largest size the apparatus accommodates. Since only medullated nerve fibers were to be counted and since, after osmic acid, these are indicated by the dense black deposit of the reduced oxide of osmium in their medullary sheaths, it was desirable to get photographs giving as much contrast as possible. For this reason, some form of the photographic plates used in "process work" was usually employed. These also allow considerable latitude in the exposure and always give strong negatives. With strong negatives, a good quality of blue print paper gives excellent results for the purpose required, and this was used throughout because of the simplicity of its manipulation as well as its inexpensiveness.

In making the counts of the fibers in a section, the photograph of the section was pinned out upon a soft pine board and the identical section itself placed under the compound microscope and subjected to higher magnification than that under which it had been photographed. After a few minutes study, any field in the photograph could be identified in the microscope. Then with a sharp pointed pencil, the photograph was divided into fields of about one inch square or less in area, the lines of division passing among and between the fibers instead of across them. The actual enumeration was done with an automatic tallying register, to the thumb-press of which had been fixed a needle holder. Each fiber in one of the outlined fields was punctured by the needle and all doubtful cases were settled by reference to the original under the microscope. The counting of one field was finished before beginning another. The counting apparatus, its use and the trustworthiness of the results obtained with it, are discussed in detail in the paper cited above. The method has since been used with little modification (DUNN '00, HATAI '02, INGBERT '03) and the results obtained have been uniformly considered satisfactory. The method has the advantage of being largely mechanical and eliminating as far as possible the psychological sources of error which are most to be feared in investigations of this kind.

It was not deemed necessary to photograph certain of the small divisions of the dorsal branches. Such as were small enough to bear a magnification of 700 diameters and still not occupy the field of the microscope, were counted by a modification of the more commonly used net-micrometer method. The procedure followed is fully described in the author's paper of 1900. By means of the projection of the squares of the micrometer and the completion of the count before the result is known, it is held that all errors of auto-suggestion are avoided.

In counting the ganglion cells an application of the net method had to be used exclusively. Here all the sections involving the ganglion had to be gone over and photography was practically out of the question. Therefore, the problem had to be approached in another way. It was first determined that but few of even the very smallest of the spinal ganglion cells have a diameter of less than 9 μ, and further that 9 μ sections were thin enough to allow the light to pass through sufficiently to distinguish the intervening structures of the cell. For this reason 9 μ was chosen as a convenient thickness. On the other hand, however, some of the largest cells of the ganglia may extend through as many as seven consecutive sections of this thickness. To obviate the danger of double counting, a procedure was adopted throughout, which I think was first described by GAULE and LEWIN (96) in their enumerations of the spinal ganglion cells of the rabbit. This consisted in counting only the nucleoli in the sections. As with them, the question of course arose as to the danger of double counting because of the existence of double nucleoli. In counting the cells. in several of the ganglia here dealt with, I kept a record of the double nucleoli appearing in the sections and found that two nucleoli occurred in the same cell at an average of about 5 cells in 1000 or at the rate of about one-fifth of 1%. Cells in which they were observed were usually among the smaller cells of the ganglia. They, of course, were not counted twice. Remembering that these double nucleoli were seen in sections of 9 μ, and that double nucleoli in a nucleus are never separated as much as 9 from each other, and further, that certainly not more than half of such cases existing have their nucleoli separated in the plane perpendicular to the plane of the knife in sectioning so that the knife may pass between them, it is therefore evident that the number of cells counted twice because of double nucleoli is probably less than one-fifth of 1%. The proabilities of double counting due to nuclei being cut in half by the knife and thus counted in the two sections, are also such as need only be considered in questions of the most absolute accuracy. In exceedingly few cases did appearances and comparison of the consecutive sections indicate this had happened. None of the conclusions drawn in this paper would be materially affected by an acknowledged error of one-fifth of 1%.

The number of cells counted in each section was recorded separately and not till all the sections of a ganglion had been counted were these numbers added to obtain the total number of cells in the ganglion. The larger ganglia often involved as many as 125 sectionă. In no case was the relation between the number of ganglion cells and the

number of fibers in the dorsal root computed till all the nerves of a specimen had been completed.

The serial sections were always followed for some distance on either side of the spinal ganglion proper in search of out-lying ganglion cells. In one case these comprised the appreciable total of 31 cells. In most cases the number was very small. In some cases they were more abundant in the beginning of the dorsal root, in others there were more in the trunk. In the Vth and VIth nerves, the mass of the ganglion shows a tendency to protrude distally along the dorsal branches instead of along the trunk. This is due to the probable fact that most of the fibers of the dorsal branches are cutaneous in their distribution.

III. General results of the enumeration.

Following the procedure indicated above, the Vth, VIth and IXth spinal nerves were investigated from 7 frogs varying in body weight from 7 to 63.4 grams. The number of ganglion cells in the spinal ganglia of each nerve was determined and the number of nerve fibers present in the dorsal root, the ventral root and the number in the dorsal branches and in the trunk taken close up to the peripheral border of the spinal ganglion but beyond the region of outlying ganglion cells. The general results of these enumerations are given in the following tabulated form:

TABLE I. Showing in their respective columns the number of fibers in the dorsal roots, the number of cells in the spinal ganglia, the number of fibers in the ventral roots and in the trunks and dorsal branches of the Vth, VIth, and IXth spinal nerves of 7 frogs varying in body weight as indicated in the first column. The ratios of the ganglion cells to the dorsal root fibers (col. C) are obtained by dividing the numbers in col. B by those in col. A. The figures in col. E result from subtracting those in col. F (fibers in the ventral roots) from those in col. G, and the ratios in col. D are obtained by dividing those in col. B by the respective numbers in col. E. The sums of fibers in the two nerve roots and the sums in the trunk and dorsal branches of each nerve are entered (col's. K and G) for purposes of comparison, but especially that the correctness of the amount of the excess of fibers on the distal side of the spinal ganglion (col. I) may be determined. The percentage of the "distal excess" (col. J) results from dividing the amount of the distal excess (col. I) by the sum of fibers in the dorsal and ventral roots (col. K). The ratios comparing the number of fibers in the ventral roots with the number of fibers in the dorsal roots (col. L) are obtained by dividing the numbers in col. A by those in col. F.

In this table the results for each of the three spinal nerves involved are grouped in the order of the body weights of the respective animals employed in order that the figures obtained for the different representatives of a given spinal nerve may be compared more readily with each other as well as with those. of the other spinal nerves.

In the first place, it is apparent as far as the three nerves presented are concerned that neither the number of fibers nor the number of ganglion cells in a given nerve of a specimen is regularly dependent upon the body weight of the specimen. This is perhaps entirely due to a fact noted previously ('99) when was given a more detailed description of the macroscopic features of the different spinal nerves of the frog, viz. that when the spinal neves of the different specimens are are compared, the relative proportion of fibers distributed to a given nerve is by no means fixed. The variations in proportional size are more frequent and marked in the VIIth, VIIIth, and IXth nerves. In the general arrangement, the VIth is much smaller than the VIIth, and the VIIIth (the largest of the lumbar nerves) is considerably larger than the IXth; but occasionally the relative size of these nerves can be observed even with the unaided eye as decidedly different in different frogs and sometimes, indeed, on the two sides of the same frog. The variations are most frequent in the VIIIth and IXth nerves, the apparent condition being that a portion of the bulk usually possessed by the VIIIth may be contributed to the IXth instead, for when the proportional size of the IXth is greater than usual, that of the VIIIth is less. In the case of the frog weighing 7.0 grams, recorded in the table, it was noticed at the time of its dissection that the IXth nerves of both sides were appreciably larger than the VIIIth nerves. It was included, however, because at the time I was unable to obtain another specimen of Rana virescens as small as this. Some of the other discrepancies in the increase in the number of fibers accompanying the increase in body weight are without doubt due to similar variations. Το determine the real rate of the increase, all the spinal nerves of the different specimens should of course be included in the