Dec. 30, 1886] 



NA TURE 



201 



command over its methods : he was always occupied 

 with something new, starting afresh and gaining 

 familiarity with new principles, new processes, new 

 modes of thought. Many of the higher lecturers 

 in the University were necessarily neglected by the 

 stutJents : they could pay but scant attention to any 

 subject which was not adequately represented in the 

 Tripos, and even in the case of the subjects which were 

 so represented they were tempted to pass lightly over 

 those investigations, however important, which from their 

 length and character were unsuitable for reproduction 

 in an examination. Now, however, all this is history. 

 When a good course of lectures upon any high subject 

 is given in the University, those students who have 

 attended the course will send in that subject as one on 

 which they desire to be examined : it will, therefore, be 

 properly represented by questions ; and the subject will 

 become one that will be increasingly studied year by 

 year. It will now be possible for any capable mathe- 

 matician, by means of his lectures, to gather pupils 

 round him who will bring his subject into prominence, 

 and make it one of special study in the University.' 

 It has been said that in mathematics we have in 

 England generals without armies : the great men who 

 are independent of circumstances have arisen among us, 

 but where are the rank and file? It is my belief that 

 the great obstacle to the existence of the rank and file 

 has now been removed. 



Whatever else it may be. Part II. is at all events a 

 "limiting form." No wider choice of subjects could be 

 given to the candidates ; no greater freedom to the 

 examiners. The schedule of subjects includes all mathe- 

 matics : the examiners may issue any kind of list. By 

 introducing numerous divisions into the classes they 

 may make it approximate as closely as they please 

 to an order of merit ; or, on the other hand, they may 

 make it merely a class list. They are empowered to give 

 to their list just such a form as they feel justified in doing 

 by the results of the examination. In the appointment 

 of examiners, also, the limiting form has been reached, 

 al! four being nominated by the same University autho- 

 rity, and holding office for one year only. 



With respect to Part I., it may be that the ultimate 

 form has not yet been reached. There are some who 

 think that, as in some other Triposes, the students should 

 have the option of becoming candidates at the end of their 

 second year. It would seem, also, that the range of sub- 

 jects is rather too restricted ; and, as may be inferred from 

 what I have said near the beginning of my address, I 

 should myself like to see the elementary portions of ellip- 

 tic functions included in the schedule of Part I. Still, 

 these are but minor points ; and I think that the prin- 

 ciple of subjecting all the candidates for mathematical 

 honours to one and the same examination in compara- 

 tively elementary subjects, and arranging the list in order 

 of merit, meets with general approval. 



A few years ago, when the old Tripos was exerting its 

 stifling influence upon the higher mathematical studies of 

 the Universities, I felt disposed to welcome the abolition 

 of the order of merit as the lesser of two evils ; but now 

 that the Tripos is divided, and that the mathematician 

 has his own examination especially framed for him, I 

 should be sorry to see a modified class list substituted 

 for the order of merit in Part I. A severe competition 

 for places has the great advantages of keeping the 

 candidates closely employed, and extracting from them 

 their best work. At present an immense amount 

 of thoroughly good mathematical work is done in 

 the University. We have received from our predeces- 

 sors a system under which the principles of mathematics 

 are efficiently taught, the powers of the students are 



In the schedule for Part II. no subjects are ignored or favoured less than 

 others, so that by the new scheme provision is made for the growth of any 

 subject which may happen to take root. 



exerted to the utmost, and upwards of a hundred persons 

 each year receive a mathematical education which is in 

 some respects unique. These are substantial advantages 

 which should not lightly be jeopardised or exchanged for 

 others that are probleinatical. Under any other system 

 I think the quantity and the quality of the mathematical 

 work done in the University would suffer. It should be 

 remembered also that there is no subject in which the 

 knowledge of a candidate can be so readily tested by 

 examination as in mathematics, and that in no other 

 subject can the results of an examination be expressed 

 with such certainty and accuracy by an order of 

 merit. 



I believe there are indeed but very few who have 

 graduated in the Tripos who would set a slight value upon 

 the advantage which their mathematical training has been 

 to them throughout life ; and on the other hand I think 

 that it has been an indirect benefit to our science that 

 among those who have won distinction in public and pro- 

 fessional life there have always been some — and those not 

 the least influential or eminent — who have passed through 

 an extensive and thorough course of mathematical study, 

 and to whom our world of symbols is no terra incognita. 

 The fact that our results, unlike the conquests of astro- 

 nomy and other branches of applied mathematics, can 

 only be expressed by means of a language of their own, 

 requiring years of study, imposes of necessity such narrow 

 limitations upon the numbers of our audience that we 

 cannot be insensible to the advantages of any system by 

 which the power of understanding and appreciating the 

 beautie; of our science is extended to others external to 

 our own ranks. Under the new scheme these advantages 

 are still retained; and, difficult as is the problem of com- 

 bining a mathematical course for the many with the 

 technical requirements of the few, I believe that a satis- 

 factory solution has rewarded the efforts of the last twenty 

 years. I believe that the University of Cambridge will 

 become a great centre of mathematical research and a 

 home of the exact sciences, and that it will be found that 

 these objects have been attained without any sacrifice of 

 the general efficiency of the training received by the bulk 

 of the candidates for mathematical honours. 



On taking a survey of the history of the Tripos during 

 the last half century, perhaps the feature that stands out 

 most strongly is the part played by the subjects of 

 electricity and magnetism — their half-recognised existence 

 before 184S, their exclusion until 1873, and the eftects 

 which followed their restoration in that year. It was the 

 extension of the dominion of mathematics over these great 

 and growing branches of physical science that broke 

 down the old system. Electricity and magnetism be- 

 came too important to be excluded ; but when included 

 the examination in its old form was too heavily weighted 

 to exist. 



The year 1S77-78, in which the syndicate of 1877 

 was endeavouring to frame a scheme that should relieve 

 the strain of the excessive competition without sacrificing 

 the order of merit, was perhaps the most eventful period 

 in the whole history of the examination : it then became 

 evident that it was impossible to retain the existing 

 system even in a modified form, and that a complete re- 

 organisation of some kind was inevitable, .'\lthough the 

 frequent changes in the last few years have been pro- 

 ductive of some inconvenience, I think it is fortunate 

 that the syndicate was so rekictant to propoze any 

 sweeping changes, and that the present scheme has 

 come into existence as it has done— not as the work of 

 any influential legislator, but as the form which the 

 examination has of itself assumed under the pressure of 

 the actual forces at work in the University. The order 

 of merit for the whole examination was not given up till 

 it was clearly shown that its retention was an impossi- 

 bility ; and, on the other hand. Part II. has grown up by 

 a process of regular development, and been moulded into 



