December 31, 1914] 



NATURE 



477 



tenement near the river, are capable of realising 

 and appreciating the contrast between the present 

 and the past in respect to the status of science 

 and art in the City of Palaces. The change was 

 great enough when the Chowringhi " jadu-gahr " 

 (home of magic), as the Indian Museum is invari- 

 ably termed by Bengalis, was first opened during 

 the later 'seventies, but the present enlarged 

 building, as photographed in the volume before 

 me, with its additional upper storey and doubled 

 frontage, renders the original structure almost a 

 doll's house in comparison, magnificent and 

 spacious as it was thought to be at the time when 

 the present writer assisted in arranging the 

 galleries. 



In housing in this magnificent and lavish style 

 the valuable collections illustrating the natural 

 history, geology, archceology, and ethnology of 

 British India, the Indian Government has done 

 its duty in a manner worthy of all praise. 

 Whether, however, the attempt to make the 

 museum a great centre of educational instruction 

 in biology will ever be realised, seems, to quote 

 from the admirable account of the rise and history 

 of the collections given by the Hon. Justice Sir A. 

 Mookerjee in the introduction to the volume, 

 more than doubtful. The introduction is followed 

 by accounts of the various departments of the 

 museum, all written in a style which renders the 

 volume a model of what a work of this nature 

 should be, and a credit to all those concerned in 

 its production. R. L. 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.'] 



The Colon as a Symbol for Ratio and Division. 



In 1902 Prof. W. W. Beman, of the University of 

 Michigan, pointed out (" L'Intermediaire des math^- 

 maticiens," T.g, Paris, p. 229, question 2424), that 

 the colon ( : ) occurs as a designation of geometric 

 ratio at the end of the trigonometric and logarithmic 

 tables published, together with William Oughtred's 

 'Trigonometria " of 1657. Beman inquires whether 

 this symbol for geometric ratio has a still earlier date. 



Before answering this question we remark that it is 

 highly improbable that the colon occurring in those 

 tables was inserted by Oughtred himself; in the 

 "Trigonometria " proper the colon does not occur, and 

 Oughtred's regular notation for ratio and proportion, 

 A . B II C . D, is followed throughout. 



In the English edition of Oughtred's " Trigono- 

 metric," printed in the same year, 1657, but subse- 

 quent to the Latin edition, the passage of the Latin 

 edition containing the : is recast, the new notation for 

 ratio is abandoned and Oughtred's regular notation 

 introduced. 



In Oughtred's posthumous " Opuscula mathematica 

 hactenus inedita " (Oxford, 1677), the colon ( : ) is 

 used frequently, but it may have been introduced by 

 the editor of the book. 

 j In answer to Beman's inquir)% we remark that the 



colon ( : ) was used to designate geometric ratio some 

 years before 1657 by at least two authors, Vincent 

 Wing, the astronomer, and a schoolmaster who hides 

 NO. 2357, VOL. 94] 



himself behind the initials '" R. B." Wing wrote 

 several works. In 1649 he published in London his 

 ■ Urania Practica," which, however, exhibits no 

 special symbolism for proportion. But his " Har- 

 monicon Coeleste" (London, 1651) contains many 

 times Oughtred's notation A , B 1 1 C . D, and many 

 cimes also the new notation, A • B II C : D, the two 

 notations being used interchangeably. Later there 

 appeared from his pen, in London, three books in one 

 volume, the '" Logistica astronomica " (1656), " Doc- 

 trina spherica " (1655), ^"^ "Doctrina theorica " 

 (1655), each of which uses the notation, A : B II C : D. 



The book by the second author is entitled ".An 

 Idea of Arithmetick at first designed for the use of the 

 Free Schoole at Thurlow in Suffolk ... by R. B., 

 Schoolmaster there " (London, 1655). One finds in 

 this text I . 6 1 1 4 . 24, and also A : a 1 1 C : c. 



It is worthy of notice also, that in a text entitled 

 ■■Johnsons Arithmetick, in Two Bookes " (second 

 edition, London, 1633), the colon ( : ) is used to 

 designate a fraction. Thus, 5 is written 3:4. If a 

 fraction be considered as an indicated division, then 

 we have here the use of : for division, at a period 

 fifty-one years before Leibniz first employed it for that 

 purpose. However, division dissociated from the idea 

 of a fraction is not designated by any symbol in 

 Johnson's text. In dividing 8976 by 15, he writes 

 the quotient 598 6 : 15. 



Florian Cajori. 



London, December 23, 1914. 



Is " Atikokania lawsoni " a Concretion? 



Has a mistake not been made in Memoir No. 28 of 

 the Geological Survey of Canada? Dr. C. D. Walcott 

 therein describes certain silicified structures in the 

 Steeprock Limestone of Lake Ontario which he names 

 Atikokania lawsoni. He considers they represent "a 

 group of organisms related to the sponges," or else 

 corals like the .Archaeocyathinae. 



He appears to have relied on three of their features : 

 li) a central cavity: (2) the general form, including an 



Coralloid ma:.s Iro.i. ihc 17-iu. " tUg" bed. Fulwcli Uitl (Quarry. X i. 



inner and outer wall, with (3) radiating tubes with 

 septae. Unfortunately they possess 'no structural 

 details." I suppose the author was unacquainted with 

 the characters met with in the Magnesian Limestone 

 of Fulwell Hill, Sunderland, where the forms are 

 entirely due to segregation or to osmotic influence. 

 His illustrations have a remarkable resemblance to 

 much seen there in what I designate coralloid — a 

 specimen of which is shown in the accompanying 

 figure. 



