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



fore we have a right to make conjectures as to 

 the plants he will probably use. The cereal 

 grains will probably remain with comparatively 

 little change, except in the direction of better 

 varieties for milling. To show how well under- 

 stood are the methods of improving plants, Dr. 

 Goodale said that if all the present cereals were 

 swept out of existence our experiment stations 

 could probably replace them by other grasses 

 within half a century. The methods are selec- , 

 tion and hybridization. New vegetables may be 

 reasonably expected from Japan, that country 

 which has already sent us many choice plants in 

 all departments, and it is likely that some of 

 the present vegetables which are much neg- 

 lected will come into greater favor and be im- 

 proved. The fruits of the future will tend more 

 and more toward becoming seedless, just as pine- 

 apples, bananas, and some oranges are now. 

 There is no good reason why we should not have 

 seedless raspberries, strawberries, and blackber- 

 ries, and also raise, by cutting, plums, cherries, 

 and peaches free from stones. The useful cabi- 

 net woods and timbers, the fibers, tanning ma- 

 terials, gums, rubbers, and other economic prod- 

 ucts from plants were taken up in order, and 

 the possible improvements were described. There 

 is little doubt that synthetical chemistry will add 

 to its triumphs many more products to those 

 formed by plants, and this will diminish the 

 zeal with which some of our economic plants will 

 be cultivated. The coming fashions in florists' 

 plants are to be in the direction of flowering 

 branches and dwarfed plants, such as dwarfed 

 cherries and magnolias. The old favorites will 

 largely keep their places. Forage plants for our 

 deserts were discussed, and reference was made 

 to the danger of introducing pests from foreign 

 countries. An example of this danger is afforded 

 by sweetbrier in Australasia, which runs wild 

 over much arable land in certain districts. The 

 study of improvement in plants is now carried 

 on in a judicious manner by the Agricultural 

 Department and by the experiment stations. But 

 there is also needed a series of gardens in differ- 

 ent parts of our country where experiments can 

 be carried on in a thorough manner in hybridiz- 

 ing and selection. The Arnold arboretum and 

 the Shaw garden were spoken of as good illus- 

 trations of what is needed, but the desirability 

 of establishing an institution on a scale com- 

 mensurate with the wants of our country was 

 pointed out, and the hope was expressed that 

 such an establishment should not be govern- 

 mental or academic. 



Proceedings of the Sections. There are 

 eight sections, each of which is presided over by 

 a vice-president. Immediately after the adjourn- 

 ment of the first general session the members 

 of the'different sections meet in the rooms as- 

 signed to them and organize. Their next duty 

 is the election of one fellow to the council, fol- 

 lowed by the election of three fellows, who, with 

 the vice-president and the secretary, form the 

 sectional committee ; the election of a member or 

 fellow to the nominating committee ; the election 

 of three members or fellows to act with the vice- 

 president and secretary as the sub-committee to 

 recommend to the nominating committee the 

 vice-president and secretary \ of the next meet- 

 ing. These duties having been performed, the 



secretaries of the sections report to the general 

 secretary, who then prepares with the sectional 

 committees the programmes for the ensuing ses- 

 sions. After the recess on the first day the read- 

 ing of the vice-presidential addresses takes place. 

 Sections. A. Mathematics and Astronomy. 

 This section was presided over by Prof. Edward 

 W. Hyde, of the University of Cincinnati, Ohio, 

 who chose " The Evolution of Algebra " as the 

 subject of his address. He gave a concise pres- 

 entation of the history of algebra, extending 

 .from before the Christian era to the present time, 

 and foretelling the future of the science. The 

 earliest traces of algebraic knowledge, he said, 

 were in ancient Egyptian manuscripts. Records 

 of an almost prehistoric Egyptian mathema- 

 tician named Ahmes, who lived and figured and 

 died some hundred years before Christ, were 

 referred to as showing that this pioneer in alge- 

 bra had left behind him evidence that he had 

 performed geometrical and some algebraical 

 problems. Scarcely anything is known of the 

 mathematics of ancient Egypt. Among the 

 early Greeks, before the Christian era, geometry 

 was cultivated extensively, but very little in the 

 way of algebra was done till about 400 A. D. 

 Then the foundation of the algebraic science was 

 laid by Diophantus of Alexandria. Algebra has 

 been classified by Nesselmann as rhetorical, syn- 

 copated, and symbolical. In the first stage al- 

 gebraic work was purely by reasoning in words. 

 In the syncopatic method abbreviations were 

 introduced and used instead of words. The sym- 

 bolical stage is the present one. Arbitrary char- 

 acters show what was once represented by spoken 

 words and later by abbreviations of written 

 words. Most of the work of the early algebraists 

 was in the rhetorical stage. Diophantus used 

 particular characters for unknown quantities, a 

 character for " minus," and represented addition 

 by juxtaposition. The square and cube of the 

 unknown quantity were represented by contrac- 

 tions of the words " power " and " cube." Dio- 

 phantus was greatly hampered by having but 

 one character- to represent the unknown quantity, 

 though he accomplished remarkable results by 

 his ingenuity and the skill with which he made 

 the necessary combinations. Algebra was early 

 cultivated in India. The first Indian methods 

 of which moderns know were those of Arya 

 Bhatta, who lived six centuries before Christ. 

 He wrote works on arithmetic, algebra, geometry, 

 trigonometry, and astronomy, stating his rules 

 and propositions in verse. His work was purely 

 of the rhetorical style. The only other ancient 

 Indian mathematician of whom moderns know 

 was Brahma Gupta, whose period was about A. D. 

 700. He also figured in verse, the name of his 

 work, Englished, being "The System of Brahma 

 in Astronomy." These Indian writings are in- 

 teresting as being the source whence the Arabs 

 derived their first knowledge of algebra. They 

 absorbed from the Greeks, through the trans- 

 lations of Euclid and others, a knowledge of 

 geometry, mechanics, and astronomy, but there 

 seems to have been no translation of the works 

 of Diophantus till after they themselves had 

 already made considerable progress. It was from 

 the Arabs that western Europe derived its first 

 knowledge of mathematics. Concerning the 

 future of algebra, he said : " We have now traced 



