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from one or more compound states, probably in the 'P and S configurations. '~'The position of the hydrogen resonance on the energy scale is in very good agreement with theoretical predictions, which range from 9.6 to 9.8 ev.Because of the difficulty of the present experiment the author had to seek advice on many aspects of the experiment. He is indebted to A. O.

An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the gravitational field is presented. Utiyama's discussion is extended by considering the 10-parameter group of inhomogeneous Lorentz transformations, involving variation of the coordinates as well as the field variables. It is then unnecessary to introduce a priori curvilinear coordinates or a Riemannian metric, and the new field variables introduced as a consequence of the argument include the vierbein components hkμ as well as the ``local affine connection'' Aijμ. The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system. The free Lagrangian for the new fields is shown to be a function of two covariant quantities analogous to Fμν for the electromagnetic field, and the simplest possible form is just the usual curvature scalar density expressed in terms of hkμ and Aijμ. This Lagrangian is of first order in the derivatives, and is the analog for the vierbein formalism of Palatini's Lagrangian. In the absence of matter, it yields the familiar equations Rμν=0 for empty space, but when matter is present there is a difference from the usual theory (first pointed out by Weyl) which arises from the fact that Aijμ appears in the matter field Lagrangian, so that the equation of motion relating Aijμ to hkμ is changed. In particular, this means that, although the covariant derivative of the metric vanishes, the affine connection Γλμν is nonsymmetric. The theory may be reexpressed in terms of the Christoffel connection, and in that case additional terms quadratic in the ``spin density'' Skij appear in the Lagrangian. These terms are almost certainly too small to make any experimentally detectable difference to the predictions of the usual metric theory.

The topic of cosmic strings provides a bridge between the physics of the very small and the very large. They are predicted by some unified theories of particle interactions. If they exist, they may help to explain some of the largest-scale structures seen in the Universe today. They are 'topological defects' that may have been formed at phase transitions in the very early history of the Universe, analogous to those found in some condensed-matter systems -vortex lines in liquid helium, flux tubes in type-II superconductors, or disclination lines in liquid crystals. In this review, we describe what they are, why they have been hypothesized and what their cosmological implications would be. The relevant background from the standard models of particle physics and cosmology is described in section 1. In section 2, we review the idea of symmetry breaking in field theories, and show how the defects formed are constrained by the topology of the manifold of degenerate vacuum states. We also discuss the different types of cosmic strings that can appear in different field theories. Section 3 is devoted to the dynamics of cosmic strings, and section 4 to their interaction with other fields. The formation and evolution of cosmic strings in the early Universe is the subject of section 5, while section 6 deals with their observational implications.Finally, the present status of the theory is reviewed in section 7.

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