February ii, 1915] 



NATURE 



643 



— one group of letters being capitals, A, B, C, and 

 the other group small letters, a, b, c. The introduc- 

 tion of this notation is ascribed by Moritz Cantor, 

 in his '"Geschichte der Mathematik," vol. iii., 1901, 

 p. 561, to the Swiss mathematician, Leonhard Euler, 

 who first used it in 1753 (" Histoire de I'Academie de 

 Berlin, Annee," 1753, p. 231). • It is the purpose of 

 this note to point out that this simple, yet important, 

 innovation was made nearly a centun- earlier. 



In the British Museum there is a pamphlet of a 

 dozen small leaves, written in Latin. Upon one side 

 of each leaf there is engraved writing (script). The 

 pamphlet is a collection of formulas for plane and 

 spherical triangles, with drawings. Apparently the 

 process of engraving was resorted to because no type 

 was available for the new symbols used. There is no 

 title-page. The first page contains " Symbola," and, 

 at the bottom, the name "Ri : Rawlinson." The place 

 and date of publication are not given. On one sheet, 

 which is larger than the rest and is folded, there are 

 drawings and time-records to illustrate the passage of 

 the moon over the disc of the sun in an eclipse of 

 Januarx^ 16, 1655, observed at Oxford. Here the 

 name '" Ri : Rawlinson " occurs a second time. Who 

 was this man? It could not be Richard Rawlinson, 

 the antiquarian, for he did not write on mathematics. 

 There is no doubt that the author of the pamphlet is 

 the Rawlingson of whom Anthony A. A\'ood speaks in 

 his "Fasti Oxonienses," edition P. Bliss, second part, 

 London, 1820, p. 257, placing him in the Oxford list 

 of "Doctors of Divinity" of the year 1661. The 

 reference is as follows : " Sept. 9. Rich. Rallingson 

 or Rawlingson of Queen's coll. chaplain to the duke 

 of Newcastle, was created while the chancellor held 

 the supreme chair in convocation.^ — He was an in- 

 genious man, well skill'd in the mathematics, but 

 had not preferment confer'd on him equal to his 

 merits. He died in 1668, being then, as I conceive, 

 rector of Pulborough in Sussex." 



Thus it appears that the pamphlet was issued be- 

 tween 1655 and 1668. Some of the symbols are the 

 same as those used by Seth Ward, Savilian professor 

 of astronomy at Oxford, in his " Idea trigonometriae 

 demonstratae," 1654. All of Ward's symbols were 

 probably originally due to William Oughtred. Ward 

 and Rawlinson used Oughtred's symbols for propor- 

 tion, A . B : :C . D ; they used a slightly modified form 

 of Oughtred's symbols for "maius" and "minus"; 

 they designated by fc' the complement of an angle h. 

 Rawlinson introduced several new symbols. In case 

 of triangles, he designated the sides by the capital 

 letters, A, B, C, and the opposite angles by a, b. c, 

 respectively. This is his most important innovation. 

 The idea of this device was not generally adopted until 

 re-introduced about a century later. Rawlinson went 

 even further. With him, A was the maximum side, 

 C the minimum. Moreover, he distinguished in his 

 notation between plane and spherical triangles by 

 writing the letters in different script. Each letter for 

 spherical triangles was curved in all its parts ; each 

 letter for plane triangles had a conspicuous straight 

 line as a part of itself. Rawlinson had symbols for 

 angulus "obliquus," "acutus," "obtusus," "rectus," 

 and "rect. et obi."; he had symbols also for "datum," 

 " latus," "complementum," "compl. com.," "latus 

 op. angu.," "angu. op. lat.," "pars media," "quae- 

 situm," " quadrans," "sinus," " tangens." Rawlin- 

 son 's symbols for "parallelus," "perpendicu.," "tri- 

 angulum," "radius" hgd been introduced into mathe- 

 matics before 1655, and are still in use at the present 

 time. His pamphlet lays extraordinary emphasis upon 

 the use of symbols. He had what Thomas Hobbes 

 called a "scab of symbols." 



During the first half and middle of the seventeenth 



NO. 2363, VOL. 94]- 



century British writers introduced symbols into trigo- 

 nometry to an extent unparalleled by contemporaneous 

 writers in other countries, but our histories of mathe- 

 matics do not reveal this fact. 



Florian Cajori. 

 7 Gordon Street, London, W.C. 

 January 30. 



Measurements of Medieval English Femurs. 



In a paper lately contributed by Dr. Alice Lee to 

 Biometrika (vol. x., Nos. 2 and 3, November, 1914, 

 p. 208), entitled a " A Table of the Gaussian ' Tail ' 

 Functions," the author does me the honour to 

 criticise some statistics which I published in the 

 Journal of Anatomy and Physiology (vol. xxxviii., p. 

 238), on the measurements and proportions of the 

 medieval English femur, derived from the study of 

 bones in the cr\pt of the Parish Church at Rothwell 

 in Northants. 



The criticism, which is undertaken from the point 

 of view of the advanced mathematician, I am 

 ashamed to say I can only partly follow, but it 

 turns largely on the very difficult question of accurate 

 sexing, and Dr. Lee brings forward mathematical 

 reasons for believing that my sexing must be in- 

 accurate. 



That this may well be so I readily allow, though I 

 am glad to see that when Dr. Lee has rearranged 

 the sexes to suit mathematical requirements, the 

 average measurements seem to be altered by only the 

 fraction of a millimetre, an amount of no possible 

 importance to the practical anatomist or anthropolo- 

 gist. 



There is, however, one method of criticism against 

 which my practical experience in cr\pts makes me 

 anxious to warn mathematicians ; it is the futility of 

 expecting that the measurable bones in a crypt will 

 show any proportion to the number of males, females, 

 and children in the population. 



■ Owing to their greater fragilit\' the children's bones 

 become disintegrated in the course of centuries long 

 before those of adult females; while, for the same 

 reason, those of females do not last as well as those 

 of adult males. 



Consequently, when Dr. Lee points out that my 

 method of sexing would mean a predominance of 79 

 per cent, of males in the population, while hers would 

 give a slight preponderance of females, I submit that 

 mv estimate is, in the circumstances, more likely to be 

 in harmonv with the proportions of measurable bones 

 in the crypt. 



If Dr. Lee could superintend the restacking of a 

 crvpt full of bones with a view to their preservation, 

 as I have done on two occasions, she would be 

 astonished at the load of damp bone meal and broken 

 fragments which have to be returned to the church- 

 vard. In this I am sure would be found the excess 

 of female bones as well as most of the bones of the 

 children, thus accounting for the pref>onderance of 

 male bones left fit for measuring. 



F. G. Parsons. 

 St. Thomas's Hospital, S.E. 



Pheasants and Gun-Firing. 



On December 16, in the morning, pheasants in the 

 woods at Dunsby and Hacconby made the same loud 

 cackling as those later on at Saxby, referred to in 

 N.ATLRE of February* 4, p. 622 ; and keepers made the 

 same remark that there was shooting out at sea. 

 These places are within a few miles of whence I write 

 — ^\-iz., Bourne, in Lincolnshire. H. Cotton Smith. 



The Abbey Vicarage, Bourne. 



