904 



SCIENCE. 



[N. ti. Vol. XVll. .No. 440. 



the second digit is the longest of the series. 

 In only one genus, Stenotatus, are any of 

 the phalanges coossified. The ungual pha- 

 langes are always long, heavy, decurved 

 and pointed, and were evidently well 

 adapted to burrowing habits. 



The pelvis varies considerably in the 

 different genera, but does not depart 

 widely from the modern type. The femur 

 is elongate and has a very prominent great 

 trochanter, which in Proeutatus reaches re- 

 markable proportions ; the third trochanter 

 is also well developed in all cases. As in 

 the recent armadillos, the tibia and fibula 

 are invariably coossified at both the prox- 

 imal and the distal ends. Like the manus, 

 the pes is always pentadactyl, though in 

 some of the genera, and especially in 

 Peltephilus, the lateral digits are much 

 reduced. The ungual phalanges are usu- 

 ally much shorter and broader than those 

 of the manus, and are often more like hoofs 

 than claws. 



In size, there is mtich variety among the 

 Santa Cruz armadillos, ranging from the 

 minute Prozaedius to Proeutatus, some 

 species of which are larger than any exist- 

 ing armadillo, except Priodontes, while the 

 very incompletely known Peltephilus 

 grandis may have equaled or even sur- 

 passed the latter. 



To sum up: The Santa Cruz armadillos 

 differ comparatively little in appearance 

 or in structure from the modern ones, and 

 yet it is apparent that they do not, as a 

 whole, represent the main line of descent 

 which ended in the recent genera. That 

 evolution must have taken place in some 

 other region of the South American con- 

 tinent, doubtless the same region as that 

 which gave rise to the true sloths and the 

 anteaters. 



W. B. Scott. 



Princeton UNrvERSiTT. 



SCIENTIFIC BOOKS. 

 The Constructive Development of Group- 

 theory; with a Bibliography. By B. S. 



Easton. Boston, Ginn & Co. 1902. Pp. 



iv + 89. Cloth, $0.75. (Publications of 



the University of Pennsylvania, series of 



mathematics, No. 2.) 



This monograph aims to present in con- 

 tinuous form, but omitting all proofs, the 

 main concepts and results of abstract and sub- 

 stitution group theory. While the theory of 

 linear groups is expressly excluded, some of 

 its results are tabulated on pages 83 and 84 

 under ' systems of simple groups.' 



Employing a set of abbreviations for the 

 journals, the author has succeeded, in the 

 short space of thirty-four pages, in giving an 

 exhaustive bibliography of the subject. In 

 it appear 157 names of authors. To further 

 indicate its extent, we note that it gives 97 

 titles by G. A. Miller, 35 by L. E. Dickson, 

 33 by C. Jordan, 23 by W. Burnside, 21 by 

 Cayiey, 20 by Cauchy and 16 by Kronecker. 



The treatise proper extends over 39 pages, 

 the successive headings being as follows : sub- 

 stitutions, groups, substitution groups, con- 

 jugacy, multiple isomorphism and quotient- 

 groups, composition series, commutators, 

 Abelian groups, groups or order a power of a 

 prime, Sylow's theorem and its extensions, 

 Hamiltonian groups, transitivity, intransitiv- 

 ity, primitivity, regular groups, imprimitivity, 

 multiple transitivity, class of a group and de- 

 gree of transitivity, automorphism, representa- 

 tion, index notation. 



The tables give the numbers of distinct 

 abstract groups of each order as far as 63 ; the 

 number of substitution groups of each degree 

 as far as 18, classified as multiply transitive, 

 other primitive, imprimitive, and intransitive ; 

 the types of group of orders p', pq, p^ pq", pqr, 

 8p(p > 2), 16, p\p > 2), p'q, 32, p"(p > 2) ; 

 simple groups of low orders; orders of com- 

 posite and soluble groups; systems of simple 

 groups. 



Some minor remarks or corrections are 

 here in order. In § 21, for ' class ' read ' de- 

 gree.' In § 44, for ' product of two elements ' 

 read ' product of any two elements.' In § 26, 

 add alternative designation ' commutative 



