The Journal of Comparative Neurology and Psychology

ON THE LENGTH OF THE INTERNODES IN THE SCIATIC NERVE OF RANA TEMPORARIA (FUSCA) AND RANA PIPIENS: BEING A RE-EXAMINATION BY BIOMETRIC METHODS OF THE DATA STUDIED BY BOYCOTT ('04) AND TAKAHASHI ('08)

SHINKISHI HATAI

Associate in Neurology at The Wistar Institute

WITH THREE FIGURES

In 1904 Boycott published an important paper on the length of the internodes under the title "On the number of nodes of Ranvier in different stages of the growth of nerve fibers in the frog.' In this work he measured 5338 internodes from twenty-six frogs which ranged in body length from 14.5 mm. to 53.9 mm. Although his observations were limited to the fibers from the thigh taken at the division of the sciatic nerve into the n. tibialis and n. peroneus, they nevertheless give us definite information as to the lengthening of the internodes first in relation to the lengthening of the leg, and second in relation to the increase of the fibers in diameter.

Four years later (1908) Takahashi published a paper on the same subject under the title "Some conditions which determine the length of the internodes found on the nerve fibers of the leopard frog, Rana pipiens," and in this investigation he examined several new points. Takahashi's observations were made not only at three different levels in the thigh, but also at levels in the shank and in the foot, as well as on some of the spinal nerve roots.

He measured altogether 3068 internodes from eight frogs mostly of a larger size than those used by Boycott. The body lengths of Takahashi's specimens ranged from 39.0 mm. to 89.4

mm.

The examination of the two interesting papers just mentioned, suggested several points for further study. It seemed desirable to determine first, how far the results obtained by the simple method of averages would agree with those obtained by the more elaborate statistical treatment of the data; and second, whether or not there is some definite law expressing the relation between the length of the internode and diameter of the fiber on which it occurs, both in different segments of the leg of the same frog, as well as on the same segment of the leg in frogs of different sizes.

In order to investigate the problems just mentioned, it was necessary to reexamine the original data used in the foregoing researches, and through the efforts of Prof. H. H. Donaldson, I was so fortunate as to get the generous permission of both Boycott and Takahashi to use their valuable original data for this investigation, and I wish to express here my thanks to all of these gentlemen.

METHOD OF TREATING THE DATA

As has been shown by Boycott and Takahashi, the length of the internode is highly variable, even on the same fiber, as well as on fibers of the same diameter, and therefore in order to get proper mean values in the case of Boycott's records, I have combined the data for several frogs, and out of the total of twentyfive frogs, made five groups according to the length of the sciatic nerve as determined by Boycott.1

Group 1. Those with a sciatic nerve measuring from 15.5 mm. to 17.0 mm.: represented by 2 frogs.

Group 2. Those with a sciatic nerve measuring from 20.0 mm. to 22.5 mm. : represented by 7 frogs.

Group 3.

Those with a sciatic nerve measuring from 24.0 mm. to 26.5 mm.: represented by 6 frogs.

The length of the sciatic nerve as defined by Boycott is the distance from the point of emergence from the vertebræ of the upper of the two larger branches of the plexus to the level of the nerve obtained by cutting across the leg through the knee joint when it is in full extension; loc. cit., p. 371.

Group 4.

to 37.0 mm.

Group 5.

Those with a sciatic nerve measuring from 30.5 represented by 4 frogs.

Those with a sciatic nerve measuring from 46.0 mm. to 53.5 mm.: represented by 6 frogs.

In the case of Takahashi's data, I found that the internodes had been measured at the lower end of the thigh in only four frogs, giving a total of 683 measurements. These frogs more

over differ so widely in body weight that the data are insufficient for biometric treatment. For this reason I have decided to analyze Boycott's data as completely as possible and then merely to compare the results obtained with Takahashi's conclusions. I shall present my results in the following order:

I. A confirmation of Boycott's and Takahashi's conclusions together with my own.

II. Analysis of Boycott's data.

a. Analytical constants.

b. Frequency distributions.

c. Mean and standard deviation.

d. On the correlation in growth between internodal length and the diameter of the fiber.

III. Takahashi's observation on the length of the internode in different segments of the same frog.

IV. Correlation tables.

I. As my principal object was to find whether there is any definite law relating to the length of the internode and its diameter in different segments of the leg from the same frog, as well as in the same segment of the leg in different sized frogs, I shall not touch many other points discussed by Boycott and especially by Takahashi. Within the range of my examination, I confirm all their findings. Since the evidence of such confirmation will be found in the following pages, I shall present here only the main facts brought out by myself.

1. In a given specimen of Rana temporaria (fusca) whatever its size, the length of an internode and its diameter are positively correlated, though the correlation is not high; therefore it can be stated that the internodal length varies as the diameter. The degree of correlation increases as the frog becomes larger.

2. When however the lengths of the internodes for given diameters in different sized frogs are compared, the larger frog has for a given diameter longer internodes than the smaller frog. Thus in this case the internode varies according to the relation given by the following general exponential equation

where the constants A and h are to be determined from the observations, y is the internodal length, x the diameter and e the base of the natural system of logarithms.

3. The equation just mentioned expresses also the relation in these two characters in the different segments of the leg from the same frog.

4. Therefore the rate of the increment of the length of the internode following the increase in the diameter is proportional to the length of the internode itself, or in mathematical terms.

This may be considered as the general formula which expresses the relation of the two characters in different segments of the leg of the same frog as well as in corresponding segments from frogs of different sizes.

II. ANALYSIS OF BOYCOTT'S DATA

a. Analytical Constants

For future reference I shall present here the various values of the analytical constants as determined from Boycott's data.

GROUP IV

GROUP V

TABLE 1

Showing the values in terms of micra of the analytical constants determined from Boycott's data on Rana temporaria

(fusca)