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A thermometer has been constructed that is suitable for use in thermal gradient chambers. The water-proof sensing element is a forward-biased constant-current Schottky-junction hot-carrier diode. The voltage across the diode decreases with temperature in an approximately linear fashion and, with suitable corrections for the diode used, enables probe temperatures to be determined to within +or-0.05 degrees C over the range -65 to +50 degrees C.

It is shown that the neutrino radiation field emitted by a star may be described by Vaidya's radiating Schwarzschild metric. The gravitational energy shift of the neutrino field is also considered, both in terms of an exact solution and in the weak field approximation.

The gravitational properties of spherically-symmetric photon and neutrino radiation fields are compared and found to be identical. A model for the photon radiation field made up of incoherent radiation is first developed, equations for photons being required to satisfy Maxwell's equations.

Summary This paper attempts to combine a ‘classroom note’ about evaluating certain determinants with a brief exposition of a lesser‐known aspect of Potential Theory.

The object was to determine whether the depletion of histidine would have a more marked inhibitory effect on human leukaemia cells than on normal human cells, thus indicating a wider use for enzymes in cancer therapy. Studies of the effect of histidine concentration on cell growth, death, metabolism, protein composition, histidine uptake and utilization by cells were carried out. The medium and intracellular concentrations of histidine required for optimum cell growth and metabolism were much lower than for any other amino acid that has been studied. Also, there was very little evidence of cell death occurring in the absence of histidine. The results showed that cells in culture have a very low histidine requirement and that although the leukaemia cells were slightly more dependent upon histidine than normal cells the effect of histidine depletion is not critical enough to show much promise as a method of controlling leukaemia by therapeutic enzymes.

The nature of the non-linear interaction between two gravitational waves in the general theory of relativity is considered. A new exact solution of the vacuum field equations describing this case is given. It describes two gravitational waves with both transverse and longitudinal components, propagating in opposite directions along ‘shearing’ and ‘twisting’ geodesic congruences with zero contraction

It is shown that, in a region of space-time containing two independent electromagnetic waves propagating in different directions, it is not possible for the two waves to follow simultaneously affinely parameterised shear-free and twist-free null geodesic congruences.

(1975). Mathematics education today. International Journal of Mathematical Education in Science and Technology: Vol. 6, No. 1, pp. 3-15.

The physical situation of a star emitting neutrinos is considered. Some difficulties in the classical theory are mentioned, and a more detailed approach to the properties of neutrino radiation in general relativity is given. The classical theory is here regarded as a one-particle theory, and by summing over many particles propagating in randon radial directions, the energy-momentum tensor of the total radiation field is shown to approximate to the ‘geometrical optics’ type satisfying other conditions defining its radial and time dependence.

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An attempt is made to clarify the concept of "spontaneous magnetization" in idealized ferromagnets such as the Ising and Heisenberg models. Some definitions in common use are discussed; their equivalence is not obvious. It is shown that a value based upon the probability distribution of the total magnetization cannot exceed the spontaneous magnetization based on bulk thermodynamic properties when the magnetization and exchange operators commute. A convexity argument shows that a definition of spontaneous magnetization based on minima in the (bulk) free energy is not applicable to systems with short-range interactions. Reference is made to difficulties arising when magnetization and exchange operators do not commute.

In the Proceedings of the Royal Society of Edinburgh, vol. xiv. [No. 123], pp. 97–106, there is a paper of mine under the above title. I wish in the present memoir to communicate to your distinguished Society further details relative to these investigations. The principle of these researches is to find some germicidal agent capable of destroying the microbes of disease, which have been proved to reside in the blood, and are the causes (directly or indirectly) of certain contagious diseases. At the same time, an aqueous solution of such an agent, while destroying the microbes of disease, must have very little or no detrimental action upon the blood. Having found such a substance, the rationale is to inject (hypodermically) a solution of the microbe-destroyer directly into the blood. By so doing, the destruction of the pathogenic organisms in situ would be the result.

The thermodynamics of critical points in multicomponent systems, more generally systems with more than two independent variables (including binary fluid mixtures, the helium $\ensuremath{\lambda}$ transition, order-disorder transitions in alloys, and antiferromagnetism) are discussed from a unified geometrical point of view, in analogy with one-component (liquid-vapor and simple-ferromagnetic) systems. It is shown that, from a few simple postulates, the qualitative behavior near the critical point of quantities such as compressibilities, susceptibilities, and heat capacities, with different choices of the variables held fixed, can be easily predicted. A number of seemingly exceptional cases (such as critical azeotropy), which arise when critical or coexistence surfaces bear an "accidental" geometrical relationship with the thermodynamic coordinate axes, are explained in terms of the same postulates. The predicted results are compared with several theoretical models and experimental data for a variety of systems.

Some thermodynamic principles useful for understanding the heat capacity of a ferromagnet in an external field near its critical (Curie) point are discussed, with special emphasis on the influence of demagnetizing effects. Two simple examples show the variety of behavior which may be expected, depending on the magnitude of the external field. The utility of considering low-field and high-field limits is pointed out, with particular reference to Ni and EuS.

In (1), Higman introduces the unrestricted free product of a set of groups, and gives it a natural topology. When this set is an infinite sequence of free cyclic groups he denotes by F their unrestricted free product; we shall denote by K the product for a general sequence {Gn} and, throughout the paper, we assume that each Gn is non-trivial and countable. Higman proves as an incidental result that the commutator subgroup [F, F] is not closed in the topological group F, and the first object of this note is to generalize this result to K. From this, the more interesting deduction immediately follows that K is never equal to L = [K, K]. Indeed, we prove in fact that the cardinal of L and its index in K are both c, the cardinal of the continuum.

The results of an investigation into parental bereavement during childhood in a series of 279 psychiatric patients from the Leeds area is presented. The series consists of 162 depressive patients (103 in-patients and 59 out-patients), 69 schizophrenic patients and 48 individuals suffering from anxiety state. Control data have been obtained from a group of 100 psychiatrically normal Leeds general hospital out-patients and from two sets of control material originally employed by Felix Brown (1961). The findings are as follows: 1. In-patient, but not out-patient, depressives show an excess of maternal bereavement before the 15th birthday which is just significant at the p < 0.05 level. 2. Schizophrenics show no excess of childhood parental mortality. 3. Patients with anxiety state show no excess of childhood parental mortality. 4. There is no excess of paternal mortality for any diagnostic category. 5. None of the diagnostic categories shows any significant excess of parental bereavement occurring at a particular stage in childhood. The significance of these findings is discussed.

After some years of patient observation and research, I have found, from direct experiment, that at certain times the contractile or pulsating vacuole of the Protozoa performs the function of a true kidney, or, in other words, its secretion is capable of yielding microscopic crystals of uric acid.Three organisms were used in these experiments, namely:- Amœba, Vorticella, and Paramœcium.

In (6), Kiang gives an example of a simply connected (closed) region D in 3-space R3, bounded by a smooth 2-sphere ∂D, whose (harmonic) Green's function Γ has a critical point for any choice of pole p ∈ Int D—contrary to the analogous 2-dimensional situation. It is not known whether any position of p exists, for which Γ is non-degenerate in the sense of Morse theory; however, we show here the following result.

Increases in electrical resistivity after quenching thin bars of uranium monocarbide have been measured and interpreted in terms of lattice vacancies. The activation energy for vacancy formation is deduced as ∼2.8 ev. From annealing experiments the activation energy for movement was found to be ∼1.1 ev and a vacancy makes 5 × 1010−1011 jumps during its lifetime.

It has been established that although an inhibitory interaction occurs when a culture of human diploid cells become crowded together (contact inhibition of growth), multiple-layered cell sheets are obtained by using a continuous medium perfusion culture. A similar effect is obtained when the culture medium is changed at frequent intervals, and this paper reports the effects of a medium change on cell growth and metabolism. A direct relationship was found between cell yield and the number of medium changes given to a culture. This was an unexpected result because normally when a culture is prolonged by additional feeding the cell yield shows a diminishing return. The amino acid and glucose uptakes and growth yields (the ratio of the amount of cell dry weight produced to substrate used) were determined and they also showed that a unit amount of growth occurred per medium change, and that cessation of growth was accompanied by cessation of nutrient uptake and metabolism. Medium changes had a profound affect on cellular metabolism, especially on DNA and protein synthesis. As a culture approached confluency, DNA, RNA and protein synthesis were sequentially inhibited. After a medium change there was a sequential stimulation of DNA, RNA and protein synthesis in the same order as they were inhibited. The inhibitory mechanism that is affected by cell crowding is obviously reversed by a medium change. The results presented in this paper suggest that contact inhibition of growth primarily affects DNA synthesis and that if the cell is able to take up a sufficient supply of nutrients in a crowded culture then this inhibition can be overcome.

The opinion of the most profound workers in the so-called “germ diseases” is, that these diseases are really due to the pathological effects of chemical substances (ptomaïnes) elaborated and secreted by certain micro-organisms. That is, a given contagious disease is rather the result of one or more compounds formed by the life-history of a micro-organism, than the mere presence of that micro-organism itself. By looking at certain cases in the above light, we can well understand why persons suffering with cholera die so rapidly. The alkaloid or ptomaïne (discovered by Pouchet in 1885) which the Comma bacillus secretes or forms is rapidly absorbed into the blood, long before the bacillus itself is capable of being absorbed by the mucous membrane of the intestine, and then into the blood. It is a well-known fact that most micro-organisms multiply with great rapidity in the media in which they live, and if particular organisms can be destroyed, the harmful effects of the products produced by their life-histories will not increase, and the disease will soon be at an end.

was to consider relationships between the local groups occurring in the Vietoris, singular and homotopy theories. The referee suggested that the local "C" and "D" groups occurring in the theory and defined in [5] and [6] (hereafter referred to as LTI and CTM respectively), were not "functorial" in the sense that the isomorphisms connected with them were merely "abstract," not induced by maps of one space into another and so not natural. He outlined a new approach using inverse and direct systems of groups, and in many cases the limits of these were isomorphic to the corresponding "C" and "D" groups; but in some cases the limits gave the "wrong" results. To overcome this, he suggested the idea of a stable system, where to postulate stability is to postulate something rather stronger than, but often equivalent to, existence of the "C" and "D" groups. (In locally Euclidean spaces and the generalized manifolds of Wilder [15], stability occurs at each point in each dimension.) We have therefore re-cast the whole of our previous theory in terms of these new concepts, thereby obtaining a more harmonious theory than before; and many of the results of the earlier draft together with analogues of results in LTI and CTM are here obtained. The plan of the paper is as follows. There are four sections: in §1 we prove all the basic results we later need on inverse and direct systems of groups, concerning their "stability" under mappings of various sorts. §11 is devoted to a discussion of certain relationships berween Singular and Vietoris homology. In §111, we derive certain results concerning homotopy, which are applied in §IV with the earlier ones to prove theorems concerning the local groups there. Corollaries of theorems in II and III give useful global results of the form:—if XCY, then under certain conditions and with different values of the functor G, the image of the injection G(X)—>G(Y) is finitely generated (see 2.33,3.14, 3.15). §IV is concerned essentially with three matters: first the proof that the Wilder manifolds, as mentioned above, have the stability property; second, implications between the various types of local connectivity, with some pathology; and third, proofs that for Singular and Vietoris homology, all the local groups we define (using stability) give the same end-product, i.e. the same class of manifolds,—with a similar but more restricted result for homotopy. Moreover, a "local" theorem of Hurewicz type is proved in 4.35.

The following results for spin‐½ Ising ferromagnets are extended to the case of arbitrary spin: (1) the theorem of Lee and Yang, that the zeros of the partition function lie on the unit circle in the complex fugacity plane; (2) inequalities of the form ≥ , where A and B are products of spin operators; (3) the existence of spontaneous magnetization on suitable lattices. Results (2) and (3) are also extended to the infinite‐spin limit in which the spin variable is continuous on the interval −1 ≤ x ≤ 1.

In (1), Higman introduces the unrestricted free product of a set of groups, and gives it a natural topology. When this set is an infinite sequence of free cyclic groups he denotes by F their unrestricted free product; we shall denote by K the product for a general sequence {Gn} and, throughout the paper, we assume that each Gn is non-trivial and countable. Higman proves as an incidental result that the commutator subgroup [F, F] is not closed in the topological group F, and the first object of this note is to generalize this result to K. From this, the more interesting deduction immediately follows that K is never equal to L = [K, K]. Indeed, we prove in fact that the cardinal of L and its index in K are both c, the cardinal of the continuum.

The infinite‐volume limit of thermodynamic functions calculated in the quantum microcanonical ensemble is shown to exist for a fairly wide class of spin systems and quantum gases. The entropy is set equal to the logarithm of the number of eigenstates in an energy interval which increases linearly with the size of the system, but is otherwise arbitrary. The limiting entropy per unit volume agrees with that calculated in the canonical formalism, and possesses certain convexity properties required for thermodynamic stability. A precise criterion, in terms of the energy spectra of large systems, is given for determining the limit of the thermodynamic entropy as the temperature approaches zero. This is not determined by the degeneracy of the ground state, contrary to the discussion of the ``third law of thermodynamics'' found in some textbooks.

Dr P. W. Latham, in the Harveian oration at the Koyal College of Physicians, on October 17, 1888, supported my own researches (which have already been published in the Proc. Roy. Soc. Edin., vol. xiv. pp. 97–106, and vol. xv. pp. 33–63), on the subject of “disease germs.” He says:—” “We might hope to find that the action and growth of the bacilli [of phthisis] might be inhibited by certain substances, and then, by injecting these substances into the blood, disease might be prevented, or if disease existed it might be arrested or cured.”

This paper details an investigation undertaken to see the influence of certain rays of white light on root-absorption and assimilation in the vegetable kingdom. One of us has been for some years investigating a problem as to the use of ferrous sulphate as a plant food (see Dr Griffiths' memoirs in Journal of Chemical Society [Trans.], 1883, 1884, 1885, 1886, 1887). In the experiments to be detailed here, we have used ferrous sulphate as an indicator of root-absorption.

Summary In June 1963 an outbreak of a dengue-like illness occurred in Jamaica. The only recorded dengue epidemic in Jamaica before that of 1963 had been in 1824, as mentioned in church records of causes of deaths. Over 450 primary inoculations of serum from acutely ill patients and from mosquitoes associated with them were made in animals and in tissue-cell cultures. A possible isolation was made in one cell culture inoculated with material from Aedes aegypti mosquitoes, as evidenced by interference studies. Otherwise, no isolation was made, although inoculated suckling mice gave signs of disease of the central nervous system. The characterization of the epidemic as “dengue-like” was based upon the clinical course of patients and upon serologic findings.

A notation for critical exponents at a tricritical point is proposed on the basis that the line of critical points observed experimentally in metamagnets, N${\mathrm{H}}_{4}$Cl, or ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures defines a special direction in the space of thermodynamic parameters. Scaling at a tricritical point implies certain relations among the exponents which are summarized in a table.

Weyl's neutrino equations are exhibited as equivalent tetrad equations, and the tetrad conditions for a pure radiation neutrino gravitational field are established. It is shown that the neutrino flux vector for the radiation field defines a shear-free and twist-free family of geodesics. A class of metrics is found which can be interpreted either as neutrino radiation or as null Einstein-Maxwell fields.

A new solution of the Einstein-neutrino field equations is given. This solution is of Plebanski class [4n]3 and describes a beam of neutrinos propagating along straight geodesies but possessing an inherent angular momentum density. Another previously known solution is also examined, and using some calculations given by Bonnor it is concluded that a uniform beam of neutrinos is gravitationally stable and that two such beams radiating in the same sense do not interact.

An inequality for correlation functions in an Ising model with purely ferromagnetic interactions between pairs of spins is established and used to show that the magnetization in such a model is a concave function of external field H for H > 0. The concavity of magnetization, which holds not only for spin‐½ but also for arbitrary‐spin Ising ferromagnets, provides a basis for certain thermodynamic inequalities near the ferromagnetic critical point, including one involving the ``high temperature'' indices α and γ.

The neutrino-gravitational field is divided into fourteen distinct classes. This classification is shown also to determine the class of the space-time. Then for four particular classes of space-time, necessary and sufficient conditions on the concomitants of the Ricci tensor are given for it to admit a neutrino field. It is further shown that for three of these classes the neutrino field is determined uniquely by the metric of space-time.

Conditions for the existence of a neutrino field are expressed in terms of spin coefficients. It is shown that a neutrino-gravitational field with positive energy density necessarily defines a null geodesic congruence. The structure of the Ricci tensor is examined and shown to be closely related to the twist and shear of the congruence.