214 REPORT— 1876. 



metic, sucli as we see in diagrams of thrust, pressure, speed, work, temperature, 

 Leat, rainfall, and so forth. But I thiiik this will take care of itself provided linear 

 drawing be taught sufficiently early. 



I should leave my remaiks incomplete if I did not make what you may at first 

 sight think a digression, namely, some observations on our practice of teaching 

 languages, especially Jjatin aud Greek. But as they do form one side of education, 

 and as we should only be half-educated ^\ithout them, it is important that they 

 should be efl'ectuaUy and economically taught. And to none is this more important 

 than to those who need to use them, but who can spare little time from their more 

 essential study of natural science. I think all who value time wiU admit, if they 

 allow themselves independent reflection on the subject, that Greek aud Latiu are 

 taught too much as exercises of grammar and too little as languages. It is the same 

 fault as we have had in mathematics, where making boys learn Euclid has been 

 taken to be the same as teaching them geometry. Now teaching grammar and 

 " construing " bears to language the same relation that drill does to marching or 

 shooting, or that swimming on a table does to taking the water. In all these 

 matters we have learnt that moderate drilling and plenty of work is the best com- 

 bination ; but we have not yet learnt this lesson in reference to the classics. Our 

 ancestors had learnt aud practised it. They spoke Latin in the schools, aud to this 

 the drill-work of grammar and sjiitax was the proper complement. I hope you 

 manage things better in Scotland ; but iu England it is the rule to spend from six 

 to eight years in learning Latin aud Greek, and it is the exception to be able to 

 read either. 



If we cannot escape the effects of this scholastic tendency to exaggerate the 

 importance of intellectual gymnastics over actual knowledge iu classical and geo- 

 metrical teaching, let us at least do our utmost to prevent its being extended to 

 other languages aud to other studies. There is a class which is exerting pressure 

 that way. 



I speak the more fearlessly on this subject, because, ha^ing most strongly advo- 

 cated the extension of pure mathematics, I cannot possibly be mistaken for an 

 objector to ex.act learning. 



Now, returning to the subject of mathematics, I think one cannot fail to be struck 

 with the increa.-ing tendency which they exhibit to pervade all study of natural 

 science. I need not ask you whether it is wanted for mechanics. In the older 

 books on chenustry, elect)'icity, and so forth, it was quite an unusual thing to meet 

 with an algebraic formula or a geometrical theorem. Now, on the contrary, we 

 find that one half of chemistry is pure algebra : organic chemistry, iu particular, is 

 nothing but a special branch of algebra coupled with the experimental — I had 

 almost said accidental — fact that its formula are represented by actual combina- 

 tions. This disguised algebra enters so largely into chemical teaching tiiat I have 

 seen full marks obtained in an elementary examination paper on chemistry by 

 students who really knew nothing of the science, but who did understand algebra 

 well. I have recently seen a great deal of scientific work passing through the press, 

 and I have been much struck by the way in which pure mathematics continually 

 present themselves in all branches of knowledge. The reason is not far to seek. 

 We have passed the merely descripti'^'e stages of knowledge in most sciences, and 

 when we come to quantitative study — that is to say, to discuss number, nieasui'e, 

 position, and force — we are using mathem.atics, whether we know it and choose to 

 call it so or not. Moreo-\er, so far as we at present know, ordinary mathematics 

 are the simplest ways of counting and measuring. 



I may mention, incidentalh', that I think there are evidences that mathematical 

 knowledge is spreading in many directions. Apart from what is doing in the uni- 

 versities and high schools, I have myself an oppoitunity of ob8er-\ ing it elsewhere, 

 as the examiner for elementary pure mathematics for the Science and Art Depart- 

 ment. This year, in particular, I am able to say that there has been a very marked 

 improvement in the Iniowledge of the candidates under examination, aud I think 

 the teaching of the science classes under the department is really beginning to tell 

 in this important subject. Compared with the requirements of this country, it is 

 but a small matter, for there are only about 7000 candidates annually, and these 

 candidates come up more than once. Nevertheless it is good so far as it goes, and 





