August 7, 190S] 



SCIENCE 



165 



lines, surfaces, and volumes, and are not the 

 results of mere gymnastics. A knowledge 

 of the graphics of analytical geometry is 

 especially valuable in mechanical work, in 

 the investigation of earth pressures, in 

 suspension, bridge work, and in many 

 other lines of engineering. 



The proper conception of the meaning of 

 the calculus is rarely carried away by the 

 student. He knows the rules and can per- 

 form the operations, but their significance 

 is beyond him; consequently he does halt- 

 ingly and bunglingiy the original work 

 which facility in the use of the calculus 

 should enable him to perform easily and 

 well. This state of affairs is a crying evil 

 which should be corrected in all schools that 

 aim to give first class engineering courses. 



Descriptive geometry is of very large 

 value in the preparation of drawings ; but, 

 in addition, a thorough knowledge of it 

 greatly aids in the conception of an object 

 in space, and, consequently, is of large 

 assistance in the evolution of original de- 

 signs. A knowledge of it prior to the 

 study of the courses in pure mathematics 

 assists materially in the conception of what 

 the latter really mean; consequently de- 

 scriptive geometry should be one of the 

 earliest courses in an engineering curric- 

 ulum. 



A sound knowledge of mechanics, the 

 foundation of engineering, is impossible 

 without a thorough understanding of 

 mathematics. It is true that mechanics 

 may be learned by rote or by so-called 

 common-sense methods; but the "rule of 

 thumb" or "pocket-book" engineer never 

 rises to noticeable heights. Such an engi- 

 neer almost invariably fails at the critical 

 moment, when a decision must be sup- 

 ported by fundamental principles. It is 

 true that the actual use of analji;ical 

 geometry, calculus, least squares, or even 

 higher algebra and spherical trigonometry, 

 is rare in the practise of most engineers; 



but an engineer's grasp of technical work 

 depends upon his knowledge of these sub- 

 jects; and it is generally conceded that a 

 heavy structure can not be continuously 

 supported on a weak foundation. 



Mathematics higher than the calculus is 

 of small value to the engineer, except pos- 

 sibly as a training for the mind; but the 

 writer is of the opinion that any such 

 further study of mathematics is a detri- 

 ment rather than a help, in that it tends to 

 a desire to reduce all work to mathematical 

 calculation and thus to weaken the judg- 

 ment. In other words, excess of mathe- 

 matical development sometimes produces 

 an unpractical engineer. 



Most graduate engineers immediately 

 after leaving their alma mater drop for- 

 ever the study of mathematics, both pure 

 and applied, except in so far as they are 

 forced to use them by their professional 

 work. No greater mistake than this can be 

 made, for it takes very few years of non- 

 use of these subjects to cause one to forget 

 them utterly. Every young engineer 

 should make it a point to devote a certain 

 portion of his time to the reviewing of the 

 mathematical studies of his technical courae 

 so as never to become rusty in them; and 

 the writer believes that it is the duty of 

 every professor of mathematics and me- 

 chanics to impress this fact continually 

 upon the minds of his students, even up to 

 the very day of their graduation. 



J. A. L. Waddell 



Kansas Citt, Mo. 



PROM THE STANDPOINT OF THE PEOEESSOR 

 OF ENGINEERING 



When I come to think of what the Math- 

 ematical Society has brought upon itself, 

 I fear that it may feel something like the 

 football when it is kicked back and forth 

 upon the field. On the one hand we have 

 the trade-school element demanding more 

 knowledge of rules and, on the other, the 



