July 13, 1905] 



NA TURE 



complicated or more advanced than anything which the 

 engineer will be likely to require. That, in itself, is not 

 an objection at all, because, as 1 have said, it is impossible 

 really to master a scientific subject up to a certain, often 

 very elementary, point without having at least a superficial 

 knowledge of a much greater extent of the subject. But 

 it is desirable, indeed necessary from our point of view, 

 *hat the advanced work in purely scientific subjects should 

 be specially chosen so as best to deepen and make certain 

 the knowledge of the earlier work. This may be, and 

 almost certainly is, a very different thing from choosing 

 it so as to form the best basis for still further study of 

 the particular science in question. In this connection I 

 must point out — at least as my opinion — that it is a 

 mistake to consider that there is only one mathematics or 

 one physics, and that either the preparatory work or the 

 whole teaching must necessarily be the same for everybody 

 — for the man who is to devote himself to engineering, or 

 for the man who intends to spend his life in physical 

 work. For instance, I think an engineering student may 

 be allowed to take for granted that A times B is equal to 

 B times A (he is always quite prepared to believe it), and 

 that it is perfectly reasonable to make to him dogmatic 

 and probably in a sense erroneous, statements as to atoms 

 {let us say) or as to the ether, without any of the qualifi- 

 cations which would be necessary supposing the atoms 

 and the ether were to form the basis of the man's future 

 ■studies. 



It is no doubt a noble conscientiousness which some- 

 times prevents a man who is in the front rank among 

 men of science from making to his students, as quite 

 :general, statements which he knows to be true only with 

 <!ualifications or limitations. But the case is one in which 

 often the general statement, given with authority, will 

 really give the student a truer conception of the facts 

 than a more accurate statement which is guarded by 

 reasoning and e.xplanations which he (that is, the student) 

 cannot understand, and will almost certainly misunder- 

 stand. As a writer in Nature put it a few days ago, re- 

 ferring to the theory of quaternions, " the truth is that 

 very few students are able to appreciate to the full an 

 absolutely logical argument until they have a certain 

 amount of practical knowledge imparted to them more or 

 less fcv authority. ^^ 



There is one matter in connection with the teaching 

 ■both of mathematics and physics to engineering students 

 which I think might well be emphasised more than is 

 generally the case. Whether it is desirable that it should 

 he emphasised in dealing with the general student I do 

 not venture to say. I mean the point that the answer to 

 any question can only be as accurate as the data of that 

 ■question. For the ordinary examination question in 

 mathematical physics it is necessary and unavoidable to 

 presuppose certain data which in real life are absurd and 

 impossible. In the ordinary everyday questions of engineer- 

 ing there is nothing more misleading than to take for 

 granted the data of the examination paper, and a very 

 great deal of the disrepute into which mathematical work 

 ■had fallen at one time among engineers was due to the 

 fact tliat although the average student was able to use 

 his methods rightly, he was unable to perceive whether 

 they led him to a right result. I think it must be 

 possible, even if it is not exactly easy, to point out to the 

 student the extent to which the accuracv of his answers 

 js influenced by the assumptions which he makes. 



It is. I am afraid, too often presumed that the method 

 of working out the answer is the chief thing: perhaps it 

 may be from some particular point of view. But for our 

 purposes, foolish as it may sound, the method of working 

 out the answer is only secondary ; the answer itself is the 

 chief thing, and we really must have that answer right 

 when it finds itself translated into steel or stone. We 

 would much sooner have a right answer got by an im- 

 perfect method than a wrong answer got by the best 

 method in the world. And an answer may be wrong in 

 two ways ; it may be wrong because the data are in 

 themselves wrong, that is to say, inapplicable to the par- 

 ticular case, or it may be wrong by being stated in a form 

 much more accurate than the real data will allow of, as 

 when we find the indicated horse-power of engines given 



NO. 1863, VOL. 72] 



to six significant figures, when we know perfectly well 

 that the fourth must always be doubtful. 



It would be most useful if our scientific professors 

 would discuss these points with their students and show 

 them speciallv the extent to which the methods and 

 theorems of the mathematician and the physicist may be 

 properly applied when the only data available for the 

 problems are such as actually are found in practice. It 

 is hardlv fair m leave the engineering professor to tell 

 his pupils, or to leave the engineer to tell his assistants, 

 that the methods they are using are quite inapplicable, 

 and the results which they are getting obviously in- 

 accurate. This is in every way inadvisable, and may 

 lead the otherwise guileless student to discount all his 

 teachers instead of only one. Every scientific experimenter 

 knows that it is often the most difficult part of his work 

 to say how alterations in data or want of knowledge of 

 accuracy in data may afl'ect the result, and I should like 

 much to see this matter systematically dealt with by the 

 teachers who have actually to do with the scientific or 

 theoretical treatment of the questions concerned. If they 

 have any doubt as to what is the general nature of the 

 complex engineering questions which have to be solved, a 

 letter addressed to anv engineer in Westminster would 

 bring them the fullest information. But happily most of 

 the university colleges now have engineers on their Senates, 

 so that the 'information can be had without going outside 

 their own walls. 



As to the more advanced part of engineering teaching 

 in colleges, I want to put forward an idea that I have 

 more than once had occasion to express. I should much 

 like to see the development of some such connection 

 between old and distinguished students of a college, who 

 become later on older and more distinguished engineers, 

 and the college at which they have studied or some other 

 college, as exists in the similar case of the medical pro- 

 fession. My suggestion is that to get the full benefit from 

 its best pupils, a college should, if possible, keep in touch 

 with them after they have left it. A few years after they 

 have left college, and when they have fairly got into the 

 swim of professional work, but before they have so much 

 lost touch with the difficulties of their college days that 

 thev no longer appreciate the student's point of view, 

 thev might be made to help in teaching by giving lectures 

 on the special branches of engineering with which they 

 were specially and actively familiar. They should do it 

 before they have forgotten what they formerly learnt, or 

 have had "it driven out of their heads by the pressure of 

 other ideas, and while college methods and points of view 

 are still familiar. They would be men still making their 

 way in their profession, still, let us hope, full of enthusiasm 

 for' their work, and certainly they would be daily finding 

 out the differences between actual and academic problems. 

 Teaching of this kind could in no way replace the general 

 preliminary teaching of engineering subjects in the college, 

 which must continue to be given, as it is given now, by 

 a professor or professors, the bulk of whose time is spent 

 at the college, and who are thoroughly in touch with all 

 the students. 



I confess that I hope a time will come when in any case 

 professors of engineering will not remain permanently 

 in academic harness, but will come out and take their 

 place— a most important one— as colleagues among the 

 active and leading engineers of the country, and will look 

 upon such a position as that which they ought to reach 

 rather than a solelv academic position, however eminent. 

 But in addition to the work of the permanent professor 

 or professors, I believe that old students coming back 

 in the fashion I have indicated, not in one only, but in 

 several branches of engineering, and giving short courses 

 of special lectures to third year students, would very much 

 help both the students and the rest of the teaching statt. 

 The arrangement would also have the very great 

 advantage of bringing about a closer and warmer con- 

 nection between the men who are at work m their pro- 

 fession and the colleges where they were trained. It 

 would also help to keep the colleges themselves in that 

 actual and continual touch with engineering things and 

 ideas which is so absolutely essential for their continued- 

 usefulness. 



