124 



NATURE 



[December io. 1891 



and brings forward evidence, collected by himself before 

 and after 1878, and by a number of well-known health 

 officers and co-workers (Mr. W. H. Power, Dr. David 

 Page, Dr. Jacob, Dr. Bruce Low, and others), which 

 conclusively proves and confirms Dr. Thome's proposi- 

 tion, first enunciated by him in 1878. Over and over 

 again has it been shown (chapter iii.) that, in schools 

 frequented by children some of whom were affected with 

 simple sore throat, outbreaks of true diphtheria have 

 occurred, for the explanation of which no antecedent 

 case of diphtheria, nor any of the generally assumed in- 

 sanitary conditions, could be brought forward. It is on 

 these grounds that Dr. Thome justly insists on a con- 

 tinued and careful inspection of the throats of the children, 

 and on immediate separation from school of any child 

 affected with sore throat. 



The part that milk plays in the dissemination of 

 diphtheria is fully discussed, and illustrated by a number 

 of epidemics that have been recorded in the Reports of 

 the Medical Officer of the Local Government Board ; 

 and the important relation of diseases of the lower 

 animals, particularly of cows and cats, is also described 

 and illustrated by epidemics in chapter iv. Last, but not 

 least. Dr. Thorne considers the question of prevention 

 and isolation. By his office as Assistant Medical Officer 

 of the Local Government Board, and from an experience 

 extending over many years, he stands in the unique 

 position of the very best authority, whose conclusions and 

 recommendations deserve carefully to be studied by 

 managers and owners of schools, by hospital authorities, 

 by sanitary officers and Boards of Health, by the owners 

 of dairies, and by all those to whom the health of the 

 community ought to be of paramount importance. 



THE NE W YORK MA THEM A TICAL SOCIE TV. 



Bulletin of the New York Mathematical Society, a 

 Historical and Critical Review of Mathematical 

 Science. Vol. I. No. i, October 1891. (New York: for 

 the Society.) 



WE have occasionally wondered that now the study 

 of mathematics is so diligently and successfully 

 prosecuted across the Stream, there was no Society to 

 bring together all such persons as were willing " to 

 encourage and maintain an active interest in mathe- 

 matical science." The " Organization of the New York 

 Mathematical Society" gives a list of 174 members, 

 mostly Professors of Mathematics or Astronomy. The 

 President is Mr. Emory McClintock, a Vice-President of 

 the Actuarial Society of America, who is also a member 

 of the London Mathematical Society, and a contributor 

 of some excellent memoirs to the American Journal of 

 Mathematics. The constitution embraces six articles, and 

 there are ten by-laws. These are apparently founded 

 upon the rules which have been drawn up for other 

 similar Societies. The date of the pamphlet {i.e. the 

 " Organization, &c.," cited above) is June 1891. From a 

 circular we gather that the Society has only recently 

 inaugurated the present state of affairs, for this document 

 states : — 



" The New York Mathematical Society has consisted 

 in the past of most of the professors and instructors of 

 mathematics at the several Colleges situated in New 

 York and the vicinity, the actuaries of a few of the larger 



NO. I 1 54, VOL. 45] 



life insurance companies, and a number of other persons 

 interested in higher mathematics. .'\t present an exten- 

 sion of membership is in progress." 



Then it goes on to say : — 



" The Society is about to undertake the publication 

 of a periodical review of pure and applied mathematics. 

 The idea is not to renter into any competition with 

 the American Journal of Mathematics, the Annals 

 of Mathematics, or any other similar journal, but it is 

 proposed to publish, primarily, historical and critical 

 articles, accounts of advances in different branches of 

 mathematical science, and reviews of important new 

 publications ; also resumes of lectures before the Society, 

 short contributions from members and correspondents, 

 and general mathematical news and intelligence. Such a 

 periodical, if circulated extensively, will do much to incite 

 an interest in mathematical studies, and to maintain the 

 interest of those who, having pursued such studies, are 

 now perhaps at a distance from others of like tastes and 

 training. It will appeal to many that our mathematical 

 journals do not reach." 



We have allowed the Society to state its aims : these 

 have been sanctioned by Profs. Newcomb, Woolsey 

 Johnson, and Craig (associate editor of the Ainerican 

 Journal of Mathematics). We wish the Society every 

 success in their endeavour " to promote a long-needed 

 spirit of active co-operation, and to establish a bond of 

 union between American mathematicians." 



The Bulletin contains an article on " Octonary 

 Numeration," by Prof. Woolsey Johnson. The con- 

 cluding paragraph is as follows : — 



" As there is no doubt that our ancestors originated the 

 decimal system by counting on their fingers, we must, in 

 view of the merits of the octonary system, feel profound 

 regret that they should have perversely counted their 

 thumbs, although Nature had differentiated them from 

 the fingers sufficiently, she might have thought, to save 

 the race from this error." 



The rest of the number is taken up with reviews of 

 several books, viz. " The Teaching of Elementary Geo- 

 metry in German Schools" (review of Schotten's " Inhalt 

 und Methode des planimetrischen Unterrichts," by Prof. 

 Ziwet) ; Bertrand's " Calcul des Probabilites " (by Prof. 

 Ellery Davis) ; Fine's " Number-System of Algebra" (by 

 G. Enestrom, of Stockholm) ; and notices of works on 

 West African longitudes and South American longitudes 

 (by the treasurer, H. Jacoby). There are several short 

 notes and a translation of Picard's demonstration of 

 the general theorem upon the existence of integrals of 

 ordinary differential equations (by the secretary, T. S. 

 Fiske). 



From this account it will be seen that there are no 

 mathematical memoirs read before the Society in this 

 part, but that such papers have been communicated 

 we learn from the fact that three are printed in the 

 current number of the American Journal of Mathe- 

 matics, viz. one by C. Steinmetz (February 6, 1891), and 

 two by the President (March 6, 1891). 



OUR BOOK SHELF. 



Delagoa Bay : its Natives and Natural History. By 



Rosa Monteiro. With Twenty Original Illustrations 



after the Author's Sketches and from the Natural 



Objects by A. B. and C. E. Woodward. (London : 



George Philip and Son, 1891.) 



Botanists and zoologists alike will remember the 



services rendered to science by the late J. J. Monteiro, 



