Thus when we take the difference between the sum of all the minus percentages and the sum of all the plus percentages by which the sheath differs from the ideal half of the area of the entire fiber, we find that for the 1540 fibers, this amounts on the average to +.45%. That is, on the average in this series, the area of the medullary sheath exceeds the ideal half by +.45%, or one-thirteenth of ± 6%, the deviation which might be expected as an error of observation in the case of a single fiber. As tending to cause deviation from the ideal standard we have already noted mechanical injury of the nerve before hardening and to this must be added delay in dissection after death. In this connection some of the material received through the kindness of Dr. HARDESTY calls for special comment—comment which is made with the full recognition of the good fortune which brought the specimens into our hands and is merely intended to indicate how readily the nerves undergo slight alterations after death. Specimens 35-38 and 40-44 inclusive were given us by Dr. HARDESTY, the animals in all cases coming from the Zoological Garden in San Francisco. Dr. HARDESTY writes as follows: "In every case the animals from which I sent you bits of nerve were dead when they came into my hands. Most of them came to me within a few hours after death, and none had been dead more than twentyfour hours. In case of the monkeys, most died of tuberculosis, some of the other animals died of pneumonia, one by dysentery, one by accident and the bear from poison." On looking over our results on this material show excessively large sheaths, giving 160 fibers with an average of 4%, while among the remainder of the mammals from San Francisco, namely the bear, Manila monkey, spider monkey, Rhesus and baboon the average is only +1.14%. We conclude from this that the nerves of the first group had suffered a slight post-mortem alteration before they could be fixed.. The deviations observed.-Table VI shows that the average deviation for all the 1540 fibers is +0.45%. On determining the deviations separately for the Fish, Amphibia, Reptiles, Birds and Mammals we obtain the following results: This tabulation serves to show that in no class do the deviations rise very high, and that with the exception of the mammals, which have been commented on already, the average deviation tends to diminish as the number of cases increases. On further looking over the individual deviations, as shown in the original records, it appears that in 580 cases (or 37% of 1540), they are more than 6% plus or minus-266 cases being minus and 314 plus. Thus the excessive deviations are rather evenly divided on either side of the average. It follows from this that 63% of the cases deviate only 6% or less, or are within the anticipated error of observation. From the foregoing it is concluded that despite the individual variations which may be often quite large, there is no tendency for the sheath to depart materially from the ideal standard, when this relation is determined by averaging the measurements obtained from groups of twenty or more fibers. Figure illustrating variations in the thickness of the medullary sheath. In order to give a meaning to the numbers that appear in the foregoing Table VI, the measurements applying to Specimens I, XI, XXII, XXIV, XXVIII, and XLV have been selected for illustration (see Fig. 1). This selection gives one specimen from each of the great classes below the mammals. In the case of each specimen, the diameter of the average fiber is taken as a standard, and this is shown, enlarged one thousand diameters, (1) with a sheath having just half the area of the entire fiber (Ideal); (2) with the sheath determined from the SHOWING VARIATIONS IN THE MEDULLARY SHEATH. Shark Spec. I Frog Average percentage Average Extreme variations. Ideal. deviation. observed. Spec. XI Turtle Spec. XXII Chick Spec. XXIV Rat Spec. XXVIII Man Spec. XIV +0.62 -1.2 +1.0 -1.6 + average of all the measurements (average observed); (3) with the smallest sheath observed in the series, and (4) with the largest sheath observed in the series (extreme variations). By the study of Fig. 1, some notion of the range in the size of the sheath is obtained, but at the same time it must be remembered that these extreme cases as seen in (3) and (4) are exceptional, and that most of the deviations in the sheath are of decidedly less extent. Conclusions. The measurements in Table VI have been compared with one another in so far as they permitted the comparison of (1) nerves having different diameters; (2) those afferent or efferent in function; (3) taken from various parts of the body; (4) in males and females; (5) at different seasons; (6) at different ages; and (7) in animals active and those slow in their move ments. From such comparisons there is no indication that any of these conditions modify the relative development of the medullary sheath. To make these statements with regard to area the basis for a statement with regard to the relative volumes of axis and sheath, is justified for the reason that the medullary sheath in the peripheral system is very nearly coextensive with the enclosed axis cylinder, and the short stretches at either end of the fiber would serve to give only a slight increase in the volume of the axis. Since in cross sections the sheath is on the average a trifle in excess of the axis, this difference would tend to make the similarity in volume even closer. If the foregoing statements are well founded it should follow that the figures which represent cross sections of nerve fibers treated by the osmic acid method and which have been published in special articles or in text-books should accord with the results here given. We have examined such figures as they appear in RANVIER ('78), Kupffer ('83), GASKELL ('85), Cajal ('99), HUBER ('00), and find that when the conditions are observed of selecting only those fibers which are nearly circular, in which the sheath is single and where there has been no increase in sheath from careless printing, the measurements show the same relations which we obtained on the specimens themselves. We feel justified, therefore, in making the broad statement that in the peripheral nerves of vertebrates above the Cyclostomes, we have in general a one to one relationship existing between the nerve sheath and the axis, whether we compare the volumes of the two or measure their areas in the cross sections of osmic acid specimens. It is to be anticipated, however, that somewhere among the fish we shall find examples of less complete development of this sheath, thus bridging the gap between the condition here found and that represented by the nerves of Cyclostomi and Acrania which are without the medullary covering. BIBLIOGRAPHY. 1. Boll ('76). Atti della R. Accademia del lincei, Vol. I, Series III, 1876. 2. Boveri ('85). Abhandl. d. K. bayer. Akad. d. Wiss., II CL. XV, Bd. II, München, 1885. 3. Cajal ('99). Textura del Sistema Nervioso del Hombre y de los Vertebrados, Nicholas Moya, Madrid, 1899. 4. 5. 6. 7. 8. Donaldson ('95). The Growth of the Brain. Contemporary Science Ser- Donaldson ('00). Journ. Nerv. and Ment. Dis., Vol. XXVII, Oct., 1900. Dunn ('00). Journ. Comp. Neurol., Vol. X, No. 2, May, 1900. 9. Dunn ('02). Journ. Comp. Neurol., Vol. XII, No. 4, 1902, p. 326. 10. Gaskell ('85). Journ. Physiol., 1885, Vol. VII, Pl. II, Fig. 6. 11. Huber ('00). Böhm-Davidoff and Huber: Text-book of Histology, 1900, P. 143, Fig. 114. 12. Kupffer ('93). Sitzungsberichte der Math.-physik. Classe der k. b. Akademie der Wissenschaften zu München, 1883, H.III, Pl. 1, Fig. A. 13. Ranvier ('78). Leçons sur l' Histologie du Systeme Nerveux, 1878, Vol. I, Pl. 2, Fig. 7. |