June 6, 1889] 



NATURE 



129 



respect for printer's ink ; hence they are always disposed 

 to believe that the book is right, and if you tell them 

 that an acceleration is not so manyy^^/ — as the book says 

 it is — but so mdiny/eet per second per second, they accept 

 the correction for politeness or for peace sake, but not 

 with any conviction. 



In addition to numerical calculation as an important 

 aid in the teaching of Mathematical Physics, I would also 

 advocate the employment oi graphic jnefhods of solution 

 in cases in which exact solution is not possible. The 

 graphic method of solution is scarcely recognized at all 

 in our text-books. Every text-book of Statics gives us, 

 indeed, its modicum of graphic representation, which is 

 usually exhausted in a bare and barren exposition of the 

 principle of the triangle of forces and the polygon of 

 forces, which has long since become stale " book-work." 



But this is by no means what I advocate. I intend 

 graphic solution at once as an aid to calculation, as a 

 means of strengthening the student's interest in the subject, 

 and as a representation to the eye of the possibilities and 

 limitations of any particular problem under discussion. 



[The problem of the equilibrium of a camp-stool was 

 then given as an illustration of the graphic method.] 



In Statics and Hydrostatics we have abundant instances 

 of this kind, and their solutions by the graphic method 

 furnish excellent practice for the ingenuity of the student, 

 giving to each problem the interest vvhich a vivid picture 

 always gives, as well as strengthening his knowledge of 

 the results and methods of pure Mathematics. 



The sum total, then, of what I have said with reference 

 to our elementary text-books comes to this — that, while we 

 are abundantly supplied with high-class scientific works 

 of an advanced character, a corresponding improvement 

 has not generally taken place in the books from vvhich 

 school-boys and other beginners have to learn ; that these 

 books are often marred, not only by inaccurate language 

 and fallacious teaching, but by a certain scrappiness in 

 their mode of treatment which is encouraged by the desire 

 of examining bodies to hurry through and skim over a 

 large number of scientific subjects at the expense of a 

 more leisurely study of the foundations of Science. 



I should like, in conclusion, to say a few words with 

 regard to the way in which the cramming of Science is 

 encouraged by examinations. 



Wherever well-worn book-work is set at an Examin- 

 at'on, it is extremely likely that cram will find its oppor- 

 tunity, and it may be impossible for an examiner to detect 

 it. Assuming that book-work must be set, I do not know 

 of any reliable safeguard against cramming except viva 

 voce examination. But a viva voce examination which is 

 made a part of the competition, and in which the candi- 

 dates do not all get the same questions, is, I think, essen- 

 tially unfair. Whenever such an examination is possible, 

 its function should be to discuss with each candidate the 

 several questions with which the written paper deals. In 

 this way, when his knowledge of any particular question 

 or method appears to the examiner of the written paper 

 to be doubtful, the doubt is very speedily settled one way 

 or the other. But, in the absence of such a corrective, an 

 examiner who is, after all, dissatisfied with the candidate's 

 working of any particular question, and yet disinclined to 

 allow him no credit whatever, is obliged to resort (at least 

 in many instances) to some systematic method of cutting 

 off marks, and this method is not infrequently a system of 

 elaborate trifling. 



As a particular example, take a question which is some- 

 times set at examinations in Science— the method of 

 determining H, the horizontal intensity of the Earth's 

 magnetic force. A part of the process consists in the 

 discussion of the vibrations of a uniform magnet bar 

 round a vertical axis under the influence of the horizon- 

 tal magnetic force. Such a bar is a compound pendulum, 

 and its motion involves a knowledge of its moment of 

 inertia and the integration of a differential equation of 



the second order. If at any instant B is the angle made 

 by the axis of the bar with the magnetic meridian, the 



expression ^ is involved in the equation. 



Now, I know a case in which the whole of this process 



was crammed up by a candidate who, although he had 



a good practical knowledge of Physics, did not know how 



to resolve a force along a line, did not know the meaning 



of the moment of a force about an axis or of the 



moment of inertia of a body about an axis, and, of course, 



dr6 

 was wholly ignorant of the meaning of the expression — —. 



dt'' 



Indeed, this last was a puzzle to him, for he always failed 



to place the two figures " 2 " in their proper places. Yet 



the whole thing was crammed up with sufficient success 



to obtain credit for the question. 



In such a case as this an examiner may have very 



grave suspicions, but he may be obliged to give a large 



measure of credit, nevertheless. Frequently the method 



of marking such an answer is something like this — the 



expression .^ involves two </'s, two 2's, a t, and a ^ ; if 



the candidate uses all these symbols, each in its proper 

 place, give him full marks ; if he uses all the symbols, 

 but one is misplaced, take off one mark ; if two are mis- 

 placed, take off two marks ; and so on. This is of course 

 an exaggeration, but it is the kind of system adopted — 

 necessary, perhaps, but extremely unsatisfactory. 



Now a viva voce examination of the candidate on this 

 question would, in a few seconds, have decided his mark 

 to be zero. 



In cases in which the number of candidates is very 

 large, it would seem to be impossible to apply a viva voce 

 test ; but there are cases in which it could be used, and 

 used, I have no doubt, with good effect. 



The setting of book-work at examinations is, I think, 

 much too frequent. It gives a hope of success to candi- 

 dates who really have no vocation for a subject, but who 

 load their memories sometimes with whole pages of work 

 of which they understand almost nothing. 



Our examination system has its defects ; but these 

 defects are almost wholly due to the shortcomings either 

 of individual examiners or of the directors of education. 

 I have spoken of the excessive haste with which educat- 

 ing bodies compel students to attempt the acquisition of 

 a large and varied assortment of knowledge ; but I must 

 not omit to add that the evils of examination are greatlv 

 aggravated by the prodigious haste which is imposed 

 on examiners themselves in some public competitions. 

 Nothing can justify a system which requires an examiner 

 to read over and determine the numerical value of every 

 one of 1200 papers in little more than a fortnight. The 

 thing is utterly impossible, and the results must be 

 untrustworthy. 



But, whatever the defects of the examination system 

 may be, I hold that the principle of examination is good. 

 [Some of the objections of the writers in the Nineteenth 

 Century were then dealt with in detail. Referring to the 

 unsatisfactory method by vvhich professors and lecturers 

 are now appointed. Prof. Minchin continued: — ] 



Mr. Frederic Harrison says, "Trust the teacher ; trust 

 him to teach, trust him to examine ; " and I should say 

 that, if we did, we should find our trust far more often 

 misplaced than it would be by trusting wholly to the 

 independent examiner. If the teachers were always 

 people who could. teach, the case would be different ; but 

 what is the method of appointing teachers, as a rule, in 

 England ? People make inquiries as to what scholar- 

 ships, prizes, and degrees, have been obtained at the 

 University by a candidate for a teaching post ; but of his 

 capacity for imparting successfully any of his own know- 

 ledge to others there does not, in most instances, exist the 

 slightest proof; and hence we are often presented with 



