latter is the number desired, it is necessary first to find the square of the radius in the case of each of these ten fibers; then to take the average of these squares and multiply by r in order to obtain the average area of the fibers. TABLE V. The squares of the foregoing radii are as follows: (Radius A)? Total 245.29 sq. Il 24.53 sq. 11 The average for the squares of the radii in the case of the axis and sheath and of the axis alone, must be multiplied by (= 3.14) to give in square pe the areas of the entire fiber and of the axis respectively. In this instance the areas are as follows: Areas. Axis 76.99 sq. u The object of this investigation is to determine whether in the cross section of the fiber the area occupied by the ring-like sheath is equal to that of the enclosed axis. By hypothesis they should be equal in area, hence in the case of the average entire fiber containing 154.9 sq. u in its section we should expect to find one-half of this area 154.9= 77.5 sq. in the axis and the other half in the sheath. With this ideal area, the area of the axis as observed is compared. Thus: Estimated area of sheath 77.5 sq. ll. Observed axis = 76.99 sq. p According to the hypothesis, the area of the axis should equal that of the sheath. The observed area of the axis is seen to be less by 0.51 sq. l, or using the ideal area of the sheath 2 as the standard, it is less by 0.6%. In this particular group, therefore, the actual area of the sheath is 0.6% greater than it would be if the assumed one to one relation of the axis and sheath were maintained. In working out the results, it is this ideal of one-half the area of the total fiber which is always taken as the standard, and the observed area of the axis is compared with it. If the area of the axis is less than one-half the area of the total fiber, then it follows that the sheath must have been more than onehalf and the percentage value of the difference is written in plus, to show that the sheath is too large by this amount, or, under the reverse conditions, as minus, to show that it is too small. This difference is designated the average percentage deviation. In the case of each of the 1540 fibers here presented (Table VI) calculations similar to those just given, have been made. It is thus possible to say in each instance by what percentage the area of the sheath departs from that of the ideal, although in the table only the percentages for the extreme cases and for the average deviation are given. Description of the Material Employed.--The following list of the specimens gives the common name; scientific name (entered only once where several specimens of the same species were examined); length of body; weight; sex; age; season when killed; nerves taken; locality; and by whom prepared. Where no statement is made; the sex is male; the season winter; the nerves are taken from the brachial plexus, and the material killed and prepared by Mr. Hoke in this laboratory. The omission of any of the other data means that they are not available. 14.2 14.7 13.9 13.3 15.9 12.5 11.9 13.5 11.2 10.3 9.8 6.2 7.7 12.4 5.8 11.6 12.8 0.20 40 40 40 3.00 40 Toad 0.52 Birds | Reptiles 40 40 0.90 1.00 40 40 40 40 20 30 20 20 20 40 40 22.0 18.6 White Rat 19.8 X X XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX | XXX | XXXI | XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIV XLV 10. I 5.0 0.90 3.50 2.70 1.60 1.10 16.7 12.5 30.0 19.5 16.7 28.3 17.5 5.0 7.2 12.8 27.5 23.7 14.4 7.2 16.0 10.3 14.2 III 13.7 7.7 16.7 0.80 40 Mammals 11.7 13:3 2.90 2.09 5.40 0.90 11.6 Rabbit Agouti Bear Fox Dog Wild Cat Cat Manila Monkey Spider Monkey Rhesus Ape Baboon Man 40 40 40 40 40 40 40 40 II.I 6.6 3.80 1.30 13.7 16.0 10.7 11.3 10.9 12.3 11.0 13.9 0.50 0.80 1.00 3.90 1.30 0.70 40 7.2 40 40 III 1540 +0.45%. Description of Specimens on which Measurements have been made. Specimen 1. Dog Shark (Mustelus canis), length 95 cm., summer, Woods Holl. Specimen 2. Dog Shark, length 95 cm., summer, Woods Holl. Specimen 3. Common Skate (Raja erinacea), length 49 cm., female, sum mer, Woods Holl. Specimen 4. Common Skate, length 48 cm., female, summer, Woods Holl. Specimen 5. Common Skate, length 45 cm., female, summer, Woods Holl. Specimen 6. Summer Flounder (Paralicthys dentatus), length 40 cm., fe. male, summer, Woods Holl. Specimen 7. Summer Flounder, length 49 cm., Woods Holl. Specimen 8. Summer Flounder, length 49 cm., summer, Woods Holl. Specimen 9. Frog (kana virescens), body-weight 22 grms., sciatic nerve, summer, summer. Specimen 10. Frog, body-weight 49.S grms., sciatic nerve. spinal nerve. Specimen 16. Frog, body-weight 74.5 grms., female, ventral root of the 7th spinal nerve. Specimen 17. Toad (Bufo lentiginosus), sciatic nerve, summer. Specimen 18. Mud-Puppy (.'ecturus maculatus) female, length 18 cm., sum mer. Specimen 19. Common Lizard (Sceloporus un/ulatus), weight 8.2 grms. DESTY, San Francisco. CISCO. Specimen 36. Gray Fox ( Urocyon cinero-argentatus), body-weight 3940 grms., Dr. HARDESTY, San Francisco. DESTY, San Francisco. grms., Dr. HARDESTY, San Francisco. Specimen 41. Spider Monkey (Ateles paniscus), body-weight 1650 grms., Dr. HARDESTY, San Francisco. Dr. HARDESTY, San Francisco. Dr. HARDESTY, San Francisco. HARDESTY, San Francisco. Accuracy of Measurements and Sources of Error.-In estimating the value of the measurements given in Table VI, it is to be remembered that with the magnification most commonly used for the larger fibers, one-tenth of a division of the ocular micrometer or 0.306 l was a shade over 3% of the diameter of a fiber 10 l in thickness. In case, therefore, that a fiber was measured as 9.7 1 or 10.3 ! instead of 10 p, the deviation in the resulting areas from that based on 104 would be approximately, I 6%. Individual cases might, therefore, readily vary by this amount as an error of observation. With fibers of greater diameter the relative value of this error would decrease, while with those of less diameter it would increase. Similarly with the higher magnification used for the smaller fibers, the value of the one division of the ocular micrometer was 1.42 y, and one-tenth, or 0.142 y would be 3% of a fiber 4.7 u in diameter. In this case also the error of one. tenth of a division in the reading, either plus or minus, would give rise to corresponding deviations in the resultant areas, with a relative decrease as the fibers become larger and an increase as they become smaller. In general, therefore, the errors of observation would increase as the fibers diminished in diameter. Such errors, however, would tend in all cases to balance out and so be reduced as the number of observations becomes large. |