52 



SCIENCE 



[N. S. Vol. XXXVIII. No. 967 



statement that, with Widman, + meant 

 simply " und " (and) is correct as a descrip- 

 tion, of Widman's general usage. There is 

 just one exception. Once, but only once, does 

 Widman in his book identify + with " meer " 

 (mehr). It is in the passage quoted by Dr. 

 Halsted, "was auss — ist, das ist minus . . . 

 vnnd das -|- das ist meer." It occurs in the 

 explanation of a small table of weights. 



Widman does not use the word " plus " ; 

 his word for addition is " vnd." As stated 

 before, with Widman + had not yet become 

 a purely mathematical sign. In his arith- 

 metic (1489), as well as in a manuscript alge- 

 bra in Latin, which he owned, + is used for 

 " vnd " or " et " even in eases where " vnd " 

 or " et " do not mean addition, as in the 

 heading, " Eegula augment! -\- decrement!. " 

 It is interesting to note that he uses the word 

 " minus " only twice in his book, and only 

 once in the sense of — . Hence, in Widman, 

 the words " plus " and " minus " do not occur 

 as ordinary terms for addition and subtrac- 

 tion. The symbol + is often used for addi- 

 tion; — is used for subtraction at times, but 

 not regularly. Apparently, the regular asso- 

 ciation of -{- with " plus," and — with 

 " minus," came after Widman. 



A further study of manuscripts and early 

 printed books may throw more light upon the 

 origin of -f- and — (as well as upon the first 

 use of the decimal point), but the evidence 

 now at hand goes against Dr. Halsted's claim 

 that the + and — , used in the sense of 

 IT = 3.14 + and tt = 3.1416 — , " is historic- 

 ally the first meaning of the signs -1- and — , 

 which arose from the marks chalked on chests 

 of goods in German warehouses, to denote 

 excess or defect from some standard weight." 

 That they were so used is not denied, but the 

 facts do not warrant the categorical statement 

 that this " is historically the first meaning." 

 No evidence has been adduced to establish the 

 early use of -f- and ■ — - as marks chalked on 

 chests. In the Bamberger Eechenbuch (1483) 

 the tare to be deduced from the gross weight 

 of a package is called " Das Minus," but the 

 symbol — is not used. On the other hand, 

 the regular connection of + with " vnd " in 



Widman's book of 1489 is unmistakable; the 

 resemblance of + with the " et " of Latin 

 manuscripts of the fourteenth and fifteenth 

 centuries rests upon independent paleographic 

 researches carried on by several writers men- 

 tioned by Cantor and Tropfke. 



Floeian Cajori 

 Colorado College 



an institute for bibliographical research 



The writer has from time to time tried to 

 interest librarians, bibliographers and men of 

 science in the matter of bibliographical re- 

 search and publication, or rather in organized 

 work along these lines, in the hope that a con- 

 certed movement in its favor might be 

 brought about — but in vain. Men of wealth 

 have also been approached, but so far the man 

 who would see his opportunity and endow this 

 important work has not been found. 



An effort is now being made to interest 

 business men in the subject. Special empha- 

 sis has lately been laid on the value of an in- 

 stitution for the organization of bibliograph- 

 ical research in the interest of agriculture, 

 manufacture and commerce. A prospectus 

 has been sent out to a number of business 

 men in Chicago calling attention to the value 

 of research along these lines for both agri- 

 culture, manufacture and commerce. A " Com- 

 mittee on Research Institute " has been 

 formed for the purpose of promoting the idea. 



While the latest endeavor has been made 

 along the line of business, the intention of the 

 writer is now, as it has always been, that the 

 only limits to the scope of the proposed insti- 

 tute should be the actual needs of those who 

 might seek its assistance. The functions of 

 the proposed research institute would be en- 

 tirely practical. The institute staff would be 

 in readiness to make researches into definite 

 subjects at the request of those desiring spe- 

 cial information ; it would also try to antici- 

 pate the needs of inquirers and compile refer- 

 ences on subjects of actual interest in advance 

 of demand. 



It has been estimated that a sum of $50,000, 

 or a guaranteed income of $10,000 a year for 

 five years, would place the institute on a basis 



