MEMOIltS OK Till!; ^'ATIONAL ACADKMV OF SCIKNCKH. 223 



fornmtion more constjintly and in a hifjlior dcpree than those of any oilier (ollcction of which we 

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



In ()l)tainin;j the index of the tiliia for tliis study we have achiptetl tlie method of Hroea; tliat 

 is, we liave measured tlie bone at the h'velof the nutrient foramen, have multiplied the tiansverse 

 dimension by UK) and dividi'd the product by the aidero-)>(>steri<)r dimension. \Ve have found in 

 the Sahido collect ion lltJ tibiju suUiciently pre.served to admit of these measurements. Ninety of 

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

 were conserved innnediately on beinp disintened, are {jiven in Table i.xxiv. Twenty six of the 

 tibia< form a miscellaneous group; they were gathered singly and belong mostly to skeletons whi<-h in 

 the earlier days of the work of excavation were allowed to disint<^'grate from exposure to the weather 

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

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

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



It is a recognized fact that the tlattened tibia does not occur in childhood, but that the pecul- 

 iarity is accpiired as years advance. To imdude immature tibia' in the general average may there- 

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

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

 cular traction, posteriorly near the junction of the i)eri)endicular with tlie obli<iue 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 wehave noted under the head of "Remarks" all instances of these disturbing factors, 

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



If we take an index of 7.5 as representing a normal tibia (and this may be regarded as a low 

 standard) we tind but four adult tibie in IIG 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 Jefl'ries 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; conseciuently the index, if expressed in the manner adopted by us, might have been a 

 fraction higher. We may safely say then that two tibise 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 Kuliff, one from Carerne de VHomme 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 39 series given by Dr. 

 Kuhflt'.t In this the lowest averages are in series having but 1 or 2 specimens in each, and they 

 therefore do not admit of comjiarison 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 03; but Dr. Kuhfif 

 gives no decimals in his table. The average of all our 11(5 tibite is (i3.54 (Table LXXV) ; the average 

 of 90 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 iu any collection will be found to show a higher average grade of flattening of 

 the tibia than our Salado series. 



The most satisfactory ex])lanation which we have noted of the origin of platycnemia is that 

 of Manouvrier.J 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 Hattening 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. Manouvrier wisely main 



• Fourth annual report of the trustees of the Peabodv Museum of American Archteology and Ethnology, Boston, 

 71, pp. 21, 22. 



t De la i>lat}cndmic dans les races bumaines. Revue d'anthropologio, second series, vol. iv, p. 255. 

 ( Platyiiieniia in men and anthro])oids. Memoirs oftlie Anthropological Society of Paris, 2d series, Vol. Iil. 

 $ Eevue d'authropologio, third series, vol. iv, laSi), pp. 207-210. 



