limbs is practically as complete as that of the limbs in their normal position. When transplanted posteriorly the distance of three segments, the third spinal nerve no longer contributes to the innervation of the limb and the function of limbs in this position is less complete (table 2, series AS3).

When transplanted posteriorly the distance of four segments, all cases studied, with one exception, show that the fourth spinal nerve no longer contributes to the innervation of the limb and that limbs in this position exhibit still greater imperfection of function (table 2, series AS4).

FIG. 2. GRAPHIC RECONSTRUCTION OF THE RIGHT BRACHIAL PLEXUS OF CASE A S426, SHOWING THE SEGMENTAL NERVE SUPPLY TO THE RIGHT ANTERIOR LIMB TRANSP LANTED THE DISTANCE OF 4 SEGMENTS POSTERIOR TO THE NORMAL POSITION. X 20

In the series AS5 in which the limbs were implanted the distance of five segments posterior to the normal position, there occurred only one case of those studied (case AS525, table 2) in which the limb received innervation from the fifth spinal nerve, the remainder being innervated by nerves posterior to the normal brachial nerves. With this general failure of the limbs in this position to receive innervation from the normal brachial nerves, it is found that still greater restrictions are placed upon their movements, there being only four cases in thirty which functioned normally (table 1 A).

In the series AS6 in which the limbs are so far removed that they receive no contribution from the normal limb nerves nor from the

sixth and seventh nerves, there are no cases which function normally, forty eight per cent being totally incapable of movements and fifty one per cent showing only greatly impaired movements (table 1 A and table 2).

Inasmuch as there are practically no structural deficiencies within the transplanted limb itself, the gradual decrease in the function of the limbs, as they are implanted more and more remote from the normal region, suggests the following possible factors as conditioning their degree of function, (a) structural deficiencies in the shoulder girdle, (b) deficiencies in the shoulder musculature, (c) the failure of certain of the shoulder muscles to receive innervation and (d) the absence of proper central neurone connections.

The shoulder girdle being a mosaic (Detwiler), there is considerable variability in the degree of its development in the transplanted position, yet it is found that its development, in general, is no less complete in cases where the limb has been removed a considerable distance from the normal region than in those where the limb has been removed only a short distance. The difference, therefore, in the degree of function of the limbs could hardly be a result of this factor alone. Secondly, a study of the cross section anatomy of the shoulder region of the transplanted limbs shows that shoulder muscle differentiation does not become less complete as the limbs are implanted more and more posteriorly. No cases have been found in which there was complete absence of any of the muscles which typically develop in the heterotopic position. Thirdly, peripheral efferent innervation to the shoulder muscles, although somewhat less complete quantitatively in the more posterior positions than in cases where the transplanted limb receives segmental nerves from all or a part of the normal limb level of the cord, is no less developed qualitatively, practically all of the individual muscles receiving some nerve fibers. Certainly the degree of defective peripheral innervation could hardly account entirely for the very imperfect movements exhibited by limbs in the series AS5 and AS6 (table 1 A).

The remaining factor viz: defective connections within the central nervous system appears to be the only one which will adequately account for the marked deficiency of function in limbs transplanted so far posteriorly as to be beyond the point where they receive peripheral innervation from the normal limb level of the cord.

Although in normal larvae of this age, the most obvious motor responses to various types of peripheral stimulation consist of total swimming reactions, under certain controlled conditions motor responses

may be almost entirely limited to co-ordinated movements of the limbs. Such responses may be carried out perfectly by the transplanted limbs when their peripheral innervation is derived from the normal limb level of the cord, but the ability of the transplanted limbs to exhibit movements, co-ordinated with the opposite intact limb, decreases markedly when their peripheral innervation is derived from segments well beyond the normal limb level (series AS6).

As has been shown by Herrick we have developed here a central nervous architecture by means of which peripheral sensory stimuli pass through more or less localized ascending sensory tracts from the cord to the medulla (tractus spino-bulbaris), to the midbrain (tractus spinotectalis) and to the thalmus (tractus spino-thalamicus). These stimuli may become finally discharged into the somatic motor centers of the spinal cord by means of descending tracts such as the tractus thalamobulbaris, tractus tecto-bulbaris, the fasciculus longitudinalis medialis and the tractus bulbo-spinalis. According to Herrick the cell bodies of the tractus bulbo-spinalis lie in the general motor tegementum of the medulla and their axones are directed ventrally into the ventral funiculi of the same and the opposite side. It is highly probable that a certain number of these fibers normally develop only as far as the third, fourth and fifth segments of the cord for specific discharge into the normal appendicular somatic motor centers. The fact that transplanted limbs, receiving peripheral innervation from these levels, exhibit movements which are co-ordinated with the opposite intact limb, strongly suggest such a condition. The behavior of limbs innervated mainly from the sixth, seventh and eighth segments of the cord (series AS5) suggests that these descending neurones, which normally end in the limb level, may be induced to continue their growth an additional segment or two to meet the functional demands imposed upon them by the transplanted limb. Their incapacity for further functional regulation is suggested by the loss of co-ordinated function and the greatly impaired movements that are exhibited by limbs of the series AS6, probably none of which receive peripheral innervation from segments of the cord anterior to the eighth.

The increase in the number of cases with total loss of function as the limbs are implanted more and more posteriorly (table 1 A) would also suggest that there occurs a corresponding increased deficiency in the connections of the purely intraspinal correlation neurones.

Additional limbs transplanted respectively three, four and five segments posterior to the normal intact limb of the host (table 1 B), never

attain the completeness of function attained by limbs in the same relative positions with the normal limb extirpated. Although such limbs may be well supplied with peripheral nerves, derived from segments of the cord posterior to the normal limb level, their greatly impaired movements appear to be a consequence of their inadequate supply of central efferent neurones, which run apparently only as far as the normal limb level where they discharge into the somatic motor centers of the normal intact limb.

The generally restricted and non-adaptive movements which these limbs do exhibit upon stimulation are probably effected through more or less imperfectly connected intraspinal, intersegmental correlation neurones of the levels from which peripheral innervation is derived.

A more complete account of the experiments reported in this paper will appear in later publications.

1 Braus, H., Morph. Jahrb., 35, 1906.

2 Banchi, A., Anat. Anz., 28, 1906.

3 Gemelli, F. A., Rev. Pathologia Nervosa Mentale, 11, 1906.

'Harrison, R. G., J. Exp. Zool., 4, 1907.

5 Detwiler, S. R., Ibid., 4, 1918.

* Herrick, C. J., J. Comp. Neur., 24, 1914.

THE INTERFEROMETRY OF RAPID VIBRATIONS1 CHIEFLY

IN RELATION TO TELEPHONE CURRENTS

BY C. BARUS

DEPARTMENT OF PHYSICS, BROWN UNIVERSITY

Communicated June 13, 1919

1. Introductory. The preceding apparatus2 with telescopic or microscopic enlargement of the telephonic vibrations, behaved on the whole so satisfactorily, that it seemed worth while to try a similar design on the interferometer. I was inclined to doubt the feasibility of the plan; but it appeared on trial that the high tension wires actually keep the auxiliary mirrors of the interferometer practically quiet; so that in the absence of alternating current it is not difficult to find the fringes. Tense wires are out of step with the usual laboratory tremors. The system needs no special damping.

The displacement of achromatic fringes due to the induced secondary current is normal to their direction. The objective of the vibration telescope is to oscillate in the direction of the fringes and to

be coupled with the primary current. A full account of the changes of phase and amplitude in any transformer system may then be obtained from the fringe ellipses usually seen in the interferometer.

2. Apparatus. Wide Bifilar. This is in large measure a modification of the apparatus described heretofore3 except that special attachments have been added for sharply reaching the resonance tension of the wire. The latter is shown at de e' d' in figure 1 (front elevation), being the thinnest steel music wire, about 0.023 cm. in diameter. Its ends are wound around the stiff screws b, b', provided with locknuts, and rotating in horizontal short strong rods a, a', attached to stout standards (not shown) fixed to the bed plate A, B of the interferometer. The wire dd' passed around the grooved pulleys w, w', and above the grooved pulley x, carried in a fork and screw stem y. The latter may be raised or lowered by the nut u, which rests upon the massive carriage BB, supported by the slides AA' of the apparatus. Provision must be made (slotted sheath and pins, not shown) to prevent y from turning on its axis. Tension is roughly given to the wire at the screws b, b', and the fine adjustment is thereafter made at the nut u. This worked very satisfactorily.

The vibrator proper cc' is attached at the middle of the wires d, d', and carries the parallel auxiliary mirrors m, m', of the quadratic interferometer. A thin steel umbrella rib seemed well adapted to fulfill the requirements of cc' though a light soft iron tube would have been preferable.

The telephones T and T' are adjustable on special standards, attached to the bed plate (carriage BB) and placed horizontally, one in front and the other toward the rear of the vibrator cc'. It is desirable that one be adjustable on a micrometer screw and spring, so that the distance of the poles of both from cc' may be regulated.

The achromatic fringes in the fine slit image of the telescope field of the interferometer must be observed with a vibration telescope, and it was found desirable to control the latter by a special electromagnet. Figure 2 is a diagram of the parts of the apparatus as a whole, M M' N N' being the mirrors of the interferometer (M' on a normal micrometer screw), m, m' the auxiliary mirrors on the vibrator cc'; T', T, are the telephones (one provided with a switch r), V the vibration telescope, I the mercury interruptor. T" is an auxiliary telephone for the ear.

The primary consists of the linear coil P described in the preceding paper, the storage cells E (usually four), and the two small electromagnets e, e', for controlling the interruptor and the objective of the