Introduction
It is well known that the whales have no hind-limb protruding on the surface of the body. But probably all of them have the rudimentary pelvis as a pair of slender bones.1) Unlike in most mammals, whose pelvic girdle consists of three elements (ischium, pubis and ilium) coalescing into a single bone, the cetacean pelvis is made of only one element, a fact stated first by Eschricht and Reinhardt (1866), who found a single center of ossification in it. This  bone is  believed  to represent the ischium, for it is connected with the crura penis or clitoridis, and also with the musculus ischiocavernosus. 2131 While in the Odontoceti the pelvis is the sole remnant of the hind-limb, most of the Mysticeti have one or two other pairs of very small bones or cartilages placed near the middle of pelvis. One pair of them is attached to the pelvis by ligaments and accompanies the third pair at its caudal end. They were found at first by Reinhardt (1848) in a newborn Greenland Right-whale and asserted then  by  Eschricht  and Reinhardt (1866) in a half-grown and a full-grown whale of the same species (Fig. 1). Later, Struthers (1881) observed eleven pairs of the rudimentary bones, studying minutely the articulations and neigh- bouring muscles. The supernumerary pelvic bones are nowadays supposed to represent femur and tibia, as sug- gested by the discoverers of them. P.....Pelvis F......Femur T......Tibia On the other hand, in the adult Humpback Eschricht found only the second pair, and afterwards Struthers (1888) confirmed also the absence of the third pair in this species. The same result was mentioned by Burmeister (1867) and Stru- thers (1872, 93) also for the Fin-whale, in which the only existing femur was extremely vestigial. Further, the lesser Fin-whale (Balaenoptera acuto-rostrata, Lac.) and the Sei-whale show, according to Struthers etc., no trace of femur and b. Sei-whale (36 feet, male) Lesser Fin-whale (14.5 feet, male) a. Greenland Right-whale (48 feet, male) Fin-whale (64 feet, male) d. C Humpback-whale (40 feet, male) e. During my Antarctic whaling voyage on board the Nissin-Maru No. 1 (1947-48), I examined the cartilages in question in the Balaenoptera-foetuses and found some noteworthy facts. The materials examined by me are as follows: Foetuses of the Blue whale (Balaenoptera musculus, L.) 9. (male, 6; female, 3; max. length, 22 feet 2 inches; min. length, 3 feet 11. inches) Foetuses of the Fin-whale (B. physalus, L.) 9. (male, 5; female, 4; max. length, 15 feet 1 inch; min. length, 2 feet 1 inch) Additionally for comparison, each one pair of pelvic bones of adult Blue and Fin-whales. Pelvic cartilages of the Blue and Fin foetuses G On the Pelvic Cartilages of the Balaenoptera-Foetuses Both species have besides a pair of pelvis another pair of very small cartilages, the third pair being completely absent. The pelvis (Fig. 3, 4) is elongated, some¬ what curved, hammerlike in form, and has a very short lateral process, corres- ponding to '' promontry '' of Struthers. The upper process, processus cranialis, is pointed at the end and deserves the name " apex cranialis " , while the lower one, proc. caudalis, is shorter, with its somewhat rounded extremity. The lateral process, the shortest of all processes, ends also inot sharpened, but has here a more or less eminent tubercle, tuberculum laterale. Near the tubercle, a little more ventrad and craniad, there is a small, ovall piece of cartilage, the upper end of which is pointed in some cases, especially 7 Fig. 4 Pelvic bone of adult whalebone-whales Fin-whale, lateral and ventrel view a, b, Blue whale, lateral and ventral view c, d, Proc. cranialis; P. ca., Proc. caudalis; P. cr., T. l., Tuberculum laterale in the Fin-whale. This small cartilage, being nothing but the remnant of femur, is covered with a thick capsule of con- nective tissue. The remnant of femur does not increase in size proportionately with the growth of the foetus: in other words, much more remarkable indivi- dual variation is seen in the size of this cartilage than in that of the pelvis. This dif- ference might be understood by the more vestigial nature of the former. It is moreover likely, that the femur is more rudimentary in the Blue whale than in the Fin-whale. For, according to my observation, the femur of considerably larger foetuses of Blue whale (12 feet 4 inches, male; 13 feet 4 inches, male; 15 feet 5 inches, female; 22 feet 2 inches, male) is sometimes made solely of connective tissue, containing The ligamentous band between femur and pelvis is very loose, and no cartilage. here I found no articular formation, though Eschricht, Reinhardt and Struthers mentioned an articulation respectively in an adult Greenland Right-whale and in an adult Fin-whale.
Ossification of the pelvic cartilages
Neither pelvis nor femur of all the foetuses, measuring from 2 feet 11 inches up to 22 feet 2 inches in length, showed any trace of ossification. It is therefore supposed that these skeletons are ossified only after the parturition. For, con- sulting the statistics published by Mackintosh, Wheeler (1927) and Matthews (1937), it seems certain  that the foetus of 22 feet is only a little before the birth.  Rein- hardt found in a newborn Greenland Right-whale an ossified portion of the femur in its middle part, but no ossification in pelvis and tibia. Position and locality of the pelvic cartilages The cartilaginous pelvis exists on each side, rather laterad and caudad, to the external genital orifice, with its axis nearly parallel to that of the whale-body. We can palpate them after removal of the skin as somewhat hard objects. All of my specimens were not so small as to settle the problem upon the presence of an external protrusion representing the hind-limb reported by Guldberg (1894, 99). and Kükenthal (1895) in Phocaena communis (Fig. 5). I have known, however, On the Pelvic Cartilages of the Balaenoptera-Foetuses Measurements of the pelvic cartilage Fig. 6. While the average of this in- dex β/γ is in the foetal Fin-whale 2.01 (max., 2.67; min., 1.63), it is in the foetal Blue whale only 1.06 (max., 1.25; min., 0.71); there is accordingly a dis- tinct difference between the both species. pFig. 7, indicates my data diagram- matically. From this figure we know that the index β/r is in the Fin foe- tuses, without exception, more than 1.5, while in the Blue foetuses it  lies  always under 1.5. It is interesting that these intimately related two species of Balaenopterides show such a remarkable difference in the form of pelvis. I can't decide, however, whether the same difference is present also in the adult whales, but the postnatal existence of approximately the same relation is unplausible. 1 1 that the pelvis is located in small foetuses under the skin more superficially, while those in larger ones lie more deeply embedded  in the muscular layer and so more hardly palpable. Difference of the foetal pel- vis in form between  Fin-  and Blue whale In the Fin foetus the  caudal process of the cartilaginous pel- vis is relatively shorter than in the Blue, viz. the pelvis of the former has the lateral process placed more caudad than that of the latter (Fig. 3). My measurements of the dis- tances 1) from the cranial apex to the caudal end (α), 2) from the cranial apex to the lateral tubercle (β), 3) from the cau- dal end to the lateral tubercle (r), and the relative length of β and  γ  (β/γ)  (Fig. 6) are shown in Table 1. 9 On the Pelvic Cartilages of the Balaenoptera-Foetuses fall between 0.3 and 0.7 (average, 0.41) for the Greenland Right-whale. And I calculated, using Struthers' data, that this ratio is for a male Megaptera of 40 0.77, i.e. an intermediate value between the Greenland Right-whale feet   long and the Blue foetus. In this way we can probably determine the kind of whale- bone-whales from the form and size of pelvis, especially by consulting the rela- tive length of the upper and lower processes.
Sexual difference of the cartilaginous pelvis
In both the Fin and Blue foetuses the β/γ index of the pelvis is larger in the female than in the male (Fig. 7). As to the Fin-whale, this index is in the female almost always more than 2.0 (average, 2.34; max., 2.67; min., 1.95 ' , while in the male it is, without exception, less than 2.0 (average, 1.75; max., 1.97; min., 1.63). In the Blue whale, the critical point of the ratio for the sexual difference is 1.0 (average for the male, 0.91; max., 0.98; min., 0.71: average for female, 1.14; max., 1.25; min., 1.00). Further investigation of the pelvic bones in the adult Fin- and Blue whales is from this viewpoint very desirable. 1 ) Angle between the cranial and caudal process of the pelvis These processes make each other at the level of the lateral process an obtuse angle opened mediad (Fig. 8). This angle, measured with gonio- meter, shows no remarkable specifical or sexual difference (Table 1), the average being in the Fin and Blue foetuses respectively 136°(male, 136°; female, 137°) and 133° (male, 124°; female, 137°); the individual varia- tion is in the Fin-whale 127°-148°, and in the Blue whale 120°-149°. Neither exists any remarkable difference be- tween the right and left pelvis (average for the Fin-male: right, 136°, left 136°; female: right, 138°, left, 136°; average for the Blue- male: right, 123°, left, 125°; female: right, 140°, left, 138°), though some instances showed the angle tolerably asymmetrical. N.B. According to Struthers, this angle appears to be in the female Green¬ land Right-whale somewhat larger than in the male, the average being res¬ pectively 139° and 124°. 12 The length of the cartilaginous pelvis in various intrauterine stages is shown By the length of the pelvis I mean the distance from the cranial apex in Fig. 9. to the caudal end (a in Table 1), and by the body length the distance from the rostral extremity to the median notch of the caudal flipper. We see from this figure that the relative length of pelvis to the whole body remains, regardless of size, sex and species of the foetuses, almost constant. 1 2 ) The cartilaginous pelvis occupies about 1.6-1.8% of the total length of the body (average, Fin-whale-male, 1.8, female, 1.7; Blue whale-male, 1.6, female, 1.7, max., 1.9. min., 1.4)(Table 1). Nearly the same ratio seems to hold good in the adult stage, for from Struthers' data, this ratio becomes 1.7 in an adult male Fin-whale of 50 feet, 1.6 in an adult male Sei-whale of 36 feet, 1.9 both in an adult male lesser Fin-whale of 14.5 feet and in an adult male Megaptera of 40 feet. But in the Greenland Right- whale the pelvis seems to be relatively larger, occupying 2.3% (max., 3.0, min., 2.0) of the total length of the body. Summary 1) From the viewpoint of the rudimentary skeletons pertaining to the hind- limb, the whalebone-whales can be classified into the following three groups: Group 1, to which the Greenland Right-whale belongs, has besides the pelvis two pairs of subsidiary bones or cartilages (femur and tibia). Group 2, in which other than the pelvis only the femur is present, comprises the Humpback, the Fin-whale and perhaps also the Blue whale. Group 3, which has neither femur nor tibia but has the pelvis only, seems to comprise the Sei-whale and the lesser Fin-whale. 2) Many foetuses of Fin- and Blue whales studied in this paper have two pairs of cartilages corresponding to pelvis and femur, which show no trace of the bony nucleus within them. Very likely, therefore, the ossification of them takes place only after the parturition. 3) The pelvis of whales, though generally it is hammerlike in form, shows remarkably different shapes according to the species. Especially the ratio of length between the anterior and posterior portions of the pelvis is characteristic to each species. In the Fin and Blue foetuses the sexual difference is marked in the form 4) of the pelvis. The ratio mentioned in the preceding paragraph is always greater in the female than in the male; namely, the female pelvis has relatively longer cranial process than the male.
14 The obtuse angle between the cranial and caudal portions of  pelvis  is  in 5) the average 136° and 133° respectively for the Fin and the Blue foetuses. It shows no remarkable variation as to species, sex, age and body-side of whales. 6) The length of pelvis is in the Fin and the Blue foetuses about 1.6-1.8% of the body length. This ratio seems to be nearly constant for almost  all whale- bone whales, regardless of species, sex and age, probably with the exception of Greenland Right-whale, which shows a ratio of far greater than 2.0%.
Literature
Schneider, J. G.; Beiträge zur Naturgeschichte der Walfischarten. Leipzig. 1795. 1) Eschricht, D. F. and Reinhardt, J.; On the Greenland Right-Whale (Balaena 2) mysticetus, L.). Ray Society, 1866. Recent Memoirs on the Cetacea. London 1866. Burmeister, H.; Preliminary descriptions of a new species of Finner whale 3） (Balaenoptera bonaerensis). Proc. Zool. Soc. London. 1867. pp. 707-713. Flower, W. H.; An introduction to the osteology of the mammals. London. 4) 1870. Second edition. 1876. 5) Struthers, J.; On some points in the anatomy of a great Fin-whale (Balaeno- ptera musculus). Journ. Anat. Physiol. 6. pp. 107-125. 1872 (1871). 6) Struthers, J.; On the bones, articulations, and muscles of the rudimentary hind-limb of the Greenland Right-whale(Balaena mysticetus). Ibid. 15. pp. 141-141 176, 301-321. 1881. 7) Struthers, J.; On some points in the anatomy of a Megaptera longimana. Part The limbs. Ibid. 22. pp. 240-282. 1888. 2. 8) Struthers, J.; On the rudimentary hind-limb of a great. Fin-whale (Balaeno- ptera musculus). Ibid. 24. pp. 291-335. 1893. 9) Kükenthal, W.; Ueber Rudimente von Hinterflossen bei Embryonen von Walen. Anat. Anz. 10. pp. 534-537. 1895. Guldberg, G.; Ueber temporäre äussere Hinterflossen bei Delphinembryonen. 10) Verh. anat. Gesellsch. 8. pp. 92-95. 1894. Guldberg, G.; Neue Untersuchungen über die Rudimente von Hinterflossen 11) und die Milchdrüsenanlagen bei jungen Delphinembryonen. Internat. Monats- schr. f. Anat. Physiol. 16. pp. 301-321. 1899. sis