of the type N (>R) =1990 R^?1.74±0.11 (m².sr.sec.)^?1 and is the first direct determination so far made in this rigidity region. The differential rigidity spectra of protons, helium nuclei and S-nuclei of the cosmic radiation in the vicinity of the earth at solar minimum (1965) have been constructed with the existing world data and it is found that for rigidities ? 10 GV, the three spectra have, within experimental errors, the same slope of 2·6. The ratio P/He and He/S of the differential fluxes have been studied as a function of rigidity. It is found that for R>2 GV, the ratio P/He has, within experimental errors, a constant value of 6·3; as for the ratio He/S, it seems that the experimental data above a GV is not inconsistent with a constant value of 14 over the entire rigidity interval considered here.     

Investigations on the multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsion

A nuclear emulsion stack was exposed over Hyderabad, India (geomagnetic latitudeλ=7·6° N) under a mean atmospheric depth of 6·8 g./cm.², on 24 March 1960. The relative and absolute intensities of Be and B nuclei and nuclei of charge Z?6 (the S-nuclei) have been determined in this stack. The intensities were extrapolated to the top of the atmosphere using measured fragmentation parameters involved in collisions of cosmic ray nuclei in graphite. The flux values of Be, B and S nuclei at the top of the atmosphere have been determined to be 0·025±0·011, 0·101±0·023 and 1·12±0·10 particles/m.² sec. sr. respectively. The ratios of intensities B/S, Be/S and Be/B have been found to be 0·09±0·02, 0·022±0·008 and 0·25±0·11 respectively. These ratios of intensities have been used (a) to compute the amount of matter traversed by the radiation before reaching the vicinity of the earth as 2·6±0·6 g./cm.², (b) to show that the Fermi mechanism of acceleration of particles is not efficient at these energies (1–10 GeV/n.) in interstellar space and (c) to show that preferential acceleration of H₁-nuclei (Z?20) is not of overwhelming importance. The derived source composition of nuclei of energy ?7·5 GeV/n suggests that N, O, F and H₃-nuclei (Z=10–15) have similar abundances in the universe and in cosmic rays, and that C and H₁-nuclei are overabundant in cosmic rays.     

Investigations on the multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsions

The interaction mean-free paths and fragmentation parameters associated with collisions of nuclei of Z?6 and E?7·5 Gev/n have been measured using emulsion-graphite sandwich stacks exposed to the primary cosmic radiation at Hyderabad, India (Geomagnetic latitudeλ=7·6° N). The results are based on a total of 213 nuclear interactions observed in graphite. Since the atomic number of graphite is very close to the mean atomic number of air, the parameters derived for graphite medium are directly applicable to air. A comparative study has been made of the results thus obtained with similar data available for nuclei of E?1·5 Gev/n.     

A study of blanketing sporadic E in the Indian equatorial region

The paper describes the nature of the sporadic E layer of blanketing type observed at Kodaikanal (Lat. 10°·2 N; Long. 77°·5 E; dip: 3°·5 N). It is shown that in the Indian equatorial region, the frequency of occurrence of this type of E _s is abnormally large when compared to similar latitudes in the west and that changes of large magnitudes occur in the F2 layer of the ionosphere as well as in the horizontal force of the earth’s magnetic field simultaneously with the appearance of the blanketing E _s . Lunar effects have also been shown to exist both in the time of appearance of blanketing E _s and in its strength. Some evidence exists to show that blanketing E _s as well as the blanketing frequency,f _b E _s , have a biennial maximum. These characteristics are discussed as part of the Far East Anomaly.     

e-e Scattering cross-section measurements using page type geometry

Experiments to measure differential scattering cross-sections in electron-electron and positron-electron scattering have been performed. Page type geometry has been employed because of its line focussing pro-perty. Moderately intense radioactive sources could, therefore, be used. Measurements of cross-sections have been carried out over a continuous range of values ofq, the kinetic energy transfer. This paper reports on the measurements of electron-electron scattering cross-sections for energies in the range (0·2–0·65) Mev using thin mylar and aluminium foils of different thickness. M?ller formula has been verified within + 4%.     

Electrochemical behaviour of zinc in alkaline solutions

The cathodic and anodic polarization of zinc in different concentrations of alkaline solutions has been studied under constant-current conditions. The changes of zinc electrode-potential with reference to a Hg/HgO/KOH system have been measured both in KOH and zincate solutions using a “Luggin” capillary and a specially designed cell, current being drawn from an electronic current stabilizer. Time-potential curves have been plotted and it is found that the anodic zinc passivates at a certain stage showing a sudden rise in potential by as much as 3–4 volts. Before the passivation, the main electrode reaction is the formation of Zn⁺⁺, while after the passivation it changes to gas evolution. No definite relationship as previously suggested by Muller, between the current density and the passivation time was found, perhaps due to migration and non-linear diffusion effects and other reasons discussed in the paper. It has been found that the behaviour of zinc differs in concentrated alkaline solutions (i.e., 0·5 N to 5 N) from that in dilute solutions (0·2 N to 0·01 N), in which case the open circuit rest-potential of zinc is indefinite and may vary by as much as 500–600 mV., while the maximum passivation jump in potential is about 2 volts only. Also the passivation and the decay of current on breaking the circuit are found to be slower than in the case of concentrated solutions. Colour changes of the zinc electrode, during the polarization, are also briefly described and discussed.     

Mean amplitudes of vibration: Pyramidal XYZ2 molecules

The theory of mean square amplitude of vibration using the symmetry co-ordinates has been applied to the pyramidal XYZ₂ molecular model. The elements of the mean square amplitude matrices and the mean amplitude quantities at 300° K. for thionyl halides have been reported.     

Electrochemical behaviour of zinc in alkaline solutions

As the whole passivation phenomenon in the case of zinc is very quick and sudden and as it cannot be fully studied and followed by galvanostatic techniques alone, the constant over-potential technique has, for the first time, been applied to zinc and results reported. A special apparatus consisting of suitable oscillator, modulator, demodulator and a stable D.C. amplifier with a gain of 100,000 was used for the purposes and is described. Potential curves for equilibrium current rates, achieved on 0·1 V. and 25 mV. steps after 1 minute each, have been obtained in 6N, N, 0·1 N KOH and zincate solutions for the complete range of ?1·3 to about ?2·0 volts with reference to Hg/HgO/KOH reference electrode. It has been found that in the first truly active region, the main electrode reaction is the formation of zinc ions while after the passivation it changes to gas evolution. Potentiostatic techniques reveal intermediary stages, undisclosed by constant current methods, of pseudo-passivation and current-plateau regions in which the anodic layer thickens, controlled by the high field cation transport. These observations and explanations are further supported by plotting rate-time transients obtained by suddenly dropping the potentials from higher to lower values, when the rates were found to cut off. Some anomalies and sudden reversal of currents with increasing over-voltages, have also been fully discussed. The influence of other factors,e.g., concentration, stirring, sudden changes in over-voltages, presence of zincate, sulphate, etc., has also been considered. Studies such as these are found to throw considerable light on the electrochemical behaviour of zinc.     

有关殆素数的二元丢番图不等式

$P_r$ 表示最多 $r$ 个素因子的正整数. 作者证明了, 对于任一足够大的实数 $N$ 和 $1相似文献   

Investigations on multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsions

The charge spectrum obtained from measurements made on tracks of 1329 nuclei of the cosmic radiation of Z?6 and E?7·5 GeV/n has been studied in detail using emulsion stacks exposed over Hyderabad, India (cut off rigidity=16·8 GV) at a depth of 6·8 g/cm² of air for 7¼ hrs. This spectrum has been compared with that available for nuclei of E≥1·5 GeV/n. Within the limits of experimental errors, no dependence of the flux values or ratios of intensities with energy are noticed. This result has important implications on the origin and history of the cosmic radiation. Integral energy spectra of M and H-nuclei have been derived making use of the flux values at the two locations; the spectra thus derived have the least errors associated with these.     

A kinetic study of the reaction of diols with hydrogen halides

The kinetics of the reaction of diols with various hydrogen halides is discussed. The reaction involves neighbouring group participation as postulated earlier, the rate of substitution being faster for a heavier nucleophile. The reactions are inert in aqueous systems as the X^? nucleophilicity becomes negligible as compared to the nucleophilicity of water. At and above 7·5 per cent. water these reactions do not occur. Variation of dielectric constant also notably affects the process.     

Spins of the first two excited states in27Mg by an angular correlation technique in the reaction26Mg (d,pγ)27Mg

Proton-gamma-ray angular correlation measurements, employing the ‘method II’ of Litherland and Ferguson, have been made in the reaction²⁶Mg (d, pγ)²⁷Mg, using 1·80 MeV deuteron beam and detecting the outgoing protons at 0° with respect to the beam. Analysis of these measurements leads to spin assignments of 3/2 and 5/2 for the 0·98 and 1·69 MeV excited states of²⁷Mg. The 1·69 MeV second excited state is found to decay almost completely to the ground state.     

华林-哥德巴赫问题:两个平方,两个立方和两个四次方

令P_r表示素因子不超过r的殆素数,按重数计.作者证明了对于充分大的偶数N,方程N=x~2+p_1~2+p_2~3+p_3~3+p_4~4+p_5~4有解,其中x是殆素数P_6,p_j(j=1,…,5)是素数.     

Recent observations on cosmic electrons and their consequences on different cosmic ray models and related astrophysical quantities

An experiment has been carried out to study the electron component of the primary cosmic radiation at energies >12 GeV using a hypersensitised nuclear emulsion stack, flown oriented in the east-west plane over Hyderabad, India. The results of this experiment, on the basis of 28 identified electrons of energy above 12 GeV are: (i) the integral flux of electrons above an effective energy of 16 GeV is 0·51±·10 per m.² sec. sr.; (ii) the differential energy spectrum between 12 and 300 GeV can be represented as N(E)dE=12·7 E^?2.1±·2 dE m.^?2 sec.^?1 sr.^?1; and (iii) the fraction of positrons among the total electrons in the energy region 12 to 30 GeV has been discussed. A critical study has been made on the applicability of different cosmic ray models by making use of the observed differential energy spectrum of electrons and the relevant astrophysical parameters associated with the confinement regions. The confinement regions considered are: (i) the universe as a whole, (ii) the super cluster to which our galaxy belongs, (iii) the galactic halo and (iv) the galactic disc. The consequences of the recently postulated universal black body radiation at 3° K. on the cosmic ray models have also been considered. Some of the crucial experiments needed to set more stringent constrains on the models which would then permit meaningful interpretation, are enumerated.     

A high resolution spectral analysis of daily relative sunspot number and 10·7 cm. Solar flux

Auto and cross-spectra of relative sunspot number and slowly varying component of solar radiation at 10·7 cm. have been computed for a 52-month period beginning September 1, 1958. Significant features of the spectra are relatively high variance at periods corresponding to one, three and four solar rotations. Statistically significant spectral peaks have been observed at three other frequencies and are ascribed to amplitude modulation of the 27-day component. The cross-spectral analysis indicates that during the period under investigation the solar 10·7 cm. flux leads the sunspot number for periods in excess of about 27·7 days; for shorter periods the flux lags behind the sunspot number. The coherence between the two time series, after an initial decrease from unity at zero frequency, assumes a maximum value of 0·985 at 27·7 days. The phase and coherence indicate that long-lived radio emission regions and spots appeared to co-rotate during 1958–62 with a period of 27·7 days.     

Isotropic background cosmic X-rays in the energy range 50–290 KeV

The observations of omnidirectional X-ray flux at the top of the atmosphere have been extended upto 200 KeV using a balloon-borne NaI (Tl) scintillator detector at Hyderabad, India. The omnidirectional flux at 60 KeV is found to be 0·0066±0·0014 photons/cm.² sec. ster. KeV. The X-ray flux in the energy range 50–290 KeV can be adequately represented by the spectrum Ke^?2.2±0.4. New upper limits to the hard X-ray flux from the quiet sun have also been obtained from the same measurement.