We develop the quantization of spherically symmetric gravitational systems using the Dirac formalism and the WKB approximation. The particular application is the nucleation of false-vacuum bubbles, which may have been the origin of the inflationary universe and matter. Consistency between our results and those obtained by the Euclidean method requires that the latter include metrics with degeneracies. Our work also raises several other questions of principle, including the meaning of the wave function and the necessity of topology change. A tentative application of this work to quantum cosmology indicates that the "Hartle-Hawking wave function" is inconsistent. 4042-

Unaccustomed eccentric exercise, in which a muscle is lengthened while generating tension, is well known to cause injury and pain. A rapid training effect has been demonstrated in a number of eccentric exercises. The mechanism for both the damage and the training has been unknown. Morgan proposed that the damage is caused by sarcomere length instabilities during operation on the descending limb of the sarcomere length-tension curve and that the training effect is an increase in the number of sarcomeres connected in series in a muscle fiber, thus avoiding the descending limb (Biophys. J. 57: 209-221, 1990). We tested this proposal by exercising rats on a treadmill set at either an incline or a decline of 16 degrees, an exercise that has previously been shown to cause damage in untrained rats and a training effect. The vastus intermedius muscles were fixed and were digested in acid, and the fiber and sarcomere lengths of representative fibers were measured. From these measurements, the mean number of sarcomeres per fiber was found for the different training regimes. A clear and repeatable difference was found, supporting Morgan's prediction of more sarcomeres after decline running, although with some differences in response that depended on the age of the rats.

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The short-range stiffness of smoothly but submaximally contracting isometric soleus muscles of anesthetised cats was measured by applying small fast stretches. The ratio of isometric tension to stiffness was plotted against tension over a wide range of muscle lengths and stimulus rates. The results fitted a straight line well, as predicted from crossbridge theory, showing the stiffness to be a function of tension only, independent of the combination of length and stimulus rate used to generate the tension. The major deviation from this line was attributed to incomplete fusion at low frequencies of stimulation. Values believed to be tendon compliance and crossbridge tension per unit of stiffness were found from the graph, and the tendon compliance correlated with the maximum muscle tension. Shortening the tendon by attaching nearer to the muscle changed the results in a manner consistent with the theory, provided that appropriate precautions were taken against slippage.

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It has been proposed that lengthening of active muscle at long lengths is nonuniformly distributed between sarcomeres, with a few being stretched beyond overlap and most hardly being stretched at all. A small fraction of the overstretched sarcomeres may fail to reinterdigitate on subsequent relaxation, leading to progressive changes in the muscle's mechanical properties. Sartorius muscles of the toad Bufo marinus were subjected to repeated lengthening (eccentric) contractions at long lengths, while controls were passively stretched and then contracted isometrically or stretched at short lengths. The muscles undergoing eccentric contractions showed a progressive shift to the right of the length-tension curve, a fall in the yield point during stretch, an increase in slope of the tension response during stretch, and a fall in isometric tension. In control muscles, changes, if any, were significantly less. In electron micrographs, muscle fibers that had been subjected to a series of eccentric contractions showed sarcomeres with A bands displaced toward one half-sarcomere, leaving no overlap in the other half. Adjacent regions often looked normal. These results are all in agreement with the predictions of the nonuniform stretch of sarcomeres hypothesis.

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SUMMARY1. A kangaroo hopping above a certain speed appears to consume less oxygen than a quadrupedal mammal, of similar weight, running at the same speed (Dawson & Taylor, 1973). This is thought to be achieved by storage of elastic energy in tendons and ligaments.2. Energy can be stored in a tendon by stretching it, but only if the muscle fibres in series with it are stiff enough to resist most of the length change. We have measured length and tension changes in the contracting gastrocnemius muscle of the wallaby Thylogale during rapid, controlled stretches, and from this determined the amount of movement in muscle fibres and tendon (method of Morgan, 1977).3. When the muscle was developing close to its maximum isometric tension, up to eight times as much movement occurred in the tendon as in the muscle fibres. This is made possible by the wallaby having a long and compliant tendon.4. Measurement of work absorption by the muscle with a full length of free tendon and when the tendon had been shortened, showed that with the shortened tendon a larger proportion of movement occurred in the muscle fibres, producing a steep rise in work absorption by the muscle and a consequent increase in energy loss.