tions of lifting and hammering which they respectively perform, but it is so proportioned to the leverage of the triceps, that the two muscles cooperate harmoniously in the action of striking a blow forward; unequal spaces being traversed and unequal resistances overcome, in the same period of time, so that the resulting position of the limb is precisely the one required: while the strength of the one set of muscles bears such proportion to that of the set with which it acts in concert, that both remain unfatigued for the same number of ac tions. It is this diversified adaptation of parts, which forms the chief characteristic of the mechanism of Nature. Working with unlimited means, she yet works with scrupulous œconomy; her structures no power is redundant, nor a single advantage lost; so that, however completely an arrangement may subserve one primary purpose, we find, upon renewed examination, an equally accurate adjustment to several secondary ends. When the means of estimating with precision the contractile force of the muscular fibre, are obtained, I have no doubt that these compound relations of power, lever, and motion produced, will form an interesting study*. Magendie † observes, that the intensity of muscular contraction depends partly upon certain peculiarities in the organization of the fibres, such as size, firmness, colour, &c., and partly upon the energy of the cerebral influence, or the "puissance de volonté," by which they are excited to action. Muscles acquire far more than their ordinary power, during those affections of the mind which stimulate the brain to strong action, such as rage, madness, &c., and also during certain convulsive *Borelli in his posthumous work De Motu Animalium, published in 1680, has entered into an elaborate analysis of the mechanical relations of the body, with a view to determining the absolute force of the muscles. But unfortunately his experimental data (see, for instance, Pars prima, cap. 8,) are as loose and unsatisfactory as the subsequent calculations are minutely accurate; and his reasonings are interwoven with a purely specu lative hypothesis of the nature of muscular fibre, which he supposes to consist of minute rhomboidal vesicles, contractile by inflation. By these means he brings out very startling results. Thus to the flexor longus pollicis manus alone, he attributes a tractile force of 3720 pounds; to the deltoid of 61,609 pounds; to the intercostals of 32,040 pounds;_to_the glutai of 375,420 pounds, &c. (see cap. 17, prop. cxxiv. et seq) Dr. Bostock considers his estimate of the force of the muscles of the thumb to be a hundred times too great. He has not noticed the twisted tendon of the pectoral in man, nor calculated its force and leverage. The only remarks upon its strength I can discover, are in cap. 22, prop. cciv., where, from its small relative size, he proves it to be impossible" ut homines propriis viribus artificiosè volare possint." + Physiologie, vol. i. p. 275. diseases which have similar cerebral effects. From these and some other facts adduced, he infers that cerebral influence on the one hand, and certain qualities of the muscular tissue itself on the other, are the two elements of muscular contractility. Mayo has indicated a method of determining the maximum strength of individual muscles, by ascertaining the weight that is required to rupture their tendons. This mode is founded upon the argument that the tension which the tendon can sustain, probably exceeds but little that which the fibres can exert; a supposition which is analogically probable, and in some measure supported by facts, since in præternatural contraction sometimes the tendon, sometimes the trunk, of a muscle gives way; proving that there is no great difference between the active and passive strength of these organs. The constant and equable stream of galvanism, afforded by Daniell's new battery, will furnish, I think, a good means of comparing the strength of muscles, of regular shape and equal size, by ascertaining the contractile force it induces in its passage through each. In order to subject any muscle to this experiment, it should be separated from its fellows, and, at the distal end, from its insertion. By the tendon, thus detached, it should be connected with a spring moving an index; and the bone, into which its opposite extremity is inserted, should be firmly fixed at a known distance from the spring. The trunk of the muscle should then be made part of the circuit; and the distance to which it moved the index during the transmission of the current for a given period (say one minute) might be taken to express the force of the muscle as compared with others submitted to the same treatment. The comparative dimensions and weight of such muscles as resemble each other in colour, firmness, and texture, would also probably bear some proportion to their comparative force. Although neither of these methods of estimating muscular contractility could be depended on alone, yet by a judicious application of each in turn, to corroborate or correct the results furnished by the others, a close approximation might at last be obtained. And since we have proof that there is an accurate balancing of muscular force in the fact that muscles, or sets of muscles working together, are fatigued, equally and simultaneously, we may fairly expect that whatever the ab • See Tetanus Cooper's First Lines of Surgery. + The contraction of the muscle only occurs at the instants of completing and interrupting the circuit. Contact must therefore be broken and renewed at regular intervals during the experiment; which is readily effected by means of a pendulum connected with the wire. See Becquerel's Traité de l'Electricité, vol. iv. p. 306. Third Series. Vol. 9. No. 56. Dcc. 1836. 3 D solute strength of muscles in different individuals may be, their relative strength will be found nearly alike in all, exception being of course made for the influence of habitual employments upon particular muscles. If, for example, in one arm the power of the biceps were one, and that of the triceps two, in another arm the power of whose triceps was two, that of the triceps would be four, or thereabouts; or if not so, the difference would be compensated by a counter-variation in the leverage. It is also probable that in the same individual, under va rious conditions of lassitude or excitement, whether produced by bodily or by mental affections, each muscle retains its normal relation in point of strength to the others, whatever may be its actual gain or loss of contractility. So that if this ratio were once established by the mean results of cautious experiments, it would be possible, from the absolute strength of one muscle, or set of muscles, to deduce by calculation the absolute strength of each of the remaining muscles in the same individual. We should of course meet with irregularities; some caused by disproportionate growth, and bearing an ascertainable relation to its degree; and others depending on circumstances beyond the range either of observation, or of calculation; but if a standard proportion does really exist, the deviations from it are certainly in opposite directions, and the true ratio will be discovered by taking the average of an extensive series of measurements and estimates. And when we reflect that within the last few years constant numerical proportions have been developed by Wenzel, Berzelius, Dalton, and others, in the chemical affinities of ponderable matter, and by Faraday in the action of the imponderable forces; and-still more to the purpose-that mathematical laws so fixed and definite as to serve for the distinction of species, have been discovered by Schimper and Braun* to regulate vegetable growth; it seems not unreasonable to surmise, that numerical proportions, as certain and invariable, may govern the secret workings of animal life, and be hereafter revealed by the discovery of accurate, though involved, mathematical relations, between the several organs of the animal machine+. A rigorous analysis of the mechanical relations of the mus Archives de Botanique, vol. i.; Martin's Abstract of Braun's Paper; Henslow's Introduction to Botany, p. 124; Lindley's Introduction to Botany, second edition, p. 91. Lindley thus states the result of the inquiry: The whole of the appendages of the axis of plants, leaves, calyx, corolla, stamens, and carpels,-form an uninterrupted spire governed by laws which are nearly constant." For the causes of the occasional deviations from these primary laws, see Henslow's Introduction, § 121. + I trust that an hypothesis thus indicated by the analogy of several ascertained laws, capable of inductive examination, and whether erroneous cular and osseous systems in various animals, would form a good foundation from whence, in future, to push forward such inquiries; and, besides this remote and dubious utility, contingent on the soundness of the foregoing speculation, such researches would be of considerable immediate advantage to science. They would give the geologist a new point of view in which to examine fossil bones, and might enable him to deduce, from the relative size, shape, and situation of the marks indicating muscular insertion, new particulars concerning the strength and speed of extinct creatures; they would probably point out to the comparative anatomist analogies and differences in the structure of animals, where none have hitherto been suspected; and above all, they would tend to introduce into physiology an exactness and certainty which the science has not yet attained. As a first step to such an analysis, I intend shortly to attempt a set of experiments on the contractility of the muscular fibre, by the several methods that have just been described. Those who undertake such researches should bear in mind that the friction of the tendons is an important element of the calculation. Muscles which are extended in a straight line between their attachments, and undergo no friction but that of the investing cellular tissue (as the gastrocnemius), have greatly the advantage of those whose tendons play over trochlear surfaces (as the obturator or not, likely to suggest to its investigators some useful experiments, will not be classed with the extravagant iatro-mathematical speculations which retarded the progress of physiology in the seventeenth and beginning of the eighteenth century. "Prudens quæstio dimidium scientiæ," says Lord Bacon, a sentiment admirably elucidated by Herschel in the Preliminary Discourse. "A well-imagined hypothesis," he says, "if it have been suggested by a fair inductive consideration of general laws, can hardly fail at least of enabling us to generalize a step further, and group together several such laws under a more universal expression,......and we may thus be led to the trial of many curious experiments, and to the imagining of many useful and important contrivances which we should never otherwise have thought of." To which may be added the following judicious remarks of Mr. R. Young: "As in practice nothing is perfect, and few things wholly without merit, so, in theories, perhaps, none are without error, nor any devoid of truth. The difference between opinions seems to lie chiefly in the different proportions of truth and error which they contain. If this be true, every advance in principles is only substituting a less imperfect theory for one more so, and the last ever leaves something for futurity to correct."-(Essay on the Powers and Mechanism of Nature, p. ix.) [We may refer the reader, on the subject of numerical proportious in animal organization, to our abstract of Dr. W. Adam's paper, "On the Osteological Symmetry of the Camel," in Phil. Mag. and Annals, vol. ix. p. 364: the paper itself will be found in the Transactions of the Linnæan Society, vol. xvi. p. 525 et seq. See also Lond, and Edinb. Phil. Mag., vol. iii. p. 457, vol. vi. p. 57, for notices of papers by Dr. Adam on the osteological symmetry of the human skeleton.-EDIT.] internus), or run in grooves (as the long head of the biceps), or perforate other tendons (as the deep flexor of the fingers), or turn through fibrous pulleys (as the digastric, the extensor of the toes, &c.). By comparing the effect of a known force acting on particular tendons, at first in their natural situations, and afterward detached and free, the influence of friction in each case would be readily determined. This source of error seems to have been very generally overlooked by writers on animal mechanics. I conclude, for the present, with suggesting that to distinguish the pectoralis major into "portio elevans" or "attollens," and "portio deprimens," might serve to impress the rationale of its peculiar insertion and twofold action, upon the memory of the student. LXXIX. Researches in the Undulatory Theory of Light, in continuation of former Papers. By JOHN TOVEY, Esq. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, HAVING deduced, (p. 500 of your last volume,) by a new method, the laws of the propagation of plane and spherical waves in elastic media, I will now, with your permission, show how the formulæ may be extended to the most simple cases which are known to occur in the undulatory theory of light, of waves not spherical emanating from a center of agitation. (1.) It will be remembered that in my paper at p. 270 of the last volume, the sums were considered as comprised in three classes, when it appeared that those of the first class, composed of odd products of the differences, vanish, in consequence of the first supposition there made respecting the arrangement of the molecules. The sums also of the second class, composed of even products involving odd powers of the differences, were neglected; because the terms of these sums must be about half of them positive and half negative, and consequently the sums themselves very small in comparison with those of the third class, which last, being composed of even powers of the differences, have their terms all positive. (2.) If the radius of the sphere of influence be not very much greater than the intervals between the molecules, the sums may or may not be sensibly the same for different directions of the coordinates, according as the intervals are the same or different for the different directions. Suppose, for example, every eight adjacent molecules to be at the corners of a rectangular parallelopiped; suppose fig. 1 to be a section of the medium, the dots denoting the molecules in their |