amalgamation of the zinc must go on in the cell to enable it to reach the steady state, and that it may not be sufficient to introduce amalgamated zincs. On this and some kindred points, however, we are still experimenting. The grey deposit can be shown to be mainly mercury in a state of very fine division. There are some indications that a slight acidity in the solutions is of use in promoting amalgamation. We have verified repeatedly an observation of Dr. Hopkinson's that the E.M.F. of a bad cell changes considerably if the cell be slightly shaken, while that of a good cell is not affected. The paper also contains an account of some experiments on the coefficient of change of E.M.F. with temperature. The value found is 0.000755 per 1° C., practically the same as that given by Lord Rayleigh. In this connexion we may mention the important observation that when the temperature is rising, even although the rise be only a few degrees, the E.M.F. of the cell may-especially if the cell be large-lag very considerably behind the temperature. On one occasion in which the temperature rose by some 5° C. in about a week, the E.M.F. of our large cell at the end of the week corresponded to a temperature nearly 3° lower than that given by a thermometer in the bath with the cell, being about 0.0027 volt too high. In this case a thick cake of crystals had formed on the top of the more solid portion of the paste, and the zinc sulphate solution only attained the state of saturation corresponding to the temperature by very slow degrees. Mr. Carhart and Mr. Swinburne have called attention to the difficulties which thus attend the practical use of the cells. They are to some extent met by using small cells. The paper also describes a new form of portable cell which may be turned into any position without harm. Experiments have also been made on the mercury chloride standards described by Von Helmholtz. A set of these has been constructed which has an E.M.F. of very nearly 1 volt. A form of standard due to Gouy, in which oxide of mercury is used, has also been examined. The E.M.F. of these cells prepared with yellow oxide is, we find, 1.381 volts, and when prepared with red oxide 1.388 volts. By the kindness of Major Cardew several of our cells have been compared with the standards of the Board of Trade. The differences are very small, being about 0.0003 volt. The average of the Board of Trade cells is less than our standard by about this amount. The Board of Trade possess seventy-two cells, and Mr. Rennie, Major Cardew's Assistant, informs us that the greatest difference between any two of them is under 0.0007 volt. It will be seen from the table given that, while the cells there considered are on the average about one of our units above our standard, they are rather over two of such units above the Board of Trade cells. Thus our standard exceeds the cells of the Board of Trade by rather over one of our units, or about 0·0003 volt. If we take the E.M.F. of our standard as 14342 volts at 15°, the cells of the Board of Trade average in E.M.F. about 1·4339 volts at 15° C., or 1·4321 volts at 62° Fahr. III. "Note on the Functional and Structural Arrangement of Efferent Fibres in the Nerve-roots of the Lumbo-sacral Plexus." (Preliminary Communication.) By C. S. SHERRINGTON, M.A., M.B., &c. Communicated by Professor M. FOSTER, Sec. R.S. Received March 14, 1892. At the commencement of some observations on the reflex mechanisms of the spinal cord in Macacus rhesus, difficulties were encountered which made it desirable to attempt for that animal a somewhat particular examination of the distribution of the efferent and afferent spinal nerve-roots belonging to the lumbo-sacral plexus. The present communication has reference to the distribution of the efferent fibres of the roots. Reil,* Scarpa,† A. Monro,‡ and Soemmering§ all paid considerable attention to the arrangement of the root-bundles in the limb plexuses, but physiological work upon the subject commenced with Van Deen,|| J. Müller,¶ and Panizza.** The former two gave an anatomical significance to the plexus, the last a physiological. At Müller's suggestion, renewed research was undertaken by H. Kronenberg++ in 1835. Kronenberg confirmed Müller's observations as to the individual inconstancy of the contribution made by any spinal root to the nerve cords of the plexus; he also concluded that the excitation of a single nerve-root before its entrance into the plexus produces contraction of almost all the muscles of the limb; and that the arrangement is intended to protect against fatigue. Later, Eckhardt, working in Ludwig's laboratory, arrived at somewhat similar conclusions. He stated that a great number of muscles obtain nerve-fibres each of them from several nerve-roots; that there is a good deal of individual variation; that when a nerve-root is 'De Nervorum Structura,' p. 14. + 'De Gangliis et Plexibus.' 'Observations on the Structure and Functions of the Nervous System,' p. 34. § Anatom.,' Pars Vta. 'De Differentia et Nexu inter Nervos Vitæ Anim. et Organ.,' Leyden, 1834. T'Physiol. des Menschen,' vol. 2, p. 586. Annali Universali di Medicina.' + Essay (De Struct. et Virtut. Plexuum Nervorum'), Berlin, 1836. 'Zeits. f. Rat. Med.,' vol. 7, p. 306, 1849. unusually thick the additional fibres in it are not all of them, perhaps none of them, used to supply the muscles usually supplied by the root, but are used to supply altogether other muscles not usually supplied by the roots; that the distribution of the fibres of a root is not to one group of muscles, but is to several groups, which are often not related to each other in function; that antagonistic groups are often supplied by one and the same root. Three years after the experiments by Eckhardt, and also under Ludwig, Peyer's experiments on the brachial plexus of the rabbit were made. As Krause, in 1861,† repeated Peyer's work on the same limb and the same species, the results of both may be here referred to together. The muscles of the limb each receive nerve-fibres from two, in some cases three, spinal roots; usually the contraction of a muscle on excitation of the spinal roots innervating it is obviously different in degree for each root: the same spinal root does not always supply in different individuals the same muscles; the further the position of a spinal root from the head, the nearer the muscles it supplies to the distal end of the limb; the peripheral trunks of the limb plexus are themselves plexuses of root-bundles. In 1881 Ferrier and Yeo‡ confirmed the above results in experiments on the spinal roots of the monkey. In addition to their experiments on the brachial plexus, they performed four complete experiments on the lumbo-sacral roots. Unlike Kronenberg, Eckhardt, and others, they do not seem to have met with any variation in the results obtained. They revived the view that the efferent distribution of each spinal nerve is based on its physiological function, and that the movement resulting from the excitation of a root is that of a highly coordinated functional synergism. Some months later Paul Bert and Marcacci§ published experiments on the lumbar roots of the cat and dog. They concluded that (i) each root produces a coordinate movement, and consists of fibres functionally associated; (ii) when a muscle is functionally divisible its rootsupply is multiple. In 1883 Forgue and Lannegrace|| published a research on the limb plexuses of the cat, dog, and monkey. The 'Comptes Rendus '¶ of the following year contain their reports. As to the lower limb, their account is prefaced by a remark that the highest lumbar root of man is tripled in the dog and monkey. What species of monkey was used is not mentioned in the Comptes Rendus.' In Macacus the 5th lumbar root is analogous not to the 3rd of man, but to the 4th, and *Arch. f. Rat. Med.,' II, vol. 4, p. 67, 1853. + 'Beiträge zur Anat. der Oberen Extremität,' 1861. § Soc. de Biol.,' July, 1881. Gaz. Hebd. des Sci. Médic. de Montpellier,' 1883. to the 6th of the dog. The chief of their conclusions, drawn from examination of both limbs, are:-The majority of muscles are innervated by several roots. Excitation of a root determines in the muscles which it supplies a total, not a partial, contraction. The tributary fibres of the root are disseminated through the muscle supplied by it, and not "cantonnées" in a special zone of it. Each root has a muscular distribution almost absolutely constant in the animals of its own species. The functions of analogous roots differ very little in different mammalian species. Each root supplies muscles of very various, often of antagonistic, action. Excitation of a root gives a combined movement, but an artificial, not a functional. The roots that pass furthest into the member occupy the lowest position in the cord. The innervation of the two planes of flexors and extensors is not always symmetrical. The superficial layers are supplied before the deep. * Herringham, by minute dissection of the human brachial plexus, and, therefore, under disadvantage from inability to distinguish clearly between afferent and efferent fibres, arrived nevertheless at facts and conclusions of great importance. He found much individual variation, but evidence of certain "laws." Thus: any given root-fibre may alter its position relative to the vertebral column, but will maintain its position relative to other fibres; of two muscles, or two parts of a muscle, that which is nearer the head end of the body tends to be supplied by the higher, that nearer the tail end by the lower, root; of two muscles, that nearer the long axis of the body tends to be supplied by the higher, that nearer the periphery by the lower, root; of two muscles, that nearer the surface tends to be supplied by the higher, that further from it by the lower, root. Recently Langley,† in the course of a paper on the sweat nerves to the foot of the cat, refers to the movements of the limb produced by excitation of roots of sciatic plexus in that animal. He desired to ascertain whether the variation, which he finds considerable in the distribution of the sweat nerves (sympathetic system), has a correlative in the distribution of the nerves to the limb muscles. Like Kronenberg, Eckhardt, and Peyer, he finds that the movements resulting from stimulation of the same nerve-roots are not uniform, and that the want of uniformity goes hand in hand with want of uniformity in the root composition of the plexus, just such as displayed in Herringham's dissections. My own observations have been made, during the past three years, chiefly on the lumbo-sacral roots of Macacus rhesus; also on the frog, rat, rabbit, cat, and dog, chiefly for the sake of comparing those types with Macacus. The animals have been deeply anesthetised *Roy. Soc. Proc.,' 1887. 'Jl. of Physiol.,' September, 1891. with chloroform and ether. The excitations of the roots have been made in the spinal canal; the single root, or a component filament from it, has been isolated in the case of the lower roots of the cat and monkey, to a length 5, 6, or 7 cm., and lifted up by a silk ligature on to small platinum electrodes sheathed almost to the points. Series of weak induced currents have been used for excitation, one pint Daniell being in the primary of the ordinary physiological inductorium (R. Ewald's pattern). The secondary coil has usually been at a distance from the primary somewhat more than twice that at which a current was detectable by the tongue. Use has also been made of absolutely minimal stimuli, and largely of mechanical stimuli. For certain purposes, stimulation by quite strong electrical excitation has been used. In these experiments it became clear that the frequency of individual variation, as regards the anatomical and physiological constitution of the efferent roots of the lumbo-sacral region, was great enough to demand the recognition of a "pre-axial" and a "postaxial" class of innervation for each muscle and movement. By pre-axial class of innervation is meant that the roots connected with the muscles and the movements are more pre-axial than the roots connected with the same muscles and the same movements in the post-axial class of innervation. Thus, in the frog there is a pre-axial class of innervation for the hind limb, in which, for instance, the viith spinal root, as well as supplying the antero-internal thigh muscles, supplies the muscles on the front of the leg (tibialis anticus). There is a post-axial class in which the pretibial muscles are supplied by the viiith and ixth roots only. The post-axial class as measured in this way is the more usual. This may be merely because the above criterion, found convenient for distinguishing in any individual case the direction which the variation has taken in it, does not coincide with the mid point about which individual variation in the species is really oscillating. By "pre-axial" and "post-axial" classes it is not intended to imply that in the range of individual variation one case is not more frequently exemplified than are others; it is only meant that so frequent is the variation that no one case is sufficiently predominant to warrant the choice of it as a "normal" type, and that therefore it is more correct to treat the composition of the plexus of the species as multiple and then for convenience divide it into classes. I have thought two classes, "pre-axial" and "post-axial," a distinction sufficient to observe in my present description. Just as in the frog, so in the other animals employed, the " pre-axial " and " post-axial" class of the plexus have both been exemplified by individuals of each species. In the rat, rabbit, cat, and dog, the 9th subthoracic root sometimes supplies the intrinsic muscles of the foot (post-axial innervation), some |