smaller subject were used for the determination of both the number of fibers and area of skin, the area of skin for each cutaneous nerve would be somewhat smaller.

V. THE BEARING OF THE AUTHOR'S ESTIMATE OF THE INNERvATION OF THE DERMAL SURFACE ON THE THEORY OF THE SPECIFIC ENERGIES OF NERVES.

It might be of interest to consider the bearing this estimate of the innervation of the skin has upon different theories as to the number of classes of nerve fibers that mediate the dermal sensations. If we assume with WEBER (1846) that impulses giving rise to sensations of heat, cold, pressure, and pain, pass over the same afferent cutaneous nerve fiber, then the above calculations will hold true, viz., one cutaneous nerve fiber, on the average, innervates 2.05 mm2. of the dermal surface, giving all these forms of sensation to that area. If, on the other hand, we assume with FOSTER (1891) that there are four classes of afferent cutaneous nerve fibers, then this estimate will have to be so changed that one cutaneous nerve fiber of each class will innervate, on the average, 4X2.05 mm2., or 8.2 mm2. of the dermal surface. To specify more in detail, one cutaneous nerve fiber of each class will have to innervate 4X1.3 mm2., or 5.2 mm2. of the dermal surface of the arm; and 4X3.15 mm2., or 12.6 mm2. of that of the trunk. If this theory be true, then a histological examination of the nerve terminations in the skin ought to show each cutaneous fiber of the dorsal roots to innervate, on the average, an area of the skin of the trunk equal to 12.6 mm2. However, until we know the amount of branching of these fibers, not only in the skin but also in the peripheral trunks, we are unable to judge whether or not it is possible for one nerve fiber to innervate so large an area of the skin.

I.

According to the estimate here made, about 79% of the medullated nerve fibers in the dorsal roots of the spinal nerves of both sides, or 1,032,730 fibers, go to innervate the dermal surface and about 21%, or 274,521, are afferent fibers

distributed to muscles and deep tissues.

The afferent fibers of

spinal ganglion origin passing in the rami communicantes are not separately considered in this estimate, but for the moment are classed with those passing to the skin.

2. According to my estimate (using the skin areas for a large man), one cutaneous nerve fiber in the dorsal spinal roots innervates, on the average, 1.08 mm2. of the skin of the head and neck, 1.30 mm2. of the skin of the arm, 2.05 mm2. of the skin of the entire body, 2.45 mm2. of the skin of the leg, and 3.15 mm2. of the skin of the trunk; and for each additional class of nerve fibers assumed we must increase the area proportionately.

3. If we assume, with FOSTER, four classes of cutaneous nerve fibers, then each fiber will have to innervate, on the average, 4.32 mm2. of the dermal surface of the head and neck, and 12.6 mm2. of the dermal surface of the trunk.

4. If there be four classes of afferent nerve fibers in the dorsal roots of the spinal nerves of man, then a histological examination of the nerve terminations in the skin ought to show each cutaneous nerve fiber to innervate, on the average, areas of skin as large as given above.

Donaldson, H. H.

VII. BIBLIOGRAPHY.

1901. Am. Text-Book of Physiol., Philadelphia, and London, Vol. II, p. 230.

Foster, M.

1891. Physiology, Pt. IV, London, p. 281.

Fubini, S. and Ronchi, J.

1881. Untersuch. z. Naturl. d. Mensch, u. d. Thiere. XII, p. 26. Funke, O. F.

1858. Untersuch. z. Naturl. d. Mensch, u. d. Thiere, IV, p. 36.

Henle, J.

1879. Handb. der Systemat. Anatomie. Braunschweig. Bd. III, Abth II, pp. 554 and 594.

Ingbert, C. E.

1903. Journ. Comp. Neur., Granville, Vol. XIII, p. 53.

Krause, C. F.

1844. Wagner's Handw. d. Physiol. Bd. II, p. 131.

Meeh, C.

1879. Ztschr. f. Biol. Bd. XVIII, p. 425.

Rauber, A.

1893. Lehrbuch der Anatomie des Menschen. 4. Aufl. Sherrington, C. S.

1894-95. J. Physiol., London, XVII, p. 211.

Stilling, B.

1859. Neue Untersuchungen über den Bau des Rückenmarks, Cassel, p. 602.

Voischvillo, I. (or Woischwillo).

1883. Relation of Calibre of Nerves to the Skin and Muscles of Man. (Russian). St. Petersburg.

Weber, E. H.

1846. Wagner's Handw. Bd. 3, Abth. 2, p. 500.

ON A LAW DETERMINING THE NUMBER OF MEDULLATED NERVE FIBERS INNERVATING THE THIGH, SHANK AND FOOT OF THE FROG-RANA VIRESCENS.

By HENRY H. DONALDSON.

(From the Neurological Laboratory of the University of Chicago.)

During the past three years, while following the studies of Dr. DUNN (1900 and 1902) on the innervation of the frog's leg, it has been my endeavor to discover whether there was any law determining the distribution of the medullated nerve fibers to the segments of the leg. This law has been found and is expressed as follows:

The nerve fibers entering the leg of the frog (Rana virescens) by the sciatic and crural nerves, are distributed to the thigh, shank and foot in numbers which, for each of these segments are equal to the sum of the efferent fibers,-taken in proportion to the weight of the muscles,—and of the afferent fibers,-taken in proportion to the area of the skin.

The data discussed in the following pages are intended to furnish the evidence for the law just stated.

To make this investigation it was necessary to know: (1) The relative number of medullated ventral and dorsal root fibers in the nerves supplied to the frog's leg.

(2) The relative weight of the muscles of the thigh, shank and foot.

(3) The relative areas of the skin for the thigh, shank and foot.

(4) The number of medullated nerve fibers entering the leg and also the number distributed to each segment.

(5) The number of medullated fibers distributed as muscular and cutaneous nerves to each segment of the leg.

With the exception of the data called for under (3), the facts needed were to be found in papers already published from this laboratory. We shall take up the points in the order just

given.

(1) The relative number of medullated ventral and dorsal root fibers in the nerves supplied to the leg.

The nerves sending fibers to the leg are the VII, VIII and IX spinal nerves as usually numbered, or, according to the recent numbering of GAUPP (1897), the VIII, IX and X.

According to the enumeration of the medullated nerve fibers in the dorsal and ventral roots of these nerves by HARDESTY (1899, p. 84), the proportion is.

The average of these two observations gives therefore 100 ventral root fibers to 176 dorsal root fibers, and this is the ratio here employed. Such being the relation found in the spinal roots, it is assumed to be the same in the sciatic and crural nerves at the point where they enter the leg. Whatever the number entering of fibers the leg, they are then to be divided, as motor and sensory, in the above proportion.

In this calculation no correction for possible efferent fibers in the dorsal roots is attempted, for we have no data with which to work. When efferent fibers appear in the dorsal roots of the frog, there is indirect evidence that the number must be quite small, and they are here neglected (HORTONSMITH 1897, WANA 1898, DALE 1901). The ventral root is assumed, therefore, to contain only motor or efferent fibers and the dorsal root only afferent or sensory fibers.

Having determined the proportional numbers of the afferent and efferent fibers, the next step is to present the measurements according to which these fibers are to be distributed, namely, the relative weights of the muscles and the relative areas of the skin in the several segments of the leg.