sympathetic neurones and to send processes toward the periphery without sending a corresdonding process into the dorsal root. Another cause for the excess of cells above the fibers being less on the distal side of the spinal ganglion, is due to the bifurcation of fibers on the distal side. Both this and the multipolar cells of the character just mentioned contribute to the formation of the excess of fibers on the distal side of the ganglion and both will be considered in the discussion of the "distal excess."

On neither side of the spinal ganglion does the number of cells per each fiber supposedly connected with the ganglion show a regular decrease with the increase in the body weight of the specimens. Such a decrease might be expected with the usual conception that the number of ganglion cells becomes fixed at quite an early period in the growth of the animal, but my counts for neither of the three spinal nerves here represented show such with any regularity. HATAI ('02) found in the rat an appreciable decrease in the value of the ratios of cells to dorsal root fibers as the animal reached maturity. Either in this respect the processes of growth in the frog are again different, or the process is so slow in the frog as to require the investigation of a greater number of nerves of a greater number of individals. Could the cells be counted at different periods of the growth of the same frog, the result might be different, for it must be remembered that each set of figures in Table I but represents the conditions in the nervous system of a different individual at a certain time.

The growth relations are shown in another way in Table II which is constructed with reference to the body weights instead of grouping with reference to the number of the spinal nerve as in the table above. Such results as may be brought out by arranging the frogs into two groups, one containing the larger and the other the smaller frogs, and summating the numbers in each will be presented later.

TABLE II. Allowing a comparison of the number of cells found in the spinal ganglia (col. B), the number of fibers in the dorsal roots (col. I) and of the number of fibers found in the trunks and dorsal branches (col. H) of the Vth, VIth and IXth spinal nerves of each specimen. The different specimens are entered in the order of their body weight. In columns C, D and G the sums of the ganglion cells, the sums of the dorsal root fibers and the sums of the fibers in the trunks and dorsal branches found in the three nerves of each frog may be compared with each other and, reading downward, the sums in each column may be compared with reference to the increase in body weight. Column E, obtained by dividing col. C by col. D, presents the ratios of ganglion cells to dorsal root fibers in the three nerves combined of each specimen and likewise col. F shows the number of cells in the combined ganglia per each fiber in the total of the trunks and dorsal branches less the ventral root fibers of each speci

men.

Table II shows (col. E) that when the numbers found in the three nerves of each specimen are combined, the ratios of the sum of the ganglion cells to the sum of the dorsal root fibers show even a less tendency to decrease with increase in the body weight than is manifested when each of the nerves is considered separately as in the previous table. Indeed, two of the three cases in which the sum ratio is highest are in the two largest specimens. The sum ratios of cells to fibers on the distal side of the ganglion (col. F) follow so closely the variations of the ratios dealing with dorsal root fibers that whatever is true for the one is practically true for the other.

By comparing columns E and F it is seen that in the sums of the cells and fibers in the three nerves of the several frogs, the number of cells per fiber on the distal side of the ganglion is only from 0.2 to 0.7 of a cell less than on the central side. The cases in which the difference is greatest are in the largest specimens. The average difference is 0.6. In was seen in Table I that when the Vth nerves alone are considered this difference averages 1. I cells, being less in the VIth and much less in the IXth nerves.

In columns B and H, Table II, better than Table I, is also illustrated the fact that the relative number of cells and fibers apportioned to a given nerve varies greatly. To the unaided eye the Vth nerve usually appears smaller than the VIth, but in three of the seven frogs here it contains appreciably more cells and fibers than the VIth. This variation from the usual proportion is more frequent in the IXth nerve but its variation is less manifest here because of the absence of figures for the nerves adjacent to it. The relatively large sums for the 7 gram frog are due to its having comparatively a much larger IXth nerve than usual for its weight. Also the IXth in the 25 gram frog

seems to have been small. In column I it is seen that the numbers of dorsal root fibers vary much as the ganglion cells and as the fibers on the distal side of the ganglion.

V. Further observations on the conditions determining the excess of fibers on the distal side of the spinal ganglion.

The distal excess was described in the previous papers and some attention was given to probable arrangements of the fibers in producing it. It was shown in a series involving all the spinal nerves of one side of a frog, (1) that of all the nerves, those which in proportion to their trunks have the largest number of fibers in their dorsal branches have also the highest percentage of distal excess; (2) that in some cases the amount of the distal excess may even exceed the number of fibers in the dorsal branches; (3) that while in a given nerve (VIth, considfrom a series of 19 frogs) the increase in weight is not accompanied by a regular increase in the value of the distal excess in this nerve, yet when the results are grouped for the small and large separately, the distal excess for this nerve shows a decided. increase with the gain in weight. It was further suggested that the distal excess is due (1) to the medullated fibers from the sympathetic system which terminate in the spinal ganglion, (2) to cells in the ganglion which send processes toward the periphery but not into the dorsal root, (3) to the bifurcation of the peripheral prolongation of the spinal ganglion neurone of Type I and (4) to the bifurcation of ventral root fibers in the region of the spinal ganglion.

The observations as to the variations and causes of the distal excess made in these papers, one using the several nerves from one specimen and the other the one nerve from several specimens, should gain significance if further based upon the findings in several nerves from each of several specimens. Table III is constructed with special reference to the distal excess and is given as indicating further some of the number relations involving it. The table is compiled from the numbers in Tables I and II and represents some relations not brought out in the previous work.

Attention is called to the following relations as shown in Table III.

1. When the different nerves of each specimen are considered indidually, the number of fibers in the nerve trunk (col. A) and those in the dorsal branches (col. B) do not show a regular increase with the increase in body weight. The same is true for the sums of these fibers in the three nerves of each specimen (col's. C and L). However, though the increase is not a regular one, the larger specimens have appreciably more fibers than the smaller ones. The same statements apply to the numbers of fibers in the dorsal and ventral roots (col's. D and E).

2. It is evident here (col's. C and D), and especially so when computed (see Table IV), that in the dorsal and ventral roots the increase of fibers with the increase in weight is not so great as in the trunks and dorsal branches. In other words, the fibers on the side of the distal excess increase more rapidly than on the central side of the spinal ganglion.

3. While the amount of the distal excess in each nerve (col. F) varies so greatly that its increase with the body weight is not very evident, yet when the sums of the distal excesses in each set of nerves are considered (col. G) there is manifest a decided and much more regular increase.

4. The most marked increase in the sums of the distal excess appears in this series between the weights of 25 and 61 grams. Between 25 and 33 grams the increase amounts to 27% and in passing from 33 to 47 grams the increase amounts to 23%, while the average increase from from one specimen to the

TABLE III. Giving number relations involving the distal excess. The various columns are either rearranged or derived from the columns of Tables I and II. The sums in columns C, D and G result from adding in adjacent columns the numbers found respectively in the three nerves of each specimen. The percentages in col. J result from dividing the sums in col. G by the respective sums in col. D of Table II; the percentages in col. K from dividing col. G by the respective sums of ventral root fibers in col. C of Table IV. The sums in column P are obtained by substracting col. D of Table II from col. C of that table and the ratios in the last column result from dividing the numbers in col. P of this table by the sums in col. G. As indicated in the headings, all the other columns set in heavier type are derived from columns accompanying them in this table. The percentages are reduced to one decimal figure and the ratios are given in round numbers.