m HARVARD UNIVERSITY Library of the Museum of Comparative Zoology .i^aUiiMliiiMriHW.......,: Number 5 August 30, 1939 A STATISTICAL STUDY OF THE RATTLESNAKES By Laurence M. Klauber Curator of Reptiles and Amphibians, San Diego Society of Natural History VI* FANGS SEP 11 1939 Table of Contents Introduction 3 Fang Growth and the Mechanism of Replacement 3 Fang Structure 13 The Fang Operating Mechanism 16 Method of Fang Measurement 20 Sexual Dimorphism 21 Intraspecific Fang Correlations 23 Parabolic Regression Equations 25 Straight Line Regressions in the Adult Range 33 Dispersion 36 Choice of a Basis of Comparison for Interspecific Studies 39 Interspecies Comparisons in Fang Length A3 Other Fang Dimensions 51 Miscellaneous Data on Fangs 55 Acknowledgments 59 Summary and Conclusions 59 * Previous sections of this study have appeared in the Occa- sional Papers of this series as follows: No. 1, Aug. 10, 1936 I Introduction II Sex Ratio in Rattlesnake Popula- tions III Birth Rate No. 3, Dec. 15, 1937 IV The Growth of the Rattlesnake No. A, May 31, 1938 V Head Dimensions If A STATISTICAL STUDY OF THE RATTLESNAKES By Laurence M. Klauber VI FA>TGS •>" '"'^'"'" "«> SEP n 1939 Introduction The length and character of the fangs of the rat- tlesnake present a study of some practical interest, since they involve several of the variables which affect the re- sults of snake-bite, as, for instance, the depth of pene- tration of the venom, the rapidity of injection, the amount of venom which may be lost externally in clothing, and the chance of fang breakage in contact. Vv'hen one extracts venom from rattlesnakes of dif- ferent species. It is at once apparent that the fang lengths, while roughly proportional to the body sizes, exhibit dif- ferences in this proportionality between species. There can be no doubt, for example, that the fangs of a Crotalus tigris are much smaller than those of a C. molossus of similar body size. But the heads of these snakes are likewise dispropor- tionate and it might therefore be assumed that the fang lengths have a fixed relation to head size. Upon investiga- tion, however, it appears that such is not the case either; there are also differences in the fangs when the head sizes are equal. The determination of the relationship between these body parts is one of correlation, which can best be attacked by statistical methods. It involves, as usual, a preliminary study of the extent of intraspecific variation and dispersion, followed by interspecific comparisons. How- ever, before this is undertaken, there are several features of the fangs and their use which should be discussed, since their presentation will clarify the application of the measurements upon which the statistical studies are based. Of particular interest are the highly specialized mechanisms of fang replacement and of fang operation. Regarding them, certain conflicting descriptions have appeared in the past, and these I will seek to correct and amplify. Fang Growth and the Mechanism of Replacement It is well known that the active fangs of the rat- tlesnakes are changed or replaced peri sdically, such renewal occurring whether the discarded member has been damaged or is still intact. Whether replacement is hastened, if a functional fang has been broken out entirely, prior to the normal time of change, is not known. The delicacy and fra- gility of the fangs, particularly in the smaller snakes, makes such a provision for replacement imperative, as does likewise the necessity for providing larger fangs as a snake grows. The mechanism whereby a new active fang comes into position has been described by several investigators; over sixty years ago two mutually exclusive descriptions were formulated, both of which have subsequently reappeared in the literature from time to time. It is desired here to point out the difference between these theories of develop- 1- Ul iC o o (jj (0 ^ u- (T loa < UJUJ xm o z li. o uj O tr I o \- lO < u < t^ "^ ^ o UJ > oc u (0 §<0 <-> ui tf)2 V) ID (/) U O o ■^€<^((«!C jO M rO Tj- u^ ^sD CO *; o w ■tj ■« ~j » X « C3 -u E Q) »-^ » a a ;3 W U O •» ■-. :ai O — t. I_ O C3 Q. ~. O) o CO CJ 0) -J e^ o o -. t. <» ■Q/1 ■" a o — Ll o >z acq - I UJ O -I <0 ment and to present a statistical verification of one of them. Dr. S. Weir Mitchell, the celebrated neurologist, ophiologist, and author, and a collaborator. Dr. Christopher Johnston, were the first to describe in detail the mechanism of change.* They state that on each side of the head there is a pair of contiguous maxillary fang sockets, making four sockets in all. Posterior to the inward socket of each pair lies a magazine holding the future fangs in an ascending order of size and completeness (Fig. 17). Of the two sock- ets, the outer usually holds the active fang, the inner be- ing normally vacant. When the time of replacement arrives, the forward reserve fang, which is also the largest and most fully developed, advances and becomes firmly seated in the vacant inside maxillary position on that side of the head. The old outer fang drops out, whereupon the new fang moves laterally to a permanent position in the outer socket, leav- ing the inner once more vacant. Thus the inner socket is used only during the transition period, the outer being the regular location of the functional fang. Charles S. Tomes, ^ on the other hand, pictures the two sockets as being used alternately to hold the active fang, the immature fangs being contained in a magazine in a staggered line behind the two sockets, the most mature of the reserve series being always behind the vacant socket (Fig. 18). When the time for a change arrives, this fang advances to the vacant socket anterior to it and becomes seated permanently therein. The superseded fang drops out, leaving a vacant socket, to which, in due course, the next replacement advances. Thus, according to Tomes, the active fangs are alternately in the inside and the outside positions. An examination of a number of specimens, and the compilation of some statistics with respect to fang positions, show conclusively that Tomes' description is correct, and that the Mitchell theory should be discarded. In every normal rattlesnake there will be found two fully formed fangs on each side of the head, in addition to the less mature members of the replacement series. When the protective sheath has been cut away to expose these two, one, the active or functional fang, will be found firmly fixed in its maxillary socket; the other is the first reserve fang and is nearly always loose, that is, with its base unanchored to any part of the skull. Upon examining a considerable number of snakes, these first reserves are found in all stages of development, from being imbedded in their native capsules, to fully-advanced to the maxillary position, but not yet firmly seated, I have described these two fangs, on a side, as being fully formed or complete. This is true of the fangs proper, but not of their bases. One, the presently fiuic- * S. Weir Mitchell: Researches upon the Venom of the Rattle- snakes. Smithsonian Contributions to Knowledge, Vol. 1, pp. 16-29, 1861. ^ Charles S. Tomes. On the Development and Succession of the Poison-fangs of Snakes. Philosophical Transactions, Vol. 166, pp. 377-385, 1877. tional fang. Is anchored solidly in its maxillary socket up- on a bony base, or pedestal. The other, the reserve which will shortly replace it, has a softened immature base. The degree of hardening of this base corresponds to the close- ness of approach of the first reserve to its socket. Some- times the first reserve is still grouped with the other, less mature reserves; again it may be found in a later stage of development, that is, advanced to the maxillary position, and with the base somewhat hardened, so that, as the maxil- lary is tilted, the reserve tends to rise also, just as does the fully functioning fang, ^hen in this condition, the re- serve can still be distinguished from the fang it is about to replace by a slight looseness at the base, evident as the fang is manipvilated with a forceps. Rarely, both of the two fangs on a side are found to be firmly set in their respective maxillary sockets, that is, at the exact interval when the new fang is fully func- tioning and the older has not yet dropped out. This occurs so infrequently, however, that we know this period of over- lap must be rather short, compared with the time between fang changes. On the other hand, so seldom is a functional fang missing and the first reserve not yet in place, that we know an overlap, i.e., an interval with two functional fangs on a side, though short, must be the normal sequence. The absence of a functional fang on one side csm no doubt be construed to be the result of some mishap incident to cap- ture; certainly this is not a condition representing a normal sequence in replacement. In choosing between the two processes of change, as described by Mitchell and Tomes, it is important to ob- serve, first, that dissection shows the advancing first re- serve to be always behind the vacant maxillary socket, which is Just as likely to be the outer as the inward cav- ity. The Mitchell theory would require the advancing fang to be always behind the inner position, and that fixed fangs should be found in a transition stage, moving from the in- side to the outside socket. Neither of these conditioos is verified. In an examination of 210 specimens of rattlesnakes of various species, fangs were found fiinctional in the in- side location in 205 of the 4.20 cases, while the outside socket was occupied by the active fang in 215 cases. This shows that there is an equal usage of the two sockets for the location of the functional fang; certainly it is far from indicating that the outside position is the sole func- tioning locality except during the transition stage. A section discloses the fact that the future fangs lie, not in a single row as pictured by Mitchell (Fig. 17), but in two alternating rows as stated by Tomes (Fig . 13) . Between these rows there is a heavy, protecting wall of tissue, of greater thickness than that which separates each succeeding fang from its fellow on the same side; thus it is impossible for one of the inner series to reach the outer maxillary socket or vice versa. This dividing wall is main- tained between the fangs even when, for a short time, there are two functional fangs on a side. The wall is not joined to the sheath anterior to the fangs. Another objection to the Mitchell theory is the difficulty entailed in holding the fang and keeping it active while in the transition stage between the inner and outer sockets, particularly as a ridge intervenes, so that a fang would have to be lifted partly out of the socket in order to move laterally. Furthermore, the fangs of the two series are slightly asymmetrical; they are not equally suited to either socket, a detail to which reference will again be made. Thus by the examination of a number of specimens showing the fangs in all positions, and by statistics and dissection, we have a view which is equivalent to seeing the process in motion; and there is no question concerning the alternating use of the inner and outer maxillary sockets to hold the active fangs. There appears to be no synchronism in the advance- ment of the fangs on the two sides to their fiinctional posi- tions. Thus, of 210 specimens. 111 had an asymmetrical ar- rangement, with one inside and one outside socket in use. In the other 99 cases the functional fangs were either both in the outside, or both in the inside positions, there being 52 with both outsides functional and 4? with both insides. This indicates that the entire arrangement is one of chance; that, in general, half of the cases should be asymmetrical; and, of the remaining half, the pairs should be equally divided be- tween inside and outside positions. Even in a group of spec- imens recently born, neither symmetry nor a definite tendency toward the inside or outside position could be detected. The statistical data here given are the result of an examination of specimens of the two rattlesnake genera, Crotalus and Sistriirus. A study of a few individuals of the other genera of the Crotalidae. the family of the pit-vipers, Bothrops. Trimeresurus. Lachesis . and Aekistrodon. indicates the employment of the same mechanism. Since Tomes' investi- gation included Vipera it is evidently the mechanism of the Viperidae also. The separation of the two sockets on each side is just sxifficient to provide an anchorage for each fang, and to prevent interference during the short Interval when both con- tain active fangs. The inside socket is a short distance anterior to the outside. In describing arcs, when erected, the two fangs on a side tend to swing toward the same point, so that the separation of the puncture points of a bite is not appreciably greater with two outside than two inside fangs. This is shown by the fact that when two active fangs are found on a side, the lateral clearance between the points is usual- ly less than the center-to-center separation of the sockets. However, one point may be advanced ahead of the other. In a large Crotalus cinereous, using the head length as a basis equal to 100 per cent, we find the fangs to be situated posterior to the rostral by about 18 per cent. The separation of the outer sockets is about 4-2 per cent of the head length and the inner sockets about 36 per cent. Thus the centers of two sockets on one side of the mouth are separated by about 3 per cent of the head length, and the head length is about 2^ times the fang separation. From data on head sizes (see Part V, this series)*, a rough approxima- * References to previous parts of this paper are cited by part niunber. The dates and numbers of the Occasional Papers of the San Diego Society of Natiiral History in which these parts ap- peared are given on the first page of this paper. tion can be made of the size of a snake that has caused an injury, if the distance between the fang punctures and the species of snake be known; however, because the articula- tion of the erecting mechanism is such as to permit a con- siderable lateral play, there can be no great accuracy in this determination. Even when still imbedded in the reserve sac, the distal section of the first reserve fang, from the middle of the upper orifice to the point, is fully hardened on the ex- terior and of full length; that is to say, the length will agree, to a fraction of a millimeter, with the length of the adjacent functional fang which it is about to replace. How- ever, above the mid-point of the upper opening or lumen the process, or pedestal, which will later engage the socket, will be found to vary considerably in completeness, depend- ing on the imminence of replacement. It is the solidifica- tion of this pedestal which anchors the fang in the socket. From a study of the paired fangs on a side, in rattlers which are exactly at the time of fang change, that is, with both the new and old fangs firmly anchored, it is observed that the solidification of the pedestal has a con- siderable effect on the direction in which the fang points. Sometimes the two fangs are parallel, with the points al- most touching each other, but often one of the points is ad- vanced somewhat ahead of the other. Occasionally one fang may be crossed over the other. In a typical case of a double-fanged adamanteus with fangs 17 mm. long, the outer fang point was 1.6 mm. ahead of the inner. The lateral clearance between points was 1.8 mm.; the center-to-center socket separation 3.0 mm. While the outer maxillary socket is always slightly posterior to the inner, and its bottom is not quite so deep, nevertheless these differences do not produce an invariable orientation of the two points. Much seems to depend on the position occupied as solidification in the maxillary takes place. Looking at the first reserves in all degrees of advancement, it is foiind that if a long time is to inter- vene prior to replacement, the first reserve fang does not move if the maxillary is tilted. On the other hand, if re- placement is imminent, the fang tends to rise as the maxil- lary is rotated, although it is not yet fixed. Finally, complete solidification in the socket takes place and then, when the maxillary is rotated, both the new functional fang, and the old fang about to be replaced, rise as a unit. Ex- amination indicates that the posterior part of the bony pedestal or frustum solidifies last. Snakes change their fangs so frequently, compared with the growth of head or body, that measurements do not ordinarily indicate a larger size of the first reserve fang, as compared with the fiinctional fang it is about to succeed. Comparisons in several species as frequently showed the functional fang to be the longer of the two, as vice versa, except in a series of yearling Crotalus ruber . Here the growth was sufficiently rapid that the first reserve fang averaged nearly 0.1 mm. longer than the functional fang. No doubt the same situation would be found in other large species, such as lucasensis and cinereous, during adoles- cence, the period of fastest growth. It is well known that the fangs of pit vipers. such as the rattlesnakes, appear to be fabricated by rolling a flat section so as to form a solid tube, much as butt- welded pipe is made; for there is a sort of joint or suture, evidenced by a dark line along the front of the fang. Both lumens are really gaps in the suture, the upper or inlet opening being short and relatively wide, while the lower, or discharge orifice, is a long and narrow slit (Figs. 19, 20, and 21) . As the two surfaces of the hypothetical flat member are both covered with dentine it follows that, after rolling or folding, the inner surface of the tube (the canal) is coated in the same way as the outer; however, the inner surface is considerably softer. The line -of the longitudi- nal suture or weld can be clearly seen in the larger fangs, but so perfect is the joint that it cannot be felt with a sharp needle, except rarely near one of the apertures. The Interior line of the joint is even more perfect, for it can be seen only with a magnifier under strong light. When a functional fang is broken, there is no tendency of the break to follow this line; yet it is a real suture, as shown by studies of immature fangs. The material of the fang is very brittle and shatters under strain. The surface can be cut with fine sandpaper or a file, or scratched with a needle point. The surface of the tip of the fang seems slightly harder than the upper parts. The growing fangs are developed or completed, not as a unit, but from the point upward, the point being fully formed and hardened long before the upper part takes shape. Also, while the form of the fang indicates derivation from a flat plate rolled into a tube, the actual growth does not proceed in this manner; for, from the earliest period of development in which the form can be ascertained, the tubular shape is in evidence. The development or growth can best be explained by describing a typical series. For this purpose the following notes were made on an adult C. cinereous having a head length of 56 mm. It should be understood that this description covers the mechanism on one side of the head only, in this case the left. Reference is also made to Fig. 22. (1) The functional fang is in the outside socket, being solidly anchored therein upon a striated pedestal of bone. The tube is translucent and the canal clear. Break- age, by inserting a needle in the lower aperture, causes shattering, but the cracks do not follow the longitudinal joint or weld. The straight line distance from the lower end of the upper lumen to the point is 12.2 mm. (2) The first reserve fang is at the head of the inside series. It is well advanced toward the inside max- illary socket, but has not yet reached its final forward position. It is loosely held. The fang seems finished and hardened from the point to the central part of the upper lumen; above this, the section which will later be imbedded in the maxillary socket, i.e., the bony pedestal, is quite soft. The base, as far as completed, is hollow; this hollow (the pulp cavity) does not communicate with the venom canal or duct. The latter is partly filled with what is evidently nurturing tissue. The upper-lumen-to-tip length is 12.2 mm., or the same as in the functional fang. Inser- tion of a needle point in the lower aperture shatters the fang, and the breakage partly follows the longitudinal weld. MAXILLARY -- BONE - ORIFICE FIGURE 19 FANG IN INSIDE MAXILLARY SOCKET -DISCHARGE ORIFICE -CUTTING OR WEARING RIDGE FIGURE 20 FANG IN OUTSIDE MAXILLARY SOCKET FIGURE 21 PERPENDICULAR VIEW OF POINT OF FANG (7 fie or I f ice iipt.f(i''s forcsl'orl rrr -f occo^isr of directtor of the ,'Olit beluK t/e central arc. FrCURE 22 RELATIVE COMPLETENESS OF SERIES OF DEVELOPING FANGS First replacement fan^ is at the left: youn^ei^t oitd on the rli^tit. Solid parts are calcified; dashed sections forved uut uncalclfied; dotted secttor.s nnforted. (3) The second reserve (outside position) fang is complete only to the lower tip of the upper lumen. It is hard at the point but pliable above. The surface is polished and fairly translucent. The length of the complete section is 11.3 mm. The lower lumen appears perfect and of full size. Insertion of a needle point, however, shows the mate- rial to be somewhat pliable, and the longitudinal weld opens quite easily and regularly. This and the subsequent fangs are closely surrounded by capsules of tissue and the tubular interiors are filled with tissue. (4.) Third reserve fang (inside). The lower end of the fang is complete but slightly pliable; the upper end is quite soft and the entrance lumen has not begun to form. The lower, or discharge aperture, seems to be perfectly formed and of full size; the point, however, is dull, not sharp as in a completed fang. The length over-all is 10.1 mm. The tubular form is as perfect as in a functional fang; the longitudinal weld is clearly to be seen, but cannot be felt with a sharp needle. However, the introduction of the needle point into the lower aperture causes the suture to separate readily. (5) Fourth reserve fang (outside). This fang is soft at the top; however, the lower lumen is quite complete- ly formed, although pliable. The point is dull, thereby showing incompleteness. The exterior, when stripped of the capsule, is shiny and transparent. The length is 7.0 mm., of which only 2.2 mm. are above the upper end of the lower lumen. (6) Fifth reserve fang (inside). There is nothing above the upper end of the lower aperture; below, the fang is of full size, and rather firm. The point is dull. The length is 4«8 mm. (7) Sixth reserve fang (outside) . A dull point and the lower end of the lower lumen are to be seen, and are moderately firm. Such part of the lower orifice as is in evidence has a crescent-shaped cross section, not flat; the ultimate form can be clearly recognized. (8) Seventh reserve fang (inside) . This is only a small conical shape attached to the magazine wall; it is evidently the future capsule, the fang not being recognized. The facts most forcibly brought to attention by the examination of this series are: first, that if the fang were originally developed from a partly folded, and thus grooved, tooth, the process is not at present repeated in the growth of the individual fangs. Secondly, the fangs do not grow by the enlargement of their parts; on the contrary, the first stage is the development of the fang in its full size in the vicinity of the lower aperture, followed by the completion of th*e point and then the gradual extension of the upper section. If there is a suggestion of derivation from a grooved fang in the present suture or weld, and the continuity of the external dentine surface with the internal surface of the canal, it is no longer evident in the develop- ment of the tubular section of an individual fang, at least prior to the deposition of dentine. The only resemblance to a grooved fang, during the present method of individual fang growth, lies in the appearance of the lower aperture during its formation. This is the part of the fang first formed, 11 FIGURE 23 LOCATION OF REPLACEMENT SERIES MAXILLARY BONE I ---' FIGURE 24 SIDE VIEW OF FANG AND MAXILLARY VENOM GLAND / / ' „ , , . . , . . ■ ■>S^ j i; r r— ---.^ >---^ — ' ■■»•' I --V VENOM DUCT FANG FIGURE 25 RELATIVE POSITIONS OF VENOM GLAND, DUCT, AND FANG and, as the aperture is in reality a deep slot, we have, in effect, a short grooved tooth. To this the upper tubular section is subsequently added. Little seems to be known concerning the normal frequency of fang change. Having noted the effect of cap- tivity upon the frequency of exuviation, I am doubtful if we can learn much from observations on captive specimens. It is to be presumed that the final loss of the obsolescent fangs usually occurs in feeding. Discarded fangs are fre- quently found in the digestive tract. Dr, Charles A. Vorhies of the University of Arizona has shown clearly in motion pictures that C. cinereous, in feeding on rabbits, uses the fangs alternately to pull the prey into the mouth, just as a colubrine snake uses its mandibular teeth. This use would no doubt break off a fang about to be lost. Just as certain- ly as striking prey or an enemy. The method of removal of the functional fangs is not known with certainty. To Judge from an examination of obsolete and defecated fangs, or observation when they are broken off in the venom-milking process, the fracture oc- curs close to the outer or distal edge of the maxillary socket, which is at the proximal end of the dentine area. This leaves a considerable aunount of bony material (the pedestal) within the socket. Whether this drops out later, or is absorbed, I am not prepared to say; at least it is not retained for use with the next fang, since a resting maxillary socket is entirely vacant. In the above discussion the reserve fangs have, for clarity, been described as lying behind the functional fang and advancing forward into position. Actually they lie rather above than behind, as shown in Fig. 23. They are not widely separated as in Fig. 18, for here they have been spread to indicate the order of succession} nor even to the extent shown in Fig. 23, wherein it was desired to illustrate the relative sizes and states of completion of the first five reserves. Instead, they are as closely crowded together in the reserve magazine as their dimensions and the surround- ing capsules will permit. With the maxillary folded into its inactive position, the base of the first reserve lies op- posite the socket in which it will be anchored*. Solidifica- tion of the bony pedestal then takes place. Fang Structiire The shape of the functional fang is such as to preclude a simple description. It may be likened to a thin or slowly tapering cone, with a spreading or buttressed base, and with the central section bent into a circular curve, this curve describing an arc of from 60 to 70 degrees (Fig. 2U) . The basal tangent section is short and is of ir- regular shape, because of spreading to form the entrance lumen, and with a general reinforcement or abutment at the anchorage. This abutment surrounds the pulp cavity, which is greatly enlarged at the base. The reinforcement is large- ly secured by massing material posteriorly around the pulp cavity, with some lateral increase as well. In this, the two fangs on a side (whose alternating occupancy of the two max- illary sockets has been discussed; are slightly asymmetrical, the inner fang spreading inwardly, and the outer in the con- trary direction. However, most of the asymmetry required by FIGURES 26 AND 27 LONGITUDINAL AND CROSS SECTIONS OF FANG a-MAXILLARY b-BONY, STRIATED PEDESTAL C-PULP CAVITY d-WEARING OR CUTTING EDGES e-ENTRANCE LUMEN f- VENOM CANAL g- DISCHARGE ORIFICE h-SUTURE the dissimilar shapes of the two sockets is not provided by the fangs proper, but by the temporary pedestal structures of bone, whose difference from the fangs is evidenced by a discontinuity in the surface, these bony frustums having a duller and softer surface texture than the dentine covered fangs. The frustums are striated or corrtigated for rein- forcement; and, as some of the striations continue across the proximal parts of the dentine covered surface, a partial continuity with the fang is indicated. The pedestal frustvims are Irregularly shaped to engage the sides (rather than the bottoms) of the bony maxillary sockets; and, in this en- gagement, the asymmetry of the two sockets' Is largely com- pensated. The tangent at the point of the fang Is propor- tionately longer than the basal tangent. The former is pro- duced, not only by the straightening of the axis of the cone, but by the elliptical opening of the discharge lumen as well. Often, especially in the larger specimens, there is a slight reverse curve In evidence at this point; this serves to pre- vent the fang, when in its resting position against the roof of the mouth, from being directed against the tissue (es- pecially the venom gland) lying immediately above it (Fig . 25). The canal within the fang tapers as does the outer section. A cross section shows the fang to be slightlv el- liptical, especially in the proximal section (Table 30) . The walls are thickened opposite the major axis, as would be desirable from a structxoral standpoint; for the forces ex- erted in biting, striking, or drawing in prey, are likely to be In the plane of the curve. At the center of the curve of an adamanteus fang, having an upper-liomen-to-point length of 13.7 mm., the interior canal was found to measure about 0.7 by 0.8 mm., the walls being 0.25 imn. thick on the shorter axis, and 0.35 mm. on the longer, making the external dimen- sions 1.2 X 1.5 mm. At the base of the fang the pulp cavity lying be- hind the venom canal, with which It has no connection, is of considerable size. There is an aperture in the rear of the basal pedestal giving access to the pulp cavity. The cavity, which has the effect of dividing the fang into a pair of tubes, one within the other, decreases in size dlstally vm- til it practically disappears at the central curve, at which place only a vestige usually remains (Figs. 26 and 27). However, in large fangs It can be traced into the very point of the fang. The extent and location of the pulp cavity can best be ascertained by pinching off successive pieces of a well dried fang; the cavity can sometimes be followed by a discoloration between the interior and exterior tubes, which tend to shatter and separate along the pulp cavity surface. The inner tube is much thinner than the outer; its polish is not so high, and It is slightly softer. Often there Is no space or color between the tubes, although they are still distinguished by a plane of separation. However, at the front, as the tubes approach the suture, they fuse into a homogeneous material. Toward the upper Itunen the thin inner tube is completely separated from the outer by the pulp cav- ity, except at the front where, along the line of the one- time suture, the two are still fused. The relationship be- tween the inner and outer tubes, and the pulp cavity, is best explained by a series of cross sections along the fang (Figs. 26 and 27). 15 On the larger fangs there can be seen a faint yel- low ridge paralleling the lower aperture just beyond its outer edge, and extending from the point to a short distance above the upper end of the opening. The ridge is slightly roughened. There is a corresponding ridge on the under side of the point; as a result of these ridges the point has an elliptical cross section, with the major axis at a slight angle with the plane of the curve, the upper end of the axis being tilted outward and the lower, inward (Fig. 26). Both fangs on a side have the points twisted in the same direction. Viewed under magnification, the fang material is sometimes transparent, sometimes translucent white, but often a mixture of the two, the transparent sections being flecked and striated with white. In the larger fangs, and in strong light, the pulp cavity can be seen as a shadow, terminating in a cone-shaped void within the fang point. While the sutiore along the front of the fang is visible on the inner surface of the duct, as can be deter- mined by examining fractured sections, it is less evident than on the exterior surface. It seems to be more of a shadow than an actual plane of separation, so perfect is the junction. Yet the experiments with immature fangs, in which the suture opens smoothly and evenly, show it to be a true joint. The Fang Operating Mechanism The bones of the rattlesnake head are illustrated and listed in Figs. 28-31. Of interest to those concerned with practical snake-bite problems is the highly special- ized mechanism, whereby the fangs of these snakes can be tilted downward and forward, from an inactive position, folded against the roof of the mouth, to a striking or bit- ing position, approximately perpendicular thereto. The fangs are so long that, were they permanently erect as in the elapine venomous snakes, they would entail a serious handicap, and, in fact, they would be so unwieldy that they could not be protected from breakage. This tilting mechan- ism is characteristic of the snakes of the families Viperidae and Crotalldae; although the bones involved differ consider- ably in shape amongst the several genera of these families, the arrangement, as a mechanical linkage, is consistently maintained. Of this the rattlers may serve as an illustra- tive example. The fangs are carried, rigidly anchored, in the paired maxillaries, one on each side of the head. The max- illaries are shortened, as compared to those of snakes of other families, and are rotatable; it is this rotation that permits the tilting of the fangs. Considering the bones of the top of the head, that is, the frontal (3) and parietal (4., Fig. 29), as a datum, we find that some of the motion is secured by a slight hinge action of the prefrontal (2) at its attachment to the frontal; but most of it results from a combined sliding and hinge action where the maxillary (l) engages the prefrontal. The bones whereby the tilting motion is trans- mitted to the maxillary are the quadrate (ll) , which drops downward posteriorly, thus causing the pterygoid (9) to ad- vance; this in turn causes the forward motion of the ecto- 16 pterygoid or transpalatine (lO) , which, being connected to the maxillary below the hinge, pushes it forward. In Figs. 32 and 33 these bones are represented as a linkage, all the other bones of the skull, except those participating in the fang movement, being omitted for clarity. It should be understood that the anterior half of the pterygoid (9) , where it is shown in parallel with the ectopterygoid (lO) has little to do with the tilting mechanism, the ectopterygoid comprising much the stronger and more essential member of the linkage. Posterior to the connection with' the ectopterygoid, the pterygoid is strong and stiff, being heavily reinforced with wide flanges in a vertical plane. Anterior to this point it is relatively weak; the connection with the pala- tine (8) is not rigid, motion being permitted in all direc- tions. At its anterior end the palatine is connected by one set of tendons to the inside face of the maxillary and, by another set, rather more loosely, to the prefrontal. The purpose of these attachments seems to be to limit the lateral movements of the forward end of the pterygoid; but all of the articulations are so loose that there is not much re- striction, and there seems to be no effect of importance with respect to the rotation of the maxillary. Returning to the ectopterygoid, at its point of connection to the pterygoid, we find this attachment to be rigid, with the effect of a splice, so that the ectopterygoid and the posterior half of the pterygoid act as a single mem- ber. The ectopterygoid is laterally compressed for stiff- ness. As it approaches the maxillary it twists into a hori- zontal plane, the upper edge outwardly, the inner edge in a contrary direction, so that when it reaches the maxillary the flange is horizontal. The front end is bow-shaped, and the outer ends of the bow form points of attachment to the sides of the maxillary, thus not only tilting it but tending to restrict its motion substantially to a vertical plane. The entire tilting mechanism is very positive in its action. The fangs on the two sides of the head are separately con- trolled, so that the snake may erect or retract either fang independently of the other. Thus he is enabled to use the fangs alternately In drawing in food, if the victim is rel- atively large or difficult to control. When a rattler is held for milking he will frequently raise one fang at a time and attempt to stab the venom cup or any other object within reach. Consideration of the shape of the fang, taken in connection with the tilting mechanism, indicates, first, that it is better designed for use upon surfaces of relatively sharp curvature than against flat surfaces, i.e., upon small- er, rather than larger animals; and that the bite which fol- lows the strike is of great importance, the fang being de- signed to take full advantage of this phase of the action. Although more attenuated in shape the fang is not \anlike the talon of a hawk. If, in the strike, a rattler's jaws are open so as to be exactly in opposition, that is, having an opening of 180 degrees, with the upper Jaw held vertically, and if the fangs are erected perpendicularlv so that the basal section points directly forward (Fig. 3l) , then the point section will be directed at an angle of about 25 degrees to any plane surface at which the blow be aim.ed, or 6 5 degrees from maxi- 17 ,23 FIGURE 30 LATERAL VIEW OF SKULL FIGURE 28 DORSAL VIEW OF SKULL C. RUBER FIGURE 29 VENTRAL VIEW OF SKULL FIGURE- 31 LATERAL VIEW OF SKULL STRIKING POSTURE FIGURE 32 FANG TILTING LINKAGE FANG FOLDED OUT OF USE FIGURE 34 METHOD OF MEASURING FANGS FIGURE 33 FANG TILTING LINKAGE FANG ROTATED FOREWARD FOR USE Key to Figures 28 to 3? The Bones of the Rattlesnake Skull 1 . Premax ilia 2. Prefrontal (lachrymal of some authors) 3. Frontal i. Parietal 5. Baslsphenoid 6. Squamosal (supratemporal of some authors) 7. Maxilla (maxillary or supermaxillary) 8. Palatine (palatal) 9. Pteryioid (internal pteryioid) 10. Ectopteryioid (external pterygoid or transpalat ine) 11. Quadrate 12. Mandible (mandibular) 12A. Dentary 12P Articular 13. Pro-otic 14. Exoccipital (lateral occipital ) 15. Poison fani 16. Mandibular teeth 17. Pteryioid teeth 18. Palatine teeth 19. Supraoccipltal 20. Stapes (or columella auris) 21. Post frontal 22. Basioccipital 23. Kasal 21, Turbinal 25. Vomer mum effectiveness. Even allov/lng for a Jaw opening greater than 180 degrees, and a tipping of the maxillary to permit the fangs to be erected more than 90 degrees (rattlesnakes can attain a greater angle, as may be observed by manipulat- ing the venom cup in milking)* there is still an oblique rather than a perpendicular, approach of the point. But once the point has gained entrance, then both the curve in the fang and the folding action of the maxillary, serve to ac- centuate the penetration produced by the squeezing pressure of the bite, particularly as the farlg has a much smaller radius of curvature (about one-sixth) than the hinge distance of the upper jaw. It is true that the folding and the curve both sacrifice depth of penetration in favor of horizontal penetration, but they insure injection below the skin of the victim, which is the important point. This combined sliding with horizontal penetration is much less likely to be stopped by a bone than perpendicular penetration, and likewise the hook effect serves to hold to the prey or enemy momentarily. When the fang is folded, the emission aperture is directed inward toward the victim, which is a further advantage to the snake. It is probable that at the end of the strike the snake's Jaws are already tending to close, in which case the motion of the fang point, by reason of the combined head ad- vance and Jaw rotation, has a resultant motion more nearly in line with the fang-point axis. The fangs of those species having the least angle, such as durissus . molossus. and polystictus . are designed for more of a stabbing and less hooking action. The fangs of certain species of Bothrops are definitely of the stabbing type, as compared to the rattilers. This feature may possibly be correlated with venom quality; it is no doubt also of phylogenetic significance. The folding is, of course, equally beneficial in providing a depository for the fang when not in use. When folded back against the upper Jaw the base and the point are approximately level; the bulge of the curve fits into a groove in the lower Jaw Just outside of the mandibles. Method of Fang Measurement Before endeavoring to determine whether there are any differences worthy of note between the fangs of the sev- eral species of rattlesnakes, we must consider the variations to be found within a single species, so that we will not con- fuse mere individual differences with specific differences. Our first study is made of fang length, follov;ed by some considerations of fang shape, especially the nature of the central arc, and the angle between the two tangent sections. The measurement of the length of a fang is found to be a rather involved procedure. First the protective sheath of tissue must be cleared away. The fang itself is of considerable fragility, especially in the smaller snakes. The active fang is imbedded in the maxillary socket, which hides the true base, so that its length over-all, either * See also series of photographs in THE SUNDAY STAR, Washing- ton, D.C., Gravure Section, p. 4, March 12, 1939. 20 along the curve, or in a straight line from base to point, cannot be determined without dissection. Nor can the jujic- tion, either with the edge of the socket or with the bony- pedestal, be used as the proximal terminus, since this is irregular and cannot be located with accuracy. After some consideration of the problem, it .was decided to use, as a criterion of length, the straight line distance from the lower end of the upper aperture, or lumen, to the point of the fang. This is, of course, merely a convenient arbitrary criterion; the actual length of the fang to the edge of the maxillary socket is greater and the full length, including the ttasic frustum, higher still. By fastening a needle to the side of a vernier caliper, so that the point protrudes about 1 mm. beyond the upper caliper jaw, and at the level of its measuring face, a convenient and practical measuring tool is provided. This point can be inserted in the upper lumen and then drawn downward until it engages the lower end of the slit; the lower jaw of the caliper is then brought up until it just contacts the tip of the fang and thus the length is determined (Fig. 34). Such a measurement can be made ac- curately to within 0.1 mm. Care must be taken not to bring up the jaw too firmly, as the extreme tip of the fang is very- brittle and the point may be broken off without being noticed. Sexual Dimorphism As is usual in problems of this character, before beginning studies of intraspecific variations, we must first give attention to individual variations (if an individual supplies more than one measurement or count) and to possible sexual dimorphism. In the present study four measurements may be made in each snake, for, as has been pointed out, al- most every specimen has two functional and two fully developed reserve fangs. V.'e began our survey with the Platteville series of Crotalus viridis viridis . which is a large and homogeneous collection of specimens. In measurements made on 43 adult snakes of this series (measuring in each the functional and first reserve fangs), it was found that the average deviation in the fang length, from the mean of the several measurements in the same snake, was 1.14 per cent, with a standard devia- tion of 1.49 per cent. The maximum range between the long- est and shortest fang (in any one snake), was found to be 0.5 mm., or 6.5 per cent, as this particular snake had fangs averaging 7.7 mm. The maximum variation of any fang from the mean of the four fangs in that specimen, was 4.8 per cent. These figures indicate a rather high degree of individual uniformity; that is, in any single snake, the two function- al fangs and the first two reserves are almost exactly equal in size. We next use the same series to determine whether sexual dimorphism is in evidence, or whether the measurements of the sexes may be combined in our subsequent studies. It has already been shown (in Part V, of this series), that rattlers, v/ith the exception of C. cerastes, have no sexual dimorphism in the ratio of head length to body- length over-all. Thus, if the fang length is found to show no sexual dimorphism on a basis of head length, it will have none with respect to body length, and it is immaterial which we use as a datiom in our study of the fangs. 21 One active fang per side — -usually the right — was measured in 588 specimens of the Platteville series, 316 males and 272 females. The results were grouped by increments of 1 ram. in the head size. Taking the adults only, where sexual dimorphism would be evident if it exists at all, and consider- ing only size-groups in which at least 9 individuals of each sex were available, to afford a fairly reliable sample, we have results which may be tabulated as follows: Head size. Number of Specimens Average Fang Length, mm. mm. Males Females Males Femaley 26.0 - 26.9 9 U 5.23 5.28 27.0 - 27.9 17 15 5.4-4 5.50 28.0 - 28.9 34 39 5.57 5.71 29.0 - 29.9 25 26 5.82 5.81 30.0 - 30.9 19 2A 5.97 5.92 31.0 - 31.9 26 23 6.21 6.35 32.0 - 32.9 23 29 6.49 6.55 33.0 - 33.9 28 31 6.74 6.56 34.0-34.9 27 U 6.97 6.72 35.0 - 35.9 16 9 7.04 7.10 36.0 - 36.9 17 11 7.16 7.01 It will be observed that the female fangs average larger in 6 size classes, and the males larger in 5; the algebraic s\m of the differences is negligibly small. The variations evidently result from the fluctuations inherent in random sampling, rather than from a consistent sexual divergence. In the same manner the San. Lucan series of about 300 adult and adolescent specimens of Crotalus lucasensis was investigated. This material, collected by Capt. F. Lewis, was chosen because it is the most homogeneous series of large snakes of the cinereous group available to me. This group of diamond-back rattlesnakes is particularly important from the standpoint of snake-bite studies, as, in the United States, it is probable that more serious cases result from the bite of C. cinereous than all other rattlers combined. While I have available several hundred specimens of cinereous, they are from scattered localities throughout the wide range of the species; and, in the initial study of sexual dimorphism and fang growth-trends, it was desired to avoid the possible complications involved in combining snakes from areas in which they do not attain the same ultimate size (as is the case with cinereous in different parts of Arizona and Texas) , since snakes of the same length might not represent the same age or point on the ontogenetic ciirve. The specimens of lucasensis. on the other hand, are from a single restricted area, and from their close relationship with cinereous it may be pre- sumed that their growth-trends will be similar. Lucasensis is a decidedly larger snake than C. v. viridis. which permits a more accurate measurement of the fangs. The sexual com- parisons in this species follow: Head size, Number of Specimens Average Fang Length, mm. mm. Males Females Males Females 40.0 - 40.9 4 7 9.8 9.4 41.0 - 41.9 5 11 9.2 9.4 42.0 - 42.9 12 9 9.8 9.6 43.0 - 43.9 7 11 9.8 9.8 44.0 - 44.9 3 14- 10-7 10.1 45.0 - 45.9 6 12 10.5 10.7 46.0 - 46.9 10 14 10.9 10.3 47.0 - 47.9 10 9 11.1 10.7 22 In this case a slight superiority of the males is indicated; however, it is of somewhat doubtful significance, owing to the relatively small numbers of specimens available in the several classes. Furthermore, it must be remembered that this series shows a considerable sexual dimorphism in body size (Part IV, p. 22); the result is that, in the higher groups in the above table, the females are decreasing in number and the males increasing. In a situation such as this the effect of grouping is to accentuate the differences between the means, which may account for the slight superi- ority of the males. Thus it appears that sexual dimorphism is absent in one of these two species and is doubtfully evident in the other, and we proceed with our subsequent studies with the sexes combined. It will be remembered (Part V, p. 37) that C. cerastes is the only rattlesnake showing sexual dimorphism in the proportion of head length to body length over-all. This species may likewise prove to have sexual dimorphism in the fangs, either when correlated with the head size as a datum, or with body size; in fact it must inevitably show one or the other. However, the accurate determination of this point would require a larger series of adult cerastes from a single locality — say two or three hundred — than is now available to me. Intraspecific Fang Correlations In considering the length of a snake's fang we have the problem of comparing the size of one part of the body with another during ontogeny; in this case the length of the fang, either with the head length, or the body length over-all. Only infrequently do two body parts maintain a fixed ratio during growth, and the same absence of constant proportionality is true respecting the size of any single body part, or organ, in proportion to the body as a whole. This greatly complicates the size-relationship of any par- ticular part, such as the fang. As a problem, the deter- mination of fang proportionality is substantially the same as that of comparing the head length with the length of the body over-all, as developed in Part V of this series, which contained a discussion of the statistical methods involved. In the present instance we have the same problem of deter- mining the character of a regression line and the nature of the dispersion about that line. For the method of attack the reader is directed to the former paper; the development will not be here repeated. In this investigation, as in the head-length studies, we find it desirable to make an intensive survey of a few species, for the primary purpose of determining the nature of the variation as a scientific fact. This requires a considerable number of measurements to learn the type of regression line involved, and the nature and extent of the dispersion about that line. This is sufficient as far as intraspecific studies are concerned. If the relationship is found to be fundamentally complicated, that is, not express- ible as a simple ratio, or even as a first degree equation, then we must determine to what extent our findings may be generalized or simplified for application to interspecific problems, without too great a sacrifice of accuracy. Such simplified expressions are essential, for the taxonomist has neither the time nor the material required for the determi- 23 \o o \ 0 Ao° "\ oN 0 Voo 0 \ o p o OO DcX'fe 0 \ o o o \ o\ o v> o M3 Q. ^ X 0 \ o z { o \ g V 1— \ k > p°«b _i o*^ oto o uj tr CC LJ I D cpo\ Hq: o\ o « o o fo z to °c ^ UJ UJ D \ c -1 _l \ => < OOP u- Z o 0 3 \ on \ ° \ ° c L ^o I (/) z o 1- 6 .o\ \ o 0 O o RE 36 LENGTH -US RU \ o -FANG CROTAL \ : BODY- 100 LU _J Q. < X L J c\j o oo to ^r VNIAI Nl HJ_e)N3n £>NVJ eg F= - 2.098L2+ 13.171L - 0.666 These curves are also shown in Figs. 35 and 36 j they seem to afford a satisfactory fit of the averages of the points. Before proceeding to the discussion of other forms of curves and other species, I wish to point out certain re- lationships which are evident from these curves by inspec- tion. If tangents be drawn from the origin to each curve, we have at the point of tangency, a period of life at which the fang is growing* at the same rate as the head, or body, as the case may be; that is to say, during this period the fang maintains a constant ratio with the head (or body) . Earlier in life the growth of the fang is proportionately more rapid than that of the head; later it is slower. The same is true of the relationship with the body. But it must be understood that these constancies of ratio with the head, and with the body, do not occur at the same period of life. Also, as the curves are relatively flat, and the dispersion is considerable, we may, for practical purposes, assume the maintenance of a constant ratio for some distance on either side of the actual point of tangency. To illustrate, we find, from the F on H curve (Fig. 35), that, in the species ruber, the fangs maintain approximately a constant ratio with the head between head lengths of about 4-3 and 4,9 mm.^ Since we do not readily visualize the size of a rattler from its head length, we may translate these figures into body lengths by using H = 0.0374.L + 8.4., as given in Table 19 of this series (Occ. Pap. No. 4., p. 38), and determine this substan- tially constant ratio to be maintained between body lengths of about 925 and 1085 mm. This is the young adult range. With respect to the F on L curve (Fig. 36), we find the point of tangency to be at about 560 mm., and a constant growth ratio to be continued from about 500 to 600 mm. This range represents rattlers of this species at an age of about 3 to 10 months. Hence it is seen that a constant ratio with body length over-all is reached early in life, followed by a pro- portionately slower grov/th of the fang than the body. Later the snake enters a period during which the fang is growing at the same rate as the head, after which it lags slightly behind the head in proportionate growth. All of these conclusions are inherent in the three equations relating to F, H, and L, but it is desired to point them out devoid of mathematical terminology. The same types of relationships are found to be true of other species, except that in some cases the con- stant term h, in the equation F= fL'^ + gL + h, is positive. Where this is true, the proportional growth-rate of the fang * The word "growing" does not, of course, mean that an in- dividual fang grows, after it has become the functional fang. Growth as here used, connotes the procession of sizes which the succession of functional fangs attain during the period under discussion. Growth is actually by a series of small steps. i The point of tangency may usually be located with suffi- cient accuracy by eye; analytically it may be found at X = Vh/f where f and h are the coefficients in the regres- sion equation F = fH^+ gH + h, or F = fL2 + gL + h, as the case may be. If f and h are of unlike signs, then there is no real point of tangency, that is, no condition of constant proportionality. 27 14 13 12 -.0 59 ^ Z' MOLbSSl LtCASpNSI S — ^ /^ ^ J // f— RIJBEF CINEREOJS // / y > ^ '/ •— VIRIDS // y r /. V f J f / L / FIGURE 37 \/A D 1 AT li^KI r\^ CAM/" 1 CM^TUI VAKIAI lUN Ur rANQj LLINvj 1 n WITH HEAD LENGTH 14 13 12 .,0 59 Z - 8 I h 7 0 10 20 30 40 50 60 HEAD L-ENGXH IN MM. (h) 70 / Ay '/ 'J ^ ^ # ffi yf^ :3 ^ / ^ r^ y / ^ (/. w K' / ^ '/ Y z 4: ;^ / / V/ / A r / / V FIGURE 38 / WITH BODY LENGTH 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 BODY L-ENGXH IN METERS (l_) Is always less than that of the body, even in the Juvenile stage. The second degree parabolic equations covering sev- eral other species, from birth to adulthood, were determined to be as follows, the ruber equations being repeated for com- parative purposes. In the F-L equations, L is in meters to simplify the expressions. No. of Snecies Specimens c. m. molossus -U c. cinereous 52 c. lucasensis 270 c. ruber 100 c. v. viridis (Platteville) 588 No. of Species SDecimens c. m. molossus M c. cinereous 52 c. lucasensis 270 c. ruber 100 c. V. viridis (Platteville) 594 F i-n Terms of H - 0.00246H2 + 0.483H - 5.680 - 0.00157H2 + 0.358H - 3.120 - 0.00225H2 + O.424H - 4. 180 - 0.00186H2 + 0.393H - 3.940 - 0.00193H2 + 0.325H - 2.100 F in Terms of L (L expressed in meters) - 3.036L2 + 15.942L - 1.224 - 0.625L2 + 9.385L + 0.298 - 1.922L2 + 12.514L + 0.158 - 2.098L2 + 13.171L - 0.666 - 2.009L2 + IO.414L + 0.039 These curves are shown in Figs. 37 and 38. A gen- eral similarity in the curves is apparent, although each spe- cies shows some individuality, as is likewise indicated by the constants of the equations. With respect to these last, it should be made clear that the original data do not justify the number of significant figures here given. However, they have been retained for the purpose of checking the quantita- tive errors introduced by the various approximations subse- quently to be discussed. Of course, there is no reason, inherent in the re- lationship between fang and head, or fang and body, why a second degree parabola should be followed. It is merely found that this curve supplies a fit, with close enough ad- herence, to give a solution satisfactory for our purposes, especially having in mind the dispersion of the points, which in part results from individual differences, and partly from the errors inherent in laboratory measurements of such irreg- ular objects as the heads and fangs of rattlesnakes. It will be worth while to investigate two other types of curves, simple parabolas of the form Y = dX^, and exponential curves of the type Y = imnx. The first produces a straight line on log -log, and the second on semi-log cross- section paper. The use of semi-log co-ordinates is found to produce no results of interest. On log -log co-ordinates we find, in the special case of the large Platteville series, a close approach to a straight line relationship for the Juve- niles and for the adults; but the two straight lines are not consistent with each other — that is, they do not intersect in the adolescent range, as would be evident if there were a 29 transition in the growth gradient as found by Huxley in cer- tain similar proportionality problems.* In the other cases, log-log co-ordinates result in rather flat, but still quite apparent, curves. Thus, parabolas of the form Y = dX^^ do not result in a complete and logical solution. However, they are worth while to determine, since they give a moderately close fit, especially within any limited life-range (adults only, for example) , and they are useful in the manipulation of ratios. The failure of the young of the year, in the Platte- ville series, to follow a regression line consistent with that of the adolescents and adults, no doubt results from the same conditions which produced a nonconformity in the correlation of body weight with length over-all, as discussed in a prior section of these studies (Occ. Pap. No. 3, p. 50). In that case it was pointed out that this series, representing young of the year at the hibernating season only, comprises what might be called a dispersion, rather than a growth group. For this reason we do not consider that the series gives a true picture of the interrelation between juvenile and adult re- gression lines. In the case of the ruber series, it is possible, without too great a stretch of the imagination, to draw two intersecting straight lines, on log -log co-ordinates, one of which represents the juveniles, and the other the adults, with a satisfactory degree of accuracy — more satisfactory than both together can be represented by a single straight line. But it is important to note that the division between the two must be selected in a purely arbitrary manner; no natural point of flexure is evident. This is contrary to what Huxley has found (loc. cit. p. 10) in certain similar situations, where he has shown a sudden change in the growth gradient. In such a case two consecutive straight lines on log -log paper, with a short flexure between, is indicated as the most appropriate graph- ical representation. It has been stated that, although curves of the form y = dX^ do not exactly fit the growth trend of the fangs throughout the entire ontogenetical range, we can secure an entirely satisfactory fit by restricting consideration to a part of the life span. As the adults of any species are of the most importance, insofar as the practical considerations of the snake-bite problem are concerned, we are Justified in concentrating our investigations on the adult range. We find the following equations to supply satisfactory fits within this range: Species Constants in F= d, Rk, Constants in F- d^L^z d, k, d^ kz C.m.molossus 0.165 1.096 0.0235 0.896 C. cinereous 0.201 l.OU 0.0192 0.899 C.lucasensis 0.251 0.970 0.0351 0.828 C. ruber 0.177 1.052 0.0207 0.899 C.v.viridis 0.209 0.934 0.0355 0.791 (Platteville) * Julian Huxley , Problems of Rel; ative Growth; New York, 1932, p. 10. 30 Exponents of the type of k in the above equations are referred to by Huxley (loc. cit. p. 8) as "constant dif- ferential growth ratios". Where L is the independent vari- able, k becomes the "growth-coefficient" of the fang. From these last equations there may be readily de- rived body-proportionality equations showing the number of times the fang length is contained in the head or body length. We have the following results: Species Constants In H/F = d3H^3 Constants in L/F = daL^* d3 k3 d4 k* C .m.molossus 6.06 -0.096 42.55 0.104 C. cinereous 4.98 -o.ou 52.08 0.101 C.lucasensis 3.98 0.030 28.49 0.172 C. ruber 5.65 -0.052 48.31 0.101 C.v.viridis 4.79 0.016 28.17 0.209 (Platteville) If these equations do nothing more, they show again that the fang length does not bear a constant ratio, either to the body or to the head length, through the adult stage, since this would follow only if k3 and k^,^ were zero. The fact that in the H/F relationship, ki approximates zero, and va- ries from plus to minus in the different species, indicates that the ratio H/F is approximately constant within the adult r ang e . Before proceeding with the dispersion studies, I wish to comment on three aspects of the results thus far ob- tained. First, it is to be remembered that our criterion of fang length (i.e. the distance from upper lumen to tip) is more or less artificial. The over-all length of the fang, along the curve, is not proportional to this straight line distance during ontogeny, because the angle subtending the arc of the central curve changes during life, as will be sub- sequently discussed. Hence, the actual length of the fang, as measured along the bend, might follow a different regres- sion equation, when correlated with head or body length, than the distance which I have arbitrarily called the fang length, F. For example, in a series of adamant eus fangs having an F length of 14 to 17 mm., the distance along the curve was found to be from 10.5 to 13.8 per cent greater than F, the average being 12.8 per cent. In addition, the distance from the lower edge of the upper lumen to the distal edge of the maxillary socket was from 3 to 4 nm. (see dimension E, Table 30) . But F does have the advantage of being measurable with considerable accuracy; also, the distance is probably of more practical importance in a consideration of snake bite than the length of the fang along the curve. I merely call attention to this arbitrary character of F as a possible ex- planation of the rathfer involved formulas which correlate F with H and with L. Secondly, I have not canvassed all the types of equations, even of the second degree, which might have proved to fit closely the actual facts in these examples. Having determined that constants for curves of the forms Y = fx2 + gX + h, for complete ontogeny, and Y = dX^^ for the adult range, could be found which would produce satisfactory fits, especially having in mind the scatter of individual 31 ■ TABLE 22 CORRELATION OF FAUG AND HEAD LENGTH: PLATTEVILLE SERIES OF C. V. vlrlQls Fang Length in Millimeters w •H a c 10 0) a: 2.0 to 2.4 2.5 to 2.9 3.0 to 3.4 3.5 to 3.9 4.0 to 4.4 4.5 to 4.9 5.0 to 5.4 5.5 to 5.9 6.0 to 6.4 6.5 to 6.9 7.0 to 7.4 7.5 to 7.9 8.0 to 8.4 Total 15.0-15.9 16.0-16.9 17.0-17.9 2 1 12 12 2 10 1 16 22 18.0-18.9 19.0-19.9 20.0-20.9 »3 1 14 9 1 2 18 12 21.0-21.9 22.0-22.9 23.0-23.9 24.0-24.9 25.0-25.9 26.0-26.9 2 3 6 1 3 7 10 3 6 23 27.0-27.9 28.0-28.9 29.0-29.9 1 16 21 9 13 39 26 2 12 14 1 1 1 32 73 51 30.0-30.9 31.0-31.9 32.0-32.9 3 1 14 7 5 24 28 15 2 12 25 1 6 1 43 49 52 33.0-33.9 34.0-34.9 35.0-35.9 22 6 24 16 12 13 17 9 2 2 1 59 41 24 36.0-36.9 37.0-37.9 38.0-38.9 1 5 1 19 8 4 2 6 5 1 1 27 16 10 39.0-39.9 40.0-40.9 41.0-41.9 1 2 1 2 3 1 2 6 2 Total 2 29 35 3 12 61 114 1 124 99 79 21 9 588 TABLE 23 CORRELATION OF FANG AND BODY LENGTH: PLATTEVILLE SERIES OF C tl. Yiridifi. Fang Length in Millimeters U ■t-» •H 2.0 to 2.4 2.5 to 2.9 3.0 to 3.4 3.5 to 3.9 4.0 to 4.4 4.5 to 4.9 5.0 to 5.4 5.5 to 5.9 6.0 to 6.4 b.5 to 6.9 7.0 to 7.4 7.5 to 7.9 8.0 to 8.4 Total 220-249 250-279 280-309 1 11 1 6 n 2 8 1 9 22 310-339 340-369 370-399 3 19 6 1 1 1 28 7 1 400-429 430-459 460-489 1 1 490-519 5 20-549 550-579 4 3 A 1 8 18 6 11 1 5 17 34 580-609 610-639 640-669 24 27 30 30 4 22 20 3 1 55 59 57 670-699 700-729 730-759 4 2 24 26 17 24 26 2 3 13 1 40 57 11 760-789 790-319 820-849 10 2 25 10 3 19 18 14 3 2 5 57 32 22 850-879 880-909 910-939 2 6 3 1 5 3 2 3 3 3 16 9 6 Total 2 28 35 3 12 61 118 126 99 80 21 9 594 points, I have deemed it unnecessary to look further. (See pp. l,k & 4''7) . Other types of curves giving close fits could no doubt be derived, but they would be no easier to use, nor more intelligible than these; and there would be no essential theoretical reason for their adoption in the place of those here proposed. In fact, if any curve Is to be justified on theoretical grounds, it is probably Y = dX^ (Huxley, loc. cit., p. 30). Thirdly, I realize that these curves are only in- teresting as showing the facts of body proportionalities; they are not in such form as to be of much service to the taxonomist. An equivalent amount of detail with respect to all species would be fruitless. If the fang size is to be of any practical interest, its relationship with the head and body sizes must be expressed in simpler form, even though some errors be introduced thereby, ^or this reason it ap- pears advisable to make some determinations of the straight lines of best fit; then we may note the, extent of the error introduced by this simplification. We must also find how nearly constant H/F and L/F are, within limited length-ranges, to see whether practical use can be made of these easily de- termined ratios in comparing species. Straight Line Regressions in the Adult Range It will be observed that the coefficients of the X^ terms of the parabolic equations are small, which means that the curves are relatively flat. This is verified by an in- spection of the ciirves themselves. Figs. 37 and 38. If we are willing to restrict the applicability of our straight lines to limited ontogenetical periods, the adult range for example, the errors introduced by using them, in the place of curves of higher degree, will not be important. As far as problems involving fang length may have any practical value, consideration of adults is certainly most important, since the adults are most dangerous. Similarly, from the taxonomic or phylogenetic standpoint, the adults are of greater interest, for species differences may be more ac- curately determined in the adult state, and are more im- pressive than differences between Juveniles. Tables 22 and 23 are correlation tables of the Platteville series of viridis on a basis of head length and body length over-all, respectively. From these the straight lines of best fit were found to be as follows: Viridis (Platteville) All ages F = 0.223H - 0.81 and F = 8.22L + 0.55 Adults and adolescents only F = 0.195H + 0.09 and F = 7.12L ••• 1.33 To simplify the F on L expressions, L is given in meters; all other quantities are in millimeters. The equa- tion presumed to represent all ages is not to be considered accurate, since the range is too wide to permit a straight line to supply a satisfactory fit. By similar methods the straight lines of best fit were determined for the four other species which we have In- 33 TABLE 2A COMPARISONS OF CALCULATED VALUES OF F USING DIFFERENT TYPES OF EQUATIONS ADULT RANGE ONLY Second Degree Parabola = fx2 + pX + h) (Y = fX gX Simple Parabola (Y = dX^) Straight Line (Y = aX + b) Viridis ■ L 500 4.74 4.84 4.89 600 5.56 5.60 5.60 700 6.34 6.32 6.31 800 7.04 7.03 7.02 900 7.78 7.71 7.74 1000 8.44 8.38 8.45 H 25 4.82 4.96 4.97 30 5.92 5.94 5.94 35 6.92 6.91 6.92 40 7.82 7.88 7.89 45 8.63 8.84 8.87 Lucasensis L 500 5.93 6.03 6.16 600 6.97 7.01 7.05 700 7.98 7.96 7.95 800 8.94 8.89 8.84 900 9.86 9.80 9.74 1000 10.75 10.70 10.63 1100 11.60 11.58 11.52 1200 12.41 12.45 12.42 1300 13.18 13.29 13.32 H 35 7.92 7.90 7.91 40 9.20 8.99 9.08 45 10.37 10.08 10.25 50 11.42 11.16 11.42 55 12.36 12.25 12.59 60 13.19 13.32 13.76 vestigated, using only adults and adolescents exceeding 500 mm. in body length. The results follow: Molossus F = 0.261H - 0.82 F = 10.50L + 1.12 Cinereous F = 0.217H - 0.11 F = 8.61L + 0.39 Lucasensls F = 0.234H - 0.28 F = 8.95L + 1.68 Ruber F = 0.228H - 0.4.I F = 9.10L + 1.17 It would have been sufficiently accurate to obtain these straight lines graphically by paralleling, as nearly as possible, the points on the parabolas representing the adults. However, this calculation gives a check on the previous com- putations. It is quite apparent that, if we assume the second degree parabola to be the true curve of best fit, we can de- termine either straight lines, or simple parabolas (as we may desire) , which will pass through any two points on the orig- inal curves. The closer the points are together — that is, the shorter the life range between them — the closer will the new approximating curves adhere to the original second degree parabola. We are now in a position to compare these results with the parabolic equations previously discussed, to learn the extent of the errors introduced by the use of the sim- plified straight line formulas. For reasons already mention- ed, we restrict our comparisons to the adolescent-adult range. The results are shown in Table 1L, for the species lucasensis and viridis . This table indicates that the differences result- ing from the use of these three types of equations are rel- atively small — small indeed, compared with the fluctuations between specimens. It will be observed that the results cal- culated by the approximate equations supply figures usually not deviating from those secured from the second degree pa- rabolas by more than 0.1 mm. Thus, consideration of the parabolic equations is Justified only as a matter of theo- retical interest; the differences are not of sufficient magnitude to warrant their retention in most studies, for to continue their use introduces a refinement hardly Justified by the accuracy of measurements involved in the original laboratory data. However, we must be careful to apply the straight line equations only to the limited length-ranges upon which they are based, and for which they are designed. If we were to use these approximate equations for the com- putation of Juvenile fang lengths, important errors would be introduced, as shown by the following examples: At a body length of 300 mm. a Juvenile ruber has a fang length of 3.1 mm.; the straight line equation gives a result of 3.9 mm., an error of 26 per cent. Similarly, a Juvenile cinereous having a head length of 20 mm. will have a fang length of about 3.4 mm. The use of the straight line formula gives a result of 4.2 mm., an error of 24- per cent. It is seen that these equations are useless when applied to periods of life for which they are inappropriate. It is quite feasible to derive multiple regression equations of the first or higher degrees to fit the correla- tions of F, H, and L, but the dispersions are too great to permit such equations (with respect to the relative sizes of the coefficients) to have much value for interspecific com- parisons, -^s an example, the first degree multiple regres- 35 slon equation for hk specimens of C. cinereous over 500 mm. in length was found to be: F = 0.00391L + 0.1033H + 0.770 While discussing the matter of straight line re- gressions, it may be noted that, if we determine from the H on L relationship developed in Part V, and the F on H equa- tion presented above, a relationship between F and L, the result may be used as a check with the new F on L relation- ship developed. We have the following results: Determination Direct Through H Determination C.v.viridis (Platteville) F = 6.93L+ 1.A5 F = 7.12L+ 1.33 C.lucasensis F = 8.78L+ 2.20 F = 8.95L+ 1.68 The discrepancies noted result from the lack of ap- plicability of the straight line formulas to the F-L rela- tionship, and in part to the least-squares theory involved in their derivation. Dispersion Coming now to the dispersion, or the scatter of in- dividual fang measurements about the regression lines which represent the average conditions of a species, I think it worth while to investigate two phases: the extent of the dispersion, and whether it remains constant during life on a proportionality basis. For this purpose I have investigated the Platteville series of C. v. viridis during the adolescent- adult stage; the Juveniles have been omitted for reasons pre- viously mentioned. Using the equations F = 0.209H°*^°^, and F = 0.0355L0.791, I have determined the deviation of the fang length of each specimen from the standard or normal fang length given by the equation, "^hese deviations were tabulated as percentages of their respective normal values; the resulting percentages were then gathered into arrays, and their stand- ard deviations calculated.* In a previous section of this study (Occ. Pap. No. 4, p. 11), I have explained my preference for this method of calculation, as an indication of the char- acter of the dispersion surface, in the place of the usual standard error of estimate. In the present instance we reach the following conclusions with respect to the Platteville series of viridis: Coefficient of variation, F on H, 5.67 per cent; and of F on L, 5.23 per cent. Further analyzing the adolescents and small adults as one group, and comparing them with the largest adult spec- imens, as a second group, we find an indication of reduced dispersion in the largest sizes. The results follow, the figures indicating the coefficients of variation: * See Occ. Pap. No. 4, pp. 13 and 22, for a more complete dis- cussion of the method. 36 Adolescents or Young Adults Large Adults Basis, head length 5.90 5.01 Basis, body length 5.19 5.03 A reduction of dispersion is evident; however, analysis shows the differences to lack significance, although approaching this level in the first case, where the differ- ence, divided by its standard error, reaches 1.55. In comparisons of the dispersions of body parts or scale counts, taken from juveniles and adults respectively, we are checking a matter of considerable intrinsic interest: What is the trend of the dispersion of any character during ontogeny — are juveniles or adults more consistent and uni- form? There are two conflicting tendencies, or forces, and it is desirable to determine which has the superior effect. First, there is the tendency to suppress aberrant Juveniles, through the unsuitability, or even the definitely lethal qualities, involved in their deviations from the species mode, thus tending to decrease dispersion as a population ages. Secondly, there are the environmental effects on the indi- vidual during growth, through such conditions as the avail- ability of food, the results of accident or disease, favor- able or unfavorable habitats, or other matters affecting any individual as compared to the fellow members of his group. Thus this diversity of conditions would increase dispersion in the adult population encountering it. In summary, juve- nile dispersion should be high because of natal aberrance; adult dispersion should be high because of the hazards of life. Particularly interesting in studies of this kind are those characters which change during growth, as, for ex- Eimple, the width of the proximal rattle, or head length as a function of body length. On the other hand, scale count dis- persions, such as the number of ventrals, which do not change during ontogeny, should show only the effect of the suppres- sion of aberrant juveniles. A statistical calculation demon- strating a significant difference in the dispersion of any character amongst the juveniles, as compared to the adults, is of utility in determining which of these conflicting ef- fects seems to have the superior influence. I have already shown (Occ. Pap. No. -4> P. I?) that the dispersion in the head length, compared with body length over-all, tends to increase with age. The opposite effect is indicated here, with respect to the fangs, but the differences lack significance. Again, this cannot be considered particu- larly important, because the true juveniles have been elim- inated— our comparison is only between adolescents and small adults on the one hand and large adults on the other. The similarity of the dispersions of the adolescents and the large adults, when computed on a percentage basis, demonstrates the validity of the logical supposition that de- viations of any individual from a mode do not remain c onstant on an absolute-measurement basis as the individual grows. On the contrary it remains constant on a basis of proportional- ity; that is, a young rattler having a fang 5 per cent great- er than the average of his fellows will continue to deviate, as he grows, by about 5 per cent, rather than maintaining a constant difference in millimeters. Were the latter the case. 37 the dispersion would decrease markedly as the snakes age, a condition apparent neither here nor in the studies of head length (Occ. Pap. No. /+, p. 11). Thus far I have shown that the dispersion about the regression line, whether on a basis of head or body length, remains constant with a coefficient of variation of about 5.5 per cent of the mean fang length at that age. A cross sec- tion of the dispersion surface is substantially normal. This figure of 5.5 per cent means that the consistency of rattle- snake fang measurements may be described thus: Half of all the fangs measured will come within I^ per cent of the mean fang length at any body size; less than 7 per cent of those measured will deviate more than 10 per cent above or below this mean. For example, take the species lucasensis. A group of specimens 925 mm. long will have fangs averaging 10 mm. long. Over half the specimens will have fangs between 9.6 and 10.4 n™«; and fewer than 7 per cent of the fangs will be less than 9 or more than 11 mm. This indicates a character consistent enough, within a species, to warrant the making of comparisons between species. As a matter of interest with respect to methods of computation, the following statistics resulting from the cor- relations contained in Tables 22 and 23 are presented. It must be remembered that the standard error of estimate thus calculated, visualizes the deviations from the regression line as being constant in amount, rather than in percentage during ontogeny; and likewise the deviations are measured from the straight line of best fit rather than from a parabola. F on H F on L Platteville viridis Adults and Juveniles Coefficient of correlation, r Standard error of estimate, mm. Standard error of estimate, '% of mean Adults only Coefficient of correlation, r Standard error of estimate, mm. Standard error of estimate, % of mean 0.961 0.353 5.93 0.887 0.3M 5.48 0.982 0.239 4.04 0.985 0.332 5.29 Similar statistics of three other species which have been fully investigated are as follows, adult ranges only being considered: Cinereous Lucasensis Ruber F on H Coefficient of correlation, r Standard error of estimate, mm. Standard error of estimate, % of mean F on L 0.944 0.659 7.29 0.903 0.650 6.20 0.893 0.899 9.96 Coefficient of correlation, r 0.967 0.924 0.919 Standard error of estimate, mm. 0.503 0.588 0.783 Standard error of estimate, % of mean 5.61 5.64 8.73 38 It will be observed that the standard error of es- timate, as a percentage of the mean fang length, is, in the case of the Platteville adults, in fair agreement with the coefficient of variation determined by the other method. Choice of a Basis of Comparison for Interspecific Studies It will be noted from these statistics that the co- efficient of correlation r is higher, when calculated between fang length and length over-all, than when the fang is cor- related with head length. However, I do not consider the fang to body-length correlation as necessarily the most im- portant, or useful, despite this result. First it may be attributed, at least in part, to the fact that body lengths can be measured more accurately than head lengths. Under such circumstances, if perfect correlation were a fact of nature, our laboratory results would indicate a higher value of r in the correlation of F on L, than in F on H. Secondly, it must be remembered that, even though the points may adhere closer to the F on L regression line, than to that of F on H, this does not mean that the fang, during ontogeny, maintains a more nearly constant ratio with L than it does with H. We have already shown that in early life L/F is more nearly con- stant, while, in the more important adult stage, H/F tends to become constant. A high coefficient of correlation means only close adherence to the regression line, which may well be a matter of accuracy in measurement as above suggested; the constancy of the ratio, however, depends on the direction of the line, which is a more important criterion in this case. After all, it must be remembered that the fang is a part of the head and a closer relationship should be expected, in both intraspecies and interspecies comparisons, between F and H than between F and L. So while we find a closer correlation, as shown by individual variations, between F and L than F and H; we find a closer relationship, as an ontogenetical proportion, between F and H than between F and L, which is increasingly manifest In later life. To illustrate this, we take the Platteville series of C. v. viridis. and the parabolic regression lines already found. Assxime a snake with a fang length of 5 mm. Vi/e find that he will have a head length of 25.7 mm. and a body length over-all of 530 mm. Now let this snake grow until he has a fang length of 10 mm. His head length becomes 55.5 mm., and his body length 1270 mm. So while his fang increases 100 per cent, his head increases 120 per cent, but his body length increases by I40 per cent. Similarly in lucasensis . an increase of fang length from 6 to 12 mm. involves an in- crease in head length of 90 per cent, in contrast to a body length increase of 125 per cent. Thus we see that the fang grows more nearly in proportion to head growth than to body growth. Of course, the same relationship will be demonstrated if we let L or H double and determine what happens to the other two variables. For example, in the Platteville series, if the body increases from 500 to 1000 mm., or 100 per cent, the head length increases 75 per cent and the fang length 78 per cent, thus showing the closer agreement in proportionality between F and H than between F and L. This is to a certain extent a repetition of the interrelations initially set forth with respect to C. ruber (p. 27), where it was shown that juvenile fangs Increase in 39 TABLE 25 COMPARISON OF FANG LENGTHS BETWEEN ON A BASIS OF HEAD LENGTH SPECIES Head Length in mm. Molossus Fang Cinereous Length in mm. Lucasensis Ruber Viridis 20 2.99 3.-40 3.41 3.17 3.63 25 A.^5 A.H 5.03 4.71 4.82 30 6.58 6.20 6.53 6.17 5.92 35 8.19 7.47 7.92 7.52 6.92 40 9.68 8.67 9.20 8.79 7.82 A5 11.05 9.79 10.37 9.96 8.63 50 12.29 10.84 11.42 11.05 9.34 55 13.41 11.80 12.36 12.03 9.95 60 u.a 12.69 13.19 12.93 10.47 65 15.28 13.49 13.91 13.73 10.89 70 16.03 14.22 14.51 U.44 11.22 TABLE 26 COMPARISON OF FANG LENGTHS BETWEEN ON A BASIS OF BODY LENGTH SPECIES Body Length Fang Length in mm. in mm. Molossus Cinereous Lucasensis Ruber Viridis 300 3.29 3.20 3.74 3.10 2.98 400 4.67 4.15 4.86 4.27 3.88 500 5.99 5.08 5.93 5.39 4.74 600 7.25 6.00 6.97 6.48 5.56 700 8.45 6.91 7.98 7.53 6.34 800 9.59 7.81 8.94 8.53 7.08 900 10.66 8.67 9.86 9.49 7.78 1000 11.68 9.56 It). 75 10.41 8.44 1100 12.64 10.41 11.60 11.28 9.06 1200 13.53 11.26 12.41 12.12 9.64 1300 14.37 12.09 13.18 12.91 10.18 UOO 15.14 12.91 13.91 13.66 10.68 TABLE 27 VARIATION OF H/F WITH H Head Length in mm. Molossus V8 Cinereous I lues of H/F Lucasensis Ruber Viridls 20 6.69 5.88 5.87 6.31 5.51 25 5.15 5.17 4.97 5.31 5.19 30 4.56 4.84 4.59 4.86 5.07 35 4.27 4.69 4.42 4.65 5.06 40 4.13 4.62 4.35 4.55 5.12 45 4.07 4.60 4.34 4.52 5.21 50 4.06 4.61 4.38 4.52 5.35 55 4.10 4.66 4.45 4.57 5.53 60 4.16 4.73 4.55 4.64 5.73 65 4.25 4.82 4.67 4.73 5.97 70 4.37 4.92 4.82 4.85 6.24 TABLE ; 28 VARIATION OF L/F WITH L Body Length in mm. Molossus Values Cinereous Luc of L/F •asensis Ruber Viridis 300 91.2 93.8 80.2 96.8 100.7 400 85.7 96.4 82.3 93.7 103.1 500 83.5 98.4 84.3 92.8 105.5 600 82.8 100.0 86.1 92.6 107.9 700 82.8 101.3 87.7 93.0 110.4 800 83.4 102.4 89.5 93.8 113.0 900 84.4 103.6 91.3 94.8 115.7 1000 85.6 104.7 93.0 96.1 118.5 1100 87.0 105.7 94.8 97.5 121.4 1200 88.7 106.6 96.7 99.0 124.5 1300 90.5 107.5 98.6 100.7 127.7 1400 92.5 108.4 100.6 102.5 131.1 > II 0 {fl Ul D J i 6.6 64 62 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 4.4 4.2 4.0 \ 1 1 FIGURE 39 V VARIATION OF HEAD -FANG RATIO 1 1 1 1 1 1 1 . 1 ... \ ^^'^ y — V ^ ^ V V ^ jjf^'-^ > ^ _ c ' Rub ER \ s^ -uuS?^^^^ ^ _MOLOSS -- - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 BODY l_ENOTH IN METERS (l.) 1.5 1.6 ^120 i I wo I 0 (DlOO 0 m u D J 90 80 70 kV^-* ^ ^ J> ^ y^' C\N« £E2 iS- ^ ^ ""^ ^ s^ -^ ^ ^ \ \> )Cf^ 0 Z^"^ \ V ^ iOLO sso^ \^^^ - > * !»i^*' 1 1 1 1 1 1 1 1 1 FIGURE 40 VA .RIA' noh A 01 - B ODY -FA NIG RAT 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 BODY l_ENIGXH IM METERS (l_) approximate proportion to body growth, but in the adult stage which is here being discussed, the growth of fangs is more nearly in proportion to head growth. This is also evident from the sample parabolic expressions of the form X/Y = dX*^, given for the adult range on p. 31, for, if k is positive, H or L, as the case may be, increases more rapidly than F. Thus the head size, rather than that of the body, constitutes the better basis of comparison during the adult stage. Interspecies Comparisons in Fang Length In discussing the correlation of head with body length I have pointed out the difficulty of making inter- species comparisons in a character which changes during in- dividual growth (Part V, p. 39). Since a constant ratio is not maintained, one is under the necessity of comparing two regression lines, which can only be done graphically; or of comparing ratios, either at some fixed value of the indepen- dent variable, or at some value of that variable related to a specific time of life; e.g., average fully-adult 'male. None of these schemes is completely satisfactory, being cum- bersome in application and involved in exposition. And in the present case the situation is further complicated by the fact that measurements are time consuming and difficult; even if adequate material were available, it would hardly be worth ^^ile to make siifficient measiirements to locate the re- gression line of each species with acciiracy. Probably the best scheme of exposition is to plot average adult fang-head (and fang-body) co-ordinates of each species in relation to the regression lines of the five spe- cies already fully determined. From their positions with respect to these regressions we can at once tell, at least to the extent of the accuracy of these average points, which species deviate materially from the five species upon which we have concentrated, and the direction of the deviations. Thus far, such interspecies comparisons as have been made, have been set forth only for the purpose of il- lustrating the differences between the different types of regression equations, and the errors Involved in the use of the abridged forms . We now turn to the differences them- selves, first discussing the five species whose regression curves have been determined. The extent of these differences, although Inherent in the constants of the equations, and il- lustrated in Figs. 37 and 38, may be rendered even more ex- plicit by sample tables, setting forth, not only values of F for different values of H and L, but also the changing ratios H/F and L/F. These data are presented in Tables 25 to 28. The second degree parabolas have been used in their computa- tion. Referring first to Table 26, this shows the varia- tion in the fang length of these five species, as the body length varies from 300 to 1^00 mm. Of particular interest from the standpoint of interspecies comparisons. Is the ratio of the fangs of any two species as the snakes increase in size. Taking viridis and molossus as examples, we find that molossus, at 600 mm., has fangs 30 per cent longer than viridis; at 900 mm. the difference is 37 per cent, and at 1200 mm., 4.0 per cent. Similarly consider ruber and cinere- 43 ous. At 600 mm. ruber has longer fangs by 8.0 per cent; at 900 mm. by 9.5 per cent, and at 1200 mm. by 7.6 per cent. We see that these fundamental differences are substantially maintained from adolescence to full growth. If we feel that these differences are only reflect- ing head-length differences which we naturally expect the fangs to follow, since they are a part of the head, we return to Table 25, wherein head lengths are varied, to note the corresponding changes in the fangs, and make the same com- parisons. At a head length of 30 mm. the molossus fang is 11.1 per cent larger than the viridis fang; at 4-0 mm. it is 23.8 per cent larger, and at a head length of 50 mm. it is 31.6 per cent larger. In the cinereous-ruber comparison we find that ruber is 2.7 per cent smaller at 25 mm., 1.4. per cent greater at J^.0 mm., and 1.9 per cent greater at a 55 mm. head length. The closer grouping of the curves in Fig. 37 as compared to Fig. 38 graphically illustrates that, interspe- cifically, the fangs more nearly follow head than body size. Thus it is clear that there are interspecies dif- ferences which, in some cases, are of considerable magnitude. We next refer to Tables 27 and 28, which show the trends in the H/F and L/F ratios through the adult ranges of these five species. It is at once apparent, as has already been determined analytically, that there is less difference in the H/F ratio than the L/F, both within a species, and between species, during ontogeny. As the head length doubles in size the change in H/F is usually less than 10 per cent, a condition inherent in the small size of the constant term in the F on H regression equation. As long as we are sure that H/F remains substan- tially constant throughout the adult range of a species, we need not be particularly concerned as to the head lengths at which we make comparisons. To the extent that there are intraspecific variations in H/F we must be careful not to compare species of markedly dissimilar adult sizes at the same head length, since we will be comparing the Juvenile ratio of the larger with the adult ratio of the smaller. In Figs. 39 and 4-0 the data of Tables 27 and 28 are presented graphically. With regard to the first diagram, it should be explained that the H values of Table 27 have been converted to values of L by the use of the constants developed in Table 19 (Part V) , since we visualize snake sizes better in terms of their total lengths than in terms of their head lengths. The trend whereby the H/F ratio falls rapidly from the Juvenile to the young adult stage, and sub- sequently rises slightly, is indicated in all five species. The L/F curves In Fig . 40 show a greater diversity in form. It is to be remembered that the scale is exagger- ated. The forms of these curves, in the smaller body sizes, depend greatly on the constant term h in the equation F = fL2 + gL + h. If this term is positive, we have a con- tinuous increase in the L/F ratio, as shown in the cases of viridis, cinereous . and lucasensis; this is not true in molossus and ruber . where h is negative. In these species, therefore, L/F decreases in the Juvenile range, and subse- quently increases, as it does in the other species. 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With curvatures in both directions as shovm, one may even hazard the guess that the true relationship is of the form L/F = a^L + hy, that is, the F on L relationship is hyperbolic rather than parabolic. The differences found by applying such curves would be important only in the Juvenile range. Data showing Interspecific comparisons of the rat- tlers are presented In Table 29. In most -cases the statis- tics are based on the measurements of five adult specimens of each species or subspecies. From these, average values of the H/F and L/F ratios have been computed, it being under- stood that the ratios were calculated separately for each specimen, and then averaged, rather than dividing the average value of H by the mean of F. In Fig. 41 the same data are shown by indicating each species as a point, determined by the co-ordinates of the average head and fang lengths, similar treatment being given the body and fang lengths in Fig. 42. In each figure the adult regression lines of the five species previously discussed are also presented; this permits us to orient the other species readily with respect to these five, and to de- termine at once those which differ essentially from the rat- tlesnake mode, as represented especially by cinereous and viridis. In considering these two diagrams, it should be emphasized that the single points which represent the spe- cies and subspecies, except those for which complete re- gression lines have been drawn, are presumed to be based on adult measurements only. I shall dispose of Fig. 42 temporarily by stating that it merely repeats much that was developed in Part V, with regard to head proportionalities. For we see that tigris, mitchellii mitchellii. and scutulatus have conspicu- ously short fangs, when compared, on a basis of body length, with the general run of rattlesnake species. But this is only because these species have small heads. Thus we show that, in general, rattlesnakes with small heads proportion- ate to their bodies, likewise have short fangs on this basis of comparison. This, of course, we might have expected in advance; yet it would not have been impossible for the rat- tlers to have developed a compensating tendency whereby this handicap might have been balanced by giving these small- headed species unexpectedly long fangs. Such we find not to . be the case. So we may say that, to the extent that longer fangs are important in snake-bite cases, snake species with large heads in proportion to their bodies are likely to be the more dangerous, other important variables being equal. Retiornlng to the more important F on H comparison shown in Fig. 4,1, we note that, if we consider cinereous to represent the mode of the larger species, and viridis that of the rattlers of more moderate size, we find the rattlers with fangs of unusually large size to be adamant eus , molossus . polystictus. and ste.lnegeri. The latter species, however, is premised on a single specimen, and therefore is not to be considered conclusive. \ \ \^ \ \ \\ \ \ 3 \ 3 s 1 \ v\\ i \ "S \\\^ Si \\ > i \ o \y -^ \ \ a \ \V ^S o \ "4N \\ ^ Kl % \ t is A \\ 1 V .1^ 2 A I \ ^i^l. \ w \ ** ■= 3 o C 1 s N ^ ^11 \ \*-%.\ \- >\ \ "PX O ^ \ \ "3 ^ O 0 » c 3 a ^ II 1 \ \v ^^ o ^ I. N.N \ ^ \ \^ \^ E 42 S OF BODY CURVE TREND \ % \ \ \ X kNv , ^ RISON S OF ECIES V. >\ ^ V 3 O li. o tc UJ z ^ i \ \ \ \ ^■5 " UJ o \\^ \ ^" 1 1 \ \ u< 1 \ \ lOz y o o UJ Ql 1 1 1 lO 0 0 OD O o O CM O fM~oo>oo»^«o»r>^ro (j) l/NkN Ml HXON3~l ONVJ It will be observed that most of the subspecies of vlrldls adhere rather closely to the virldls vlrldls line, although the desert forms, lutosus . abyssus, and or eg anus from eastern Washington, have somewhat shorter fangs. Sim- ilarly, ruber, lucasensis. tortugensis, and exsul comprise a well-knit group. Scutulatus. as is the case with many char- acters, is closer to viridls than to cinereous, notwithstand- ing its superficial resemblance to the latter. I would call attention to the manner in which the viridis line cvirves over and across the cinereous and ruber lines. Viridis. especially the Platteville series from east central Colorado, is a smaller snake than the other two. I am of the opinion that if we had accurate regression lines of the smallest species, we would find them, in turn, curving over the viridis line. This is Inevitable unless they have, proportionately, much shorter fangs when Juveniles than when adults, a condition not found to exist in the species fully investigated. However, be this as it may, we must remember that constant ratios are represented by straight lines ra- diating from the origin; and, with all of the smaller spe- cies concentrated below a line Joining the origin with adult viridis. we reach the conclusion that the adults of small species of rattlesnakes have shorter fangs, proportionate to their head lengths, than larger rattlesnakes. Cerastes and willardi have rather larger fangs, *iile pricei and klauberl have fangs smaller than the mode of these smaller species. With respect to the stunted forms, we find that these fall close to the regression lines of their prototypes. Thus, we find tortugensis near the cinereous line; exsul on the ruber line; and Coronados Islands or eg anus, and nuntius, on, or near, the viridis line. This indicates that stunted forms have the fang proportionalities of the adolescents of their prototypes, and hence larger fangs than the mode for adult rattlers of non-stunted species of similar head size. As we study Fig. 41, we cannot fail to observe, in the F on H points, a rather definite trend which has no es- sential relationship to the regression line of any particu- lar species — a sort of generic regression line of which the variates are the adult averages of the individual species. We might fit a straight line to these data, but in this case it would not pass through the origin. A straight line in F/H appears more appropriate. By elementary curve fitting we find F/H = 0.0025H + 0.095 to fit the scattered points quite well. Thus, our generic regression line becomes F = 0.0025h2 + 0.095H. This likewise has been drawn In Fig. 41. Notwithstanding its inexactness, this line may be considered a better guide in judging species deviations from the rattlesnake mode than the ontogenetic line of any single species. It is seen that the majority of species do not de- viate from it very greatly. Insofar as our incomplete data indicate, it would appear that stejnegeri. polvstictus. exsul. and molossus have unusually large fangs, while klauberi. triseriatus. and the northern or eg anus have small. It is hardly necessary to point out that. In locat- ing the points to be used in deriving a generic relationship of this type, it is important that all of the points repre- sent approximately the same period in the life history of each species (e.g., average fully-adult male), because the ontogenetic curves are not parallel with the generic curve. For example, if our data indicate that a large adult male 49 ruber has a head length of 4.O mm., and a corresponding fang length of 8.8 mm., the point does not fall on our generic curve. However, if the ruber head size which corresponds to the ontogenetic conditions under which the other species were determined, is 51 mm., then the ruber point does fall on the generic curve. The generic curve obviously shows that a species having a head size twice that of another, has fangs more than twice as long. For example, a species with an adult head length of 30 mm. would have fangs 5.1 mm. long, while one with a head length of 60 mm. would have 14..7 mm. fangs. Thus, with an increase of head length of 100 per cent, the fangs in- crease 188 per cent. This is not what happens as a growing rattler follows the ontogenetic curve of its species . For example, as ruber grows from a head length of 30 to 60 mm., its fangs increase from 6 .17 to 12.93 mm., or only 110 per cent. It may be pointed out that while there may be consider- able uncertainties in the generic and ontogenetic curves which I have deduced, particularly with respect to the exact values of the coefficients, there can be no question concerning the directional trends, or the fact that the generic curve is steeper than the ontogenetic curves. That is, there is no doubt that larger species of rattlers have fangs exceeding in length those of the smaller species in greater degree than would be expected from what we know of intraspecies trends, or from a direct proportionality with the other bones of the skull. Assuming that long fangs are an advantage, if not carried to too great an extreme, we may hazard the guess that these long fangs are possible and necessary to a larger spe- cies because it has the weight to drive them in, in a strike, or the muscle to Imbed them in a bite, whereas the smaller snake would lack the essential momentum or muscular power. For we have been discussing linear dimensions only; whereas the weight of a rattler increases even faster than the cube of his body length (Part IV, p. 44.), and his muscular power at least as rapidly as the square. Thus, the larger snake is provided with the power to drive in a proportionately longer and heavier fang. Again, viewing the venom and fang as a prey-securing mechanism, we must recognize the fact that, if both prey and required venom dosage vary approximately as the third power of the snake's length, the fang should be longer than that involved in a constant ratio with head length. As to the difference in the trend of the ontogen- etic cxirves, these seem to be designed to give to each spe- cies its highest F/H ratio (or lowest H/F ratio, see Fig. 39) at the time of most rapid Increase in bulk, that is, between adolescence and young adulthood, when presumably, its food requirements are at a maximum. Although I consider the F on H relationship the most logical and important for study in interspecific re- lationships, the F on L criterion is also of considerable interest. After all, it is of some value to know that tieris has very small fangs proportionate to its body length, even though this may result from tigris' having a remarkably small head. Hence, we return to Fig. 42. Again, we draw an approximate generic curve in contradistinction to the onto- genetical curves of the five selected species. The situa- tion of the scattered points is found to be fairly satisfied by the equation F/L = 3L + 6, or F = 3L2 + 6L, F being ex- pressed in millimeters and L in meters. Once more, it should 50 be stated that this very approximate equation refers only to adult snakes, and these of an average adult size rather than to \inusually large specimens. Upon this direct body-length criterion, and making no amendments by reason of disproportionate head sizes which deviate from the rattlesnake mode, we find that the forms with unusually large fangs are ste.jnegeri. willardi. cerastes, exsul. polvstictus. molossus. lucasensis, ruber, and adam- anteus. Species with conspicuously small fangs, compared to their body lengths, are pricei. klauberi. tieris. enyo. mitchellii mitchellii. Washington or eg anus, lutosus. and scutulatus* Again, we find, as when using head length as a basis of comparison, that larger species have fangs longer in proportion to their bodies, than small species. Thus, if two species fall close to the generic curve and one reaches an average adult length of 600 mm. while the other attains 1200 mm., the first will have fangs 4,. 68 mm. long, iriiile the larger snake will have 11.52 mm. fangs, an increase of M? per cent, compared with the body increase of 100 per cent. Hence, regardless of head size, it is in general true that larger species have proportionately longer fangs than small- er species. Other Fang Dimensions Thus far in discussing both intra- and interspe- cific variations, I have treated them only on a basis of the single dimension F, the distance from the bottom of the upper lumen to the point. As I have stated, this was selected as the dimension most readily and accurately meas\irable. It is now desired to mention some of the other dimensions and mor- phological characteristics. First as to intraspecific variation. A series of some twenty specimens of C. ruber at all ages were studied, measurements i3eing made of the radius and angle of the cen- tral curve, and the thickness at the mid-point, these being correlated with F. It was found that the fang does not re- tain a form of constant proportions, as the individuals of this species grow in size to maturity. The thickness at the mid-point does maintain proportionality up to the time the snake is a young adult, in this particular species, about 900 mm. long. Subsequent to this time there is a more rapid Increase in diameter than in length, so that the fangs of the larger snakes are proportionately thicker, heavier walled, and stronger. When it is remembered that the snakes have relatively shorter fangs (proportional to body) in the large sizes, it would appear that the diameter of the tube continues to increase more nearly in proportion to the body length of the snake. The radius of curvature increases gradually from the smaller to the larger snakes, but apparently reaches a maximum at about 900 mm., subsequent to which there is no further increase in this radius. In this species it is found that this maximum is about 6 mm., which remains constant for fangs between 10 and I4. mm. long. Necessarily this means that the longer fangs have a greater arc of curvature, or longer tangents, since the radius of curvature is not in- creased as the fangs lengthen. 51 2 ^: ? 2 3 t ^ s O uj o < ? TO N MILL Ul Uj -J ^ — 5 2 z ^ 5 ti' ><, 71 — > cr J o 3 Ul ^ ROM J S RUBI ENGTH OF 5 2 U. D -^ AND SHAPE OF CROTAL ZATES THE OVERALL o 2 u O li- 2 -iU 1 M — ^ ffl NGE OF FANG Si: SER FIGURE BELOW EACH FANG -n < Uj I J II- IIU 2 u ■^ The external angle, made by the two terminal sec- tions produced, is difficult to measure with accuracy, es- pecially in the smaller snakes, because of the irregularity of the tangent sections. However, there is a definite in- dication that this angle does increase as the snakes grow to maturity. For instance, in the Juvenile snake having a fang length of 4. mm., this angle, which equals the central angle of the curve, is approximately 65 degrees, while in the fully adult specimens with fangs approximately 12 mm. in length, the angle averages 72 degrees. Thus, the arc of curvature increases with age, and the larger snakes have a relatively more hooked fang. I have not so\ight to present these onto- genetical changes in the form of equations because the meas- urements, at best, are not highly accurate and the coeffi- cients of the equations would be of doubtful value. The trends which have been mentioned are, however, unquestioned. For the better illustration of the changes which take place with growth. Fig. 4.3 has been prepared. This shows a series of ten ruber fangs taken from snakes varying in sizes from about 350 to 1350 mm. at intervals of about 100 mm. The changes in the radius and angle of the central arc are evi- dent. The best method of indicating some of the species differences in fang shape and proportions is by means of a tabulation of dimensions. Such data are set forth in Table 30, together with Fig. 44, which explains the measurements which are listed. It will be noted that the shape and proportions have a certain uniformity, when allowance is made for varia- tions in F, the total length of the fang. As previously noted, F is considered the basic length, since it is the dimension which can be most acciirate- ly measured. Of the other dimensions the thickness of the fang as given by G, J, K, and N, can be measured with con- siderable acciiracy. E, which represents both the length of the upper liunen and the distance to the edge of the socket, cannot be determined with any degree of certainty, except in the largest fangs, and therefore this is to be taken only as an approximation. The size of the lower aperture, N, is easily determined in some specimens, but not in others, be- cause of the method by which this aperture is formed} the lower end of the slit often merges gradually with the point and therefore the lower terminus is not definitely fixed. The angle also must be considered only an approximation, since the two tangent sections which are presximed to make it are short and somewhat irregular, and therefore their direc- tions difficult of determination. On the other hand, the radius of curvature of the outer edge, which, in the central part of the fang, closely approximates a circular curve, can be determined quite acciirately by comparing with arcs of circles of known diameter. It may be noted that the propor- tionality in the fang is carried even to the point, for the tip is much sharper in the smaller fangs than in the larger, even though the latter may be fresh and therefore unworn. With reference to the angle. It is observed that the cinereous group, in general, has a greater angularity than the others, followed by the viridis group. Durissus and molossus have conspciuously flat fangs, as is the case also with polystictus. Some of these differences in shape are illustrated in Fig. 45. Small species also tend to have 53 TAhLE 30. SAMPLE FAtiC CIBEUSIONS (Dlmens Letters ions a refer re In 3m./10, except L In mm. to dimensions si.o«n In Fipure ) 44 Lenfth L Head a Fang F B E li J K U N P 10 B 10 f 55 C. durissiu aurissus C. duruaiu t«rrificu8 12U 5-!4 C. builiseiu 737 650 310 128 59 147 65 24 9 27 9 13 8 13 5 12 4_ 42 12 _i0_ 6 6 62 63 1123 530 133 150 21 21 17 10 920 490 105 122 16 H 10 8 6 25 9 55 C. adamaatetu 1685 1630 730 700 171 160 197 17£_ 35 27 4' 25 23 21 15 12 14 12 54 35 9 9 72 82 C. tortuzenaia C Iucsmhsu 1015 1258 420 590 84 133 94 U9 13 13 15 22 13 6 12 6 11 20 3 73 555 118 17 21 17 9 9 33 7 70 li31 375 93 105 19 17 13 9 3 23 5 88 400 87 96 15 16 11 7 6 26 6 64 872 375 75 36 15 12 10 6 6 18 5 62 o29 274 48 55 9 8 7 5 4 17 4 59 931 430 34 97 19 U 9 7 6 19 1173 500 33 101 17 17 H 8 7 25 6 61 628 261 42 49 3 7 6 4 3 16 3 60 C. vindia oreganua 1052 490 93 104 15 13 15 3 3 31 6 C. mitchellii mitchellii 390 335 57 74 15 13 7 6 5 10 18 41 3 7 71 C. mitehellii pyrrhua C. nutcheUii stephenai 335 330 71 78 11 16 11 6 6 19 5 68 772 280 43 50 9 8 7 5 4 10 2J 69 767 370 31 83 10 u 9 7 6 23 5 67 905 390 102 116 20 13 11 8 7 21 9 a C. horridus horTidua 116 2 460 102 118 20 19 13 9 9 30 7 70 979 413 100 112 15 16 11 7 7 2b, 7 60 C. lepidua klauberi 693 327 51 59 13 9 8 5 4 15 5 53 C. tnseriatua tnacriatua 520 280 33 39 6 6 5 4 4 15 24 62 558 265 36 40 6 7 6 4 4 13 4 48 C. wiUardi 517 275 52 57 7 7 6 4 3 13 3 68 S- ravuB 409 210 33 43 7 6 5 3 3 9 ■■^i 49 S miliariua miliariua S miliarius barbouri 550 295 54 63 10 9 6 4 3 12 5 65 i25 235 37 44 8 6 5 3 3 11 3 61 S. catenatua catenatua 737 326 55 62 10 11 3 5 4 15 5 69 S. catenatua lerBemmua = 1 1 ^^Angle ♦ FIGURE 44 DIMENSIONAL KEY TO TABLE 30 J IS ± THICKNESS AT G flat fangs, thus showing a generic tendency similar to the ontogenetic trend found in ruber . As to the thickness, an Investigation of F/K indicates a tendency for an increased value with the larger snakes, as was evident with growth in ruber . This also is to be expected, for, if the forces (es- pecially transverse) exerted on the fang increase in propor- tion to the weight of the snake (roughly the cube of the length), then the cross section of the fang must increase more rapidly than would be involved in a mere proportionate increase in linear dimensions, which would increase the cross section only as the square. The structural problem is somewhat similar to that of the cross section of the leg bones of mammals, which cannot bear a constant proportional- ity, since the compressive strength would increase only as the square of the linear dimensions, while the weight to be supported increases as the cube. Miscellaneous Data on Fangs It should be understood that the statistical data which I have presented apply only to the rattlesnakes, gen- era Crotalus and Sistrurus. I do not have available ade- quate series of other genera, either of the pit vipers of the family Crotalidae. or the true vipers, family Viperidae. to determine anything of interest concerning their ontogenetical trends. However, even a superficial survey indicates that generic differences are likely to be considerably greater than interspecific differences, as might well be expected. For example, the fer-de-lance, Bothrops atrox. a common pit viper occurring from southern Mexico to Brazil, has a straighter fang than any rattlesnake. 1'he central curve ex- tends continuously from upper lumen to point, instead of comprising a shorter-radius arc between two tangents, as in the rattlesnakes. A B. atrox fang 18.7 imn. long follows a circular arc with a radius of 17 mm. The radius of the cen- tral arc of a C. adamanteus fang of substantially the same length is only 9 mm., for as has been stated, the adult rat- tler fang comprises a short circular arc between two tangents. Thus the rattler fang is more sharply hooked — it is better designed for biting, and the Bothrops fang for stabbing. The latter somewhat resembles a juvenile Crotalus fang in shape, probably Indicating a more primitive form (Fig./+6). The lateral twist at the point of the Bothrops atrox fang is more pronounced than in the rattlesnake fang, bringing the ridges to the top and bottom. This gives the point, in spite of the presence of the distal aperture, a dagger-like end with the long axis in the plane of the curve. The fang of a large B. .lararacussu does not show the ridges exaggerated to the same extent, although the central curve has the characteristic Bothrops arc. The Bothrops fang is somewhat longer than that of C. adamanteus on a basis of body length, but the difference is not great when comparisons are corrected for the sharp bend in the rattlesnake fang. Another neotropical pit viper, the bushmaster, Lachesis muta, is said to have very long fangs; however, whether these are out of proportion to its body length I cannot say; the bushmaster is the longest (but not the heaviest) of the venomous snakes of the Americas, reaching a length of 12 feet. The African Gaboon Viper, Bitis gabonica. an extremely heavy-bodied snake belonging to the family Viperidae. is said to attain fangs closely approach- 55 IT H a. O o ■< o ~ ii.