MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 223 



formation more constantly and in a higher degree than those of any other collection of which we 

 have seen a record. Furthermore, the series is extensive. 



In obtaining the index of the tibia for this study we have adopted the method of Broca; that 

 is, we have measured the bone, at the level of the nutrient foramen, have multiplied the transverse 

 dimension by 100 and divided tin- product by the antero-posterior dimension. We have found in 

 the Salado collection 116 tibia- sufficiently preserved to admit of these measurements. Ninety of 

 these, which were collected along with the skulls or other bones of the same skeletons, and which 

 were conserved immediately on being disinterred, are given in Table LXXIV. Twenty-six of the 

 tibia' form a miscellaneous group; they were gathered singly and belong mostly to skeletons which in 

 the earlier days of the work of excavation were allowed to disintegrate from exposure to the weather 

 or were crushed under the feet of thoughtless visitors. Since many of this miscellaneous set art- 

 cracked and warped, we repose less .confidence in their dimensions than we do in the dimensions 

 of the series of 00; hence we devote to them a separate table (LXXV). 



It is a recognized fact that the flattened tibia does n<Jt occur in childhood, but that the pecul- 

 iarity is acquired as years advance. To include immature tibia? in the general average may there- 

 fore be. thought to improperly diminish the average of platycnemia and increase the average index. 

 We have two skeletons in which there is an exostotic crest, apparently the result of unusual mus- 

 cular traction, posteriorly near the junction of the perpendicular with the oblique line. This 

 formation, on the other hand, by falsely increasing the antero posterior diameter, may be 

 thought to improperly increase the average of platycnemia and decrease the average index. In 

 Table LXXIV we have noted under the head of "Kemarks" all instances of these disturbing factors, 

 and we have calculated averages both inclusive and exclusive of such instances. 



If we take an index of 75 as representing a normal tibia (and this may be regarded as a low 

 standard) we find but four adult tibaj in 116 which may be regarded as normal. The lowest Ameri- 

 can index we have seen recorded is one of 48 in a tibia from a mound in Michigan. This instance 

 is mentioned by Jeffries Wyman,* who expresses the index by saying that the transverse diameter 

 is 0.48 of the antero-posterior diameter. In this connection he never uses more than two decimal 

 figures; consequently the index, if expressed in the manner adopted by us, might have been a 

 fraction higher. We may safely say then that two tibia) of the Salado series (those of H. 19) are 

 as low as the lowest American known. Absolutely the lowest for all races we have seen recorded 

 are 3 mentioned by Kuhff, one from Cnre.rne dc VHommc Mort, having index 47, and two from 

 the Grand Canaries, having indices 42 and 36. 



The most extensive table of averages we have observed is one of 30 series given by Dr. 

 Kuhff.t In this the lowest averages are in series having but 1 or 2 specimens in each, and they 

 therefore do not admit of comparison with ours. The lowest average he gives in any series com- 

 prising more than 2 specimens is that of certain prehistoric bones ("Lehm de Kollwiller") 

 from Alsace, of which there are 11 specimens. The average index is stated at 63; but Dr. Kuhff 

 gives no decimals in his table. The average of all our 116 tibia- is 63.54 (Table LXXV) ; the average 

 of 00 of the more perfect part of the collection, as shown in Table LXXIV, is 62.71; while the 

 average of 78 adults free from complicating exostoses is only 61.88. We may safely say that no 

 series of equal size in any collection will be found to show a higher average grade of flattening of 

 the tibia than our Salado series. 



The most satisfactory explanation which we have noted of the origin of platycnemia is that 

 of Manouvrier.f We regret that we have never seen his, original paper on this subject; we 

 derive a knowledge of his work entirely from a review. He has concluded from a careful study 

 of the tibia in its anatomical relations that the flattening is entirely due to " lengthening and 

 straightening of the postero external surface of this bone; that is to say, of the surface of insertion 

 of the posterior tibial muscle," and this lengthening and flattening, Mr. Mauouvrier wisely main- 



* Fourth aiinual report of the trustees of the Peabody Museum of American Archaeology and Ethnology. Boston, 

 1871, pp. 21, L'L>. 



tDe la platyenemie. dans les races huinaines. Revue d'anthropologio, second spries, vol. IV, p. 255. 



} Platyenemiii in men and anthropoids. Memoirs oflhe Anthropological Society of Paris, 2d series, Vol. III. 



$ Eevue d'anthropologie, third series, vol. iv, 1889, pp. 207-210. 



