NA TURE 



[December 30, 1909 



evidence which would show that they had actually seen 

 the book to which they refer. We have gathered informa- 

 tion about all Wingate's mathematical books which 

 De Morgan did not examine. We shall state where copies 

 can be found, so that the data given here can be verified 

 by those who are near the libraries named. We take up 

 Wingate's books, one after the other, and show that none 

 contains the slide rule. 



(i) " L'Usage de la R^gle de Proportion," Paris, 1624. 

 De Morgan's assertion that this book describes nothing 

 more than Gunter's scale' is corroborated by P. M. N. 

 Benoit," who examined copies in the Bibliothfeque nationale 

 and the Biblioth^que Mazarine in Paris. There is a copy 

 in the Bodleian Library. 



Wingate brought out in 1626 in London a translation 

 under the title " Use of the Rule of Proportion." Later 

 editions appeared in 1628, 1645, 1658, and 1683. De 

 Morgan saw the 1645 edition, a copy of which is in the 

 British Museum. Wingate died in 1656. 



(2) " Arithm(5tique logarithmique," Paris, 1626. De 

 Morgan described this book.' He saw also the " Logarith- 

 meticall Table," London, 1635, which is anonymous, but 

 is attributed to Wingate.* 



(3) " Construction and Use of the Line of Proportion," 

 London, 162S. Copy in the British Museum. The " line 

 of proportion " here described is merely a mechanical table 

 of logarithms. There are no sliding parts. 



(4) " Of Naturall and Artiticiall Arithmetique," London, 

 1630. Copy in the Bodleian Library. Describes only the 

 instrument named in the preceding text. The first part of 

 this book was enlarged by John Kersey the elder in 1650 

 under the new title " Arithmetique Made Easie." De 

 Morgan saw the editions of 1673 and 1760.' The second 

 part was re-edited by Wingate in 1652. Copy in the 

 British Museum. The instrument described here is still 

 the " line of proportion." 



(s) " Ludus Mathematicus," London, 1654, 1681. De 

 Morgan " inspected the first edition. 



(6) " Use of the Gauge-rod," London, 1658 (second 

 edition). 



(7) " The Clarks Tutor for Arithmetick and Writing . . . 

 being the Remains of Edmund Wingate," London, 1671. 

 Copies of both books in tlip Bodleian Library. Neither 

 contains an account of the slide rule. 



MASO'NRy ARCHES. 

 A MEMOIR dealing with a subject of great interest to 

 •^"^ the engineer has recently been issued as a Drapers' 

 Company Research Memoir.' It must be admitted that 

 the ordinary treatment of the masonry arch is by no 

 means satisfactory, and therefore any solution of the 

 problem which would give more accurate and trustworthy 

 results without involving excessive labour in the necessary 

 calculations would be welcomed by every engineer who 

 may in the course of his professional duties have to deal 

 with the design and erection of masonry or brick arches. 



After discussing the ideal arches for different load con- 

 ditions, the authors show that for the fairly flat arches of 

 modern practice designed to carry (i) a uniform load per 

 foot run of the rib, or (2) a vertical load rising to a 

 horizontal at a height l'/Sr + r/6 above the central line at 

 the crown, the elliptic arch is the proper design. 



The rest of the memoir is devoted to an investigation of 

 the extent of the applicability of the elliptic arch. It is 

 shown that for the loads usual in masonry arches the 

 elliptic arch is only closely approximate to the ideal if the 

 ratio of rise to span be small, this latter condition in- 

 volving large horizontal thrusts and great compressive 

 stresses. 



The authors then show that a close approximation to 

 the arch the line of pressure of which coincides with its 

 central line can be obtained with no great labour of calcu- 

 lation, and such an arch they term a pseudo-elliptic arch. 



1 "Arithm. Books," p. 42. 



- " La Regie .'i Calcul expliquife," p. vi. (Paris, 1853.) 



3 " Penny Cyclop.." Art. " Tables." p. 497. i Loc. cit., p. 498. 



I ,, Anthm. Books," pp. 48, 73. t, Q/:. cit., p. 44. 



' " On a Practical Theory of Elliptic and Pseudo-elliptic Arches, with 

 Special Reference to the Ideal Masonry Arch." By Prof. Karl Pearson, 

 W. D. Reynolds, and W. F. Stanton. Pp. 23+6 plates. Drapers' Company 

 Research Memoirs, Technical Series, VI. (London : Dulau and Co. , 1909.) 



The necessary equations to give the required solution are 

 obtained, and an example is worked out in detail to show 

 the application of the method and to prove that the labour 

 of the necessary calculation is not a serious obstacle to 

 the employment of this method. The memoir is illustrated 

 by six plates reproduced from actual drawings. 



The applied mathematics department of University 

 College is to be congratulated on this valuable addition to 

 the series of research memoirs dealing with difficult 

 engineering problems for which Prof. Karl Pearson and 

 his students have been responsible. T. H. B. 



NO. 2096, VOL. 82] 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Graduates of the late Royal University of Ireland who 

 desire to be registered as graduates of the Queen's Uni- 

 versity of Belfast, or enrolled as members of Convocation, 

 should communicate as early as possible with the secretary 

 of the latter University. The first meeting of Convocation 

 must be held within the next four months. 



We learn from Science that, according to figures avail- 

 able in the office of the auditor, the University of Chicago 

 holds investments representing permanent endowment that 

 amount to 2,974,000!. In addition, its buildings and 

 grounds devoted entirely to university use represent 

 1,783,540/. ; equipment, scientific apparatus, furniture, &c., 

 being put at 383,260/. additional. These figures do not 

 include the funds destined for the erection of the Harper 

 Memorial Library, estimated in round figures to cost 

 180,000/., nor the cost of the classical building, the con- 

 struction of which is in contemplation, and on which about 

 50,000/. will be expended. 



Dr. Charles Graham, at one time professor of chemistry 

 at University College, London, and a prominent member of 

 the Society of Chemical Industry, who died on 

 November 13, has left the residue of his estate for medical 

 research. The amount available will probably be 35,000/., 

 and it is left to the Senate of the University of London 

 to found a fund, to be known as the Charles Graham 

 Medical Research Fund. The fund is to be applied in aid 

 of any research carried on by a teacher or student of the 

 school of advanced medical studies of the University 

 College Hospital for the prevention, cure, or alleviation of 

 human disease or suffering. If any student or teacher 

 conducts a research which is considered of sufficient merit 

 a gold medal of appropriate value is to be awarded to him. 

 The committee of the school is also to pay to such teacher 

 or student conducting the research an annual sum not 

 exceeding 200/. per annum for two years, such person to 

 be known as the " Charles Graham Student in Pathology.'' 



The Department of Agriculture and Technical Instruc- 

 tion for Ireland has issued a syllabus (Circular 70) of 

 the examination which it proposes to hold in the principles, 

 methods, and history of education, with special reference 

 lo science teaching. The examination will be held in June 

 of each year. The examination is provided for candidates 

 seeking recognition of qualification to teach science. 

 Among the subjects included in the syllabus are : — The 

 general characteristics of the curriculum and methods of 

 instruction in science as determined by tlie laws of general 

 development ; the correlation of science with other subjects 

 of the curriculum. The methodology of instruction in 

 science as determined by the laws of development of know- 

 ledge ; the functions and relations of laboratory work and 

 class-teaching. The critical study of the history of a 

 special branch of science so far as it bears upon the 

 teaching of the subject. The use of note-books and text- 

 books in science teaching; methods of recording and treat- 

 ing observational data. The construction and use of 

 pictorial illustrations, diagrams, and models ; the construc- 

 tion of apparatus. Laboratory organisation and manage- 

 ment. 



The " Regulations for Secondary Schools " of the Board 

 of Education lays it down that in all fee-charging secondary 

 schools free places must be offered, under certain condi- 

 tions, at the beginning of each school year to pupils enter- 

 mg from public elementary schools. The number of such 

 places offered must ordinarily be 25 per cent, of the total 

 number of pupils admitted to the school during the previous 



