ASSOCIATIONS FOR THE ADVANCEMENT OF SCIENCE!. (AMERICAN.) 



north-central Indian type seems to have extended 

 across the continent and to have branched in all 

 directions, while a similar, but not so extensive 

 branching, northeast and south, seems to have 

 been the course of the Toltecan type." This led 

 up to an expression of his belief that " the Ameri- 

 can continent has been peopled at different times 

 and from various sources; that in the great lapse 

 of time since the different immigrants reached 

 the continent there has been in many places an 

 admixture of the several stocks and a modifica- 

 tion of the arts and customs of all, while natu- 

 ral environment has had a great influence upon 

 the ethnic development of each group." The 

 reasons for this belief were then given in detail, 

 and included a discussion of the " mound build- 

 ers." Concerning these he showed the universal- 

 ity of such mounds, and said that " the earth 

 mounds, like the shell mounds, were made by 

 many peoples and at various times." He then 

 said : " That man was on the American conti- 

 nent in Quaternary times, and possibly still 

 earlier, seems to me as certain as that he was in 

 the Old World during the same period. The Cala- 

 veras skull, that bone of contention, is not the 

 only evidence of his early occupation of the 

 Pacific coast. On the Atlantic side the recent 

 extensive explorations of the glacial and imme- 

 diately following deposits at Trenton are con- 

 firmatory of the occupation of the Delaware 

 valley during the closing centuries of the glacial 

 period, and possibly also of the interglacial time. 

 The discoveries in Ohio, in Florida, and in vari- 

 ous parts of Central and South America all go 

 to prove man's antiquity in America. Admit- 

 ting the great antiquity of one or more of the 

 early groups of man on the continent, and that 

 he spread widely over it while in the palaeolithic 

 and early neolithic stages of culture, I can not 

 see any reason for doubting that there were also 

 later accessions during neolithic times and even 

 when social institutions were well advanced. 

 While these culture epochs mark certain phases 

 in the development of a people, they can not be 

 considered as marking special periods of time. 

 In America we certainly do not find that corre- 

 lation with the Old- World periods which we are 

 so wont to take for granted." He then paid a 

 deserved tribute to the museums and expedi- 

 tions through which material was being collected 

 for study. In closing he said : " Anthropology 

 is now a well-established science, and with all 

 this wealth of materials and opportunities there 

 can be no doubt that in time the anthropologists 

 will be able to solve that problem which for the 

 past half century has been discussed in this asso- 

 ciation the problem of the unity or diversity 

 of prehistoric man in America." 



Proceeding's of the Sections. The associa- 

 tion is divided into nine sections, each of which 

 is presided over by an officer having the rank of 

 vice-president of the association. Subsequent to 

 the opening proceedings each section meets by 

 itself and effects its organization by electing a 

 fellow to represent it in the council, a sectional 

 committee of three fellows, a fellow or member 

 to the nominating committee, and a committee 

 of three members or fellows to nominate officers 

 of the section for the next meeting. As soon 

 as this organization is effected the secretary of 

 the section reports to the general secretary, who 

 then provides him with a list of papers that, 

 having been considered suitable by the council, 

 may be read and discussed before the section. 

 A press secretary, whose duties are to prepare ab- 

 stracts of the papers read and to give them to 

 reporters of newspapers, is also commonly chosen. 



A. Mathematics and Astronomy. The presid- 

 ing officer of this section was Prof. Alexander 

 Macfarlane, of Lehigh University, Bethlehem, 

 Pa., who presented an address on The Funda- 

 mental Principles of Algebra. 



In this paper he confined his discussion to the 

 advances made in the present century, and began 

 a description of the results that followed the 



recognition of the analogy between , the sym- 

 bol of differentiation, and the ordinary symbol 

 of algebra. The work of Peacock, who flourished 

 in Cambridge from 1812 on, as well as the ad- 

 vances made by D. F. Gregory, a younger mem- 

 ber of the Cambridge school of mathematics, 

 were carefully considered. In chronological 

 order followed references to Augustus de Morgan 

 and to George Boole, both of whom were logicians 

 as well as mathematicians. Much attention was 

 devoted to the famous Sir William R. Hamilton, 

 who did considerable in advancing mathematical 

 science, and to whom we owe the method of 

 quaternions. Grassmann and Hankel followed 

 Hamilton, and their contributions received due 

 consideration. Clifford, of whom so much was 

 hoped, and who died too soon, was the next 

 whose work was analyzed, and then the newer 

 publications of Chrystal were discussed. The 

 work of Whitehead, the most recent of writers 

 on algebra, was then taken up. Dr. Macfarlane's 

 conclusions were : " If the elements of a sum or 

 of a product are independent of order, then the 

 written order of the terms is different, and the 

 product of two such sums is the sum of the par- 

 tial products: but when the elements of a sum 

 or of a product have a real order, then the writ- 

 ten order of the elements must be preserved, 

 though the manner of their association may be 

 indifferent, and a power of a binomial is then 

 different from a product. This applies whether 

 the sum or product occurs simply or as the index 

 of a base. Descartes wedded algebra to geome- 

 try; formalism tends to divorce them. The prog- 

 ress of mathematics within the century has been 

 from formalism toward realism; and in the com- 

 ing century, it may be predicted, symbolism will 

 more and more give place to notation, conven- 

 tions to principles, and loose extensions to rigor- 

 ous generalizations." 



The following-named papers were read and dis- 

 cussed before the section: Report on Progress in 

 Non-Euclidean Geometry, by George B. Halsted; 

 Report on Progress in the Theory of Linear 

 Groups, by Leonard E. Dickson; The Aberration 

 Constant from Observations of Polaris, by Asaph 

 Hall, Jr.; Ancient Eclipses and Chronology, by 

 Robert W. McFarland; Some Points in the De- 

 sign of a Spectroscope, by H. C. Lord; Note on 

 Grassmann's Proof that there can be but Two 

 Kinds of Lineal Multiplication of Two Factors, 

 by Joseph V. Collins: The Theory of Mathe- 

 matical Inference, by G. J. Stokes; Recent Prog- 

 ress in Positional Astronomy, by John R. East- 

 man; Practical Astronomy during the First Half 

 of the Present Century, by Truman H. Safford; 

 Internal Forces that generate Stellar Atmos- 

 pheres, by J. Woodbridge Davis ; On the Commu- 

 tators of a Group, by George A. Miller; and Linear 

 Vector Functions, by S. Kimura. 



On Aug. 24 this section met in joint session 

 with Section B to listen to the following papers: 

 Recent Progress in Theoretical Meteorology, by 

 Cleveland Abbe: The Determination of the Na- 

 ture of Electricity and Magnetism, including a 

 Determination of the Density of the Ether, by 

 Reginald A. Fessenden. 



B. Physics. This section was presided over by 



