June 2, 1905.] 



SCIENCE. 



863 



Since we may assume the origin of the first 

 system of ordinates arbitrarily, we may take 



in other words, we take the geometrical center 

 of gravity of the first body as the origin of 

 our system of ordinates. Then 



i. e., the two bodies must be so placed that 

 their geometrical centers of gravity coincide. 



Provided the two forms are symmetrical, 

 this result gives a complete . solution of the 

 problem. If the forms are irregular, the de- 

 gree of toi'sion must be determined which will 

 give the best result. In most cases the form 

 in question will be symmetrical in at least 

 one direction, so that torsion in one direction 

 only need be considered. Starting with the 

 geometrical center of gravity as the origin of 

 a system of polar coordinates, we have for 

 any given pair of points the coordinates V 

 and I" as distances from the center, and a 

 and a" as angles with the zero line. If we 

 give the second system of points the torsion 



we find that 



+ — 2mcos (f +a''— a')} 

 must be a minimum; or 



-ZVl" sin -\-a" ~a') = 0, 

 _ -^I'V sin {a" — a') 



Theoretically, the problem can, therefore, be 

 solved. By using a limited number of well- 

 selected points a good superposition of the 

 two forms can be made. 



Experiments, so far as carried out, indicate 

 that alveolar point, nasion, bregma, lambda, 

 basion and pterion give a good superposition 

 of skulls. 



It will be noticed that if this method is pur- 

 sued the arbitrary element in composite draw- 

 ings or photographs may be eliminated. 



Franz Boas. 



xuala and guaxule. 

 The location of two Indian villages, Xuala 

 and Guaxule, mentioned in some form by all 

 of the chronicles of Hernando de Soto's wild 

 and unfortunate expedition (1539-41) through 



the territory now included in the southern 

 states, are important in determining the route 

 of this Spanish adventurer. If the location 

 of these two villages — especially the first — 

 can be determined with reasonable certainty 

 it will enable us to fix the route of the Ade- 

 lantado with comparative accuracy from his 

 landing place at Tampa Bay, Florida, until 

 he reached the vicinity of Mauvilla in Ala- 

 bama. 



The widest variation in opinion of the nu- 

 merous authorities touching upon the subject, 

 relates to the position of Xuala; these views, 

 however, may be classed in two unequal 

 groups, as is evident from the following list: 

 The map of Cornelius Wytfliet in his ' De- 

 scrip. Ptolemaica (1596)' locates this village 

 on the west side of Savannah River near the 

 head. DeLisle's map (1707?) in French's 

 ' Hist. Coll. La.,' though indefinite, places it 

 west of the Savannah. Later authorities lo- 

 cate it as follows : Pickett (' Hist. Alabama,' 

 I., p. 8) ; C. C. Jones, Jr. (' Hernando de 

 Soto,' p. 13) ; Cyrus Thomas (5th ' Ann. Rep. 

 Bur. Eth., p. 95) ; and Theodora Irving (' Hist. 

 Cong. Florida,' II., p. 8), all locate it west of 

 the upper Savannah in Nacooche valley, Ha- 

 bersham County, Georgia, or in that imme- 

 diate vicinity. Mr. James Mooney (19th 

 ' Ann. Rep. Bur. Eth.,' pt. 1, p. 195) and Wood- 

 bury Lowery (' Spanish Settlements within the 

 United States,' p. 230, in the text, but not on 

 the map) locate it in the ' piedmont ' region of 

 North Carolina, about the head of Broad 

 river — which would be about Henderson 

 County. Gilmore Shea in his article entitled 

 ' Ancient Florida,' in Justin Winsor's ' Narra- 

 tive and Critical History of America, II.,' 

 follows, in this part of De Soto's route, the 

 course given by C. C. Jones, Jr. Bucking- 

 ham Smith on the map in his ' Narrative of 

 De Soto' (Bradford Club Series, V., pi. 5) 

 places Xuala about Habersham County, 

 Georgia, but locates Guaxule to the north- 

 west, apparently about Towns County of the 

 same state, or possibly over the line, in Ten- 

 nessee. Although Shipp (' De Soto and 

 Florida ') does not locate Xuala, he places 

 Guaxule in Bartow County, Georgia, thus 

 agreeing substantially with Pickett, Jones and 



