June 29, 1893J 



NATURE 



J 99 



miims their scalar product. The change suggested would enable 

 students to gradually accustom themselves to the notation of the 

 calculus, which would in fact then. form an abridged notation 

 for the cartesian expressions and operations which enter into 

 physical investigations. 



1 would ask Prof. Knott to give this suggestion his careful 

 consideration, as I am sanguine enough to believe that in it, 

 simple as it appears, lies the possible reconcilement of the new 



-school of vector analysts with the quaternionists. Possibly some 

 symbol other than S would have, at any rate at first, to be em- 

 ployed for this new scalar product. Perhaps, with Prof. 

 Mactarlane, it might be called the cos-product, though that 

 notation properly belongs to the scalarproductof twovectorsonly, 

 and loses its significance if applied to the scalar product of three 

 or more vectors. No single letter symbol could be better than 

 S, as it is distinctive and quick to write. However, the first 

 question is whether there is any possibility of the modification 

 being adopted. 

 The quaternionic product of a vector by itself would be minus 



I its scalar square, but without any mystery attached to the fact. 



- For the product of two vectors = vector product — scalar pro- 

 duct, and therefore, if the vector product is zero, the quaterni- 



.onic product = — the scalar product. Hence, instead of 

 havii g 



(a -r j3)2 = 0^-1- 2So^ ■(- fl^ ' 



we should have 



S(o + $)■ = S(o'^ + 20/3 -I- ;3'). 



Reciprocal vectors satisfy the equation 0~^0 = i, so that 

 S0~'S = - I, i.e. $''-, /3 are oppositely directed vectors. 

 The quaternion 



-1 _ o3 _ Vttg - Sag __ 



Vo(8 ^ SaB 



S0-' 



+ 



S/3^ 



showing clearly that both the vector and scalar products o' 

 o3 ' are opposite in sign to those of a/3, as must, of course, be 

 the case since j8 ' and /8 are oppositely directed vectors. This 

 fact is obscured with the orthodox notation. In fact, so far as I 

 have been able to test the proposed change, I have found no 

 drawbacks, but rather an improvement. Alfred Lodge. 



Sagacity in Horses. 



From the window opposite, as I write, I have just witnessed 

 an interesting performance on the part of two horses. Border- 

 ing the park is a strip of land, doomed to be built upon, but 

 meanwhile lying waste, and used for common pasturage, on 

 «hich the horses under notice were leisurely grazing. A pony 

 in a carl, having been unwisely left by the owner for a time un- 

 attended on the grass, suddenly started off, galloping over the 

 uneven ground at the risk of overturning the cart. The two 

 horses, upon seeing thi?, immediately joined in pursuit with evi- 

 dent zest. My first supposition, that they were merely joining 

 in the escapade in a frolicsome spirit, was at once disproved by 

 ihe methodical and business-like manner of their procedure. 

 They soon reached the runaway, by this time on the road, one 

 on one side of the cart, and one the other ; then, by regulating 

 their pace, they cleverly contrived to intercept his progress by 

 gradually coming together in advance of him, thus stopping him 

 immediately in the triangular corner they formed. Until the 

 roan came up to the pony's head they remained standing thus 

 together quite still ; when the two horses, evidently satisfied that 

 all was now right, without any fuss trotted back again together 

 to iheir grass. 



The sagacious conduct of the horses, acting in such perfect 

 cooperation, formed a pretty sight ; and it was apparent that, 

 instead of making the pony more excited, they really pacified 

 and calmed him. Why should they not receive " honourable 

 mention " as much as if they were proud human beings ? 



William White. 



The Ruskin Museum, Sheffield, June 20. 



TERCENTENARY OF THE ADMISSION OF 

 WILLIAM HARVEY TO GONVILLE AND 

 CAWS COLLEGE, CAMBRIDGE. 



■JDORN at Folkestone, and educated at the King's 

 *-^ School, Canterbury, William Harvey was admitted 

 to Gonville and Caius College as a minor scholar in his 

 sixteenth year, on May 31, 1593. The tercentenary of 



NO. 1235, VOL. 48] 



this event was celebrated by Harvey's College on Wed- 

 nesday, June 21, this being the earliest day after the date 

 of his admission at which rooms were available for those 

 coming from a distance. The guests were received and 

 welcomed by the Master and Fellows, at five o'clock, in 

 the large Combination Room, where tea was provided. 

 In the smaller adjacent room were exhibited a number 

 of objects of interest connected with Harvey, including 

 his pestle and mortar, from the Museum at Folkestone, 

 a rubbing from his mother's tomb, an autograph letter 

 of Harvey, lent by the Master of Sidney Sussex College, 

 and a coloured drawing of Harvey's coat-of-arms, re- 

 cently discovered on the walls of the buildings of the 

 University of Padua. The latter was presented to ihe 

 College by the University of Padua, followed on the day 

 of the festivity by a long congratulatory Latin telegram 

 from the Rector, on behalf of the University, which ran 

 as follows : — " Universitatis Patavina: quae cum aliis 

 Britannis discipulis tum Harveio Caioque gloriatur, 

 quorum alterius merita insigne Collegium vestrum 1 unc 

 isecolit nomenque ex altero invenit, festi in Harveii 

 honorem indicti participem se profitetur et in renovanda 

 cum celeberrima Universitate Cantabrigiensi vetere 

 studiorum amicitiajque memoria summopere Isetaiur, 

 pro Academico Senatu, Ferraris Rector." Also an auto- 

 type of the panel portrait of Harvey from Rolls P. irk, 

 Chigwell, Essex, presented to the College by Sir Andrew 

 Clark, as one of a series of eight, consisting of a central 

 portrait of Harvey's father, surrounded by those of his 

 seven sons. Some early editions of the works of Harvey 

 and of some of his more immediate predecessors and 

 followers were also displayed, together with the admis- 

 sion book of the College, containing the original record 

 of his admission. At seven o'clock the guests assembled 

 once mure in the Combination Room, whence they pro- 

 ceeded to dinner in the College Hall, led by the butler, 

 bearing the original " caduceus," as- used by Dr. Caius 

 when President of the College of Physicians. The dinner 

 was presided over by the Master of Gonville and Ca)us 

 College, the Rev. N. M. Ferrers, D.D., F.R.S., above 

 whose chair were displayed a copy of the bust Irom the 

 Harvey Memorial, crowned with a laurel wreath, and the 

 much-prized portrait of Harvey from the Master's Lodge. 

 After dinner the Grace Anthem of the College, composed 

 by Mr. C. Wood, was sung. The Master then proposed 

 the usual loyal toasts, after which Sir James Paget pro- 

 posed the toast of the evening, " The Memory of William 

 Harvey." 



He remarked that the reason why he had the honour of 

 being asked to propose that toast was his relationship to 

 his brother, who, he believed, made the proposal that 

 there should be that tercentenary of the admission of 

 William Harvey. He desired to remeinber that, and to 

 speak as he thought his brother would have spoken if he 

 had had the opportunity. He was sure that if he had 

 been present he would have referred to the honour which 

 was due to the college which Caius founded. He would 

 have done that out of the deep sense of gratitude which 

 he had for the College. For it was the Fellowship founded 

 by Caius that led his brother to the study of inedicine, 

 and, on the occasion of that Fellowship which he held 

 becoming vacant, to give himself entirely to it. To that 

 he owed a great part of the happiness of his life, and he 

 hoped he (the speaker) would not be deemed wrong if he 

 said that indirectly he himself was also deeply indebted to 

 Caius College, lor it was through the large income which 

 was associated with that Fellowship that his brother was 

 enabled, out of his abundant generosity, to help him 

 greatly in the study of his profession at St. Bartholomew's 

 Hospital, of which Harvey was so great an ornament and 

 honour. He wished that they knew more of the time and 

 the w ork he did in Caius College. Indirectly Harvey owed 

 to Caius himself the opportunity of being a student of the 

 College. It was not, he thought, known whether Harvey 



