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SCIENCE. 



[N. S. Vol. XIX. No. 478. 



could not be classified with, the man who 

 describes an unrecorded bug, or the one 

 who makes a new but useless chemical com- 

 pound. The latter work without the hope 

 of direct money return for their labors. 

 Therefore, theirs is the true method and the 

 higher life even when their disinterested 

 consecration to science is mingled with a 

 hope that a little fame will bring them 

 an increase in salary from some practical 

 person or persons who appreciate their un- 

 selfish efforts. 



However all of this may be, we know that 

 the essence of any engineering work worthy 

 the name is its independence. With this 

 there is usually some degree of originality, 

 as it seldom happens that the same 

 problem repeats itself in every particular. 

 What is more, with the independence 

 and originality of the engineer must 

 come character— confidence in his own men- 

 tal processes and a willingness to shoulder 

 responsibility in embodying his conclusions. 

 A scientist may announce his discovery of 

 the tidal evolution of the moon and yet 

 be forgiven if later it should be shown that 

 he is in error. Not so with the engineer. 

 When his bridge falls under prescribed 

 conditions of safe load, his own ruin as well 

 as that of his structure is complete. Of all 

 men living the intellectual life the engineer 

 is the one most interested in sound and log- 

 ical training for his profession and most 

 intolerant of all shams. It is not surprising 

 then that the one subject in secondary 

 schools whose natural purpose is to train the 

 student to severe logical and productive 

 thinking should respond most fully to his 

 influence. Neither is it surprising that 

 from the ranks of the engineers should 

 come the reformer who sees clearly the de- 

 fects of our present mathematical woi-k in 

 the lower grades and who is moving power- 

 fully to secure better conditions. 



We may sum up what now seem to be the 



best ideals in secondary mathematics as 

 follows : 



These ideals come from the engineering 

 professions. 



They insist upon quality rather than 

 quantity. 



They insist that the problems shall be 

 largely concrete and shall be worked out to 

 an accurate numerical result. 



They insist that the thought shall pre- 

 cede the form, that the symbol shall not 

 conceal the thing symbolized. 



They insist that systematic and progres- 

 sive problems based upon every-day ex- 

 perience and observation shall be, to a much 

 greater extent, the materials of education. 



They demand that the several elementary 

 mathematical subjects from arithmetic to 

 the calculus shall develop side by side in 

 the boy's mind. 



They demand that the mastery of these 

 subjects shall be more the work of the judg- 

 ment than of the memory. 



They demand that from first to last, at 

 least during the secondary period, mathe- 

 matical ability and the ability to think 

 clearly, investigate closely and conclude cor- 

 rectly shall develop together, and to the 

 extent that four well-spent years will on 

 the average permit. 



Those who formulate these ideas contend 

 that they lead to the correct mathematical 

 training for all professions and all careers. 



It remains for us to consider the mathe- 

 matical courses in our technical colleges. 

 What is their relation to the development 

 of the engineer ? What shall they include ? 

 How shall they be administered? These 

 are not new questions, neither has the last 

 word been said in answer to them. Fifteen 

 years spent in directing engineering mathe- 

 matics gives the writer some excuse to un- 

 dertake some further discussion of them. 



Important contributions were made by 

 Professor Mansfield Merriman in 1894, and 

 Professor Henry T. Eddy in 1897, whose 



