298 



SCIENCE 



[N. S. Vol. XXVIII. No. 714 



By Arthur S. Hathaway, Professor of 

 Mathematics, Rose Polytechnic Institute. 



In a paper on "Pure Mathematics for 

 Engineering Students," published in the 

 Bulletin for March, 1901, I expressed opin- 

 ions which coincide with those given here 

 to-day. I then said that instruction in 

 mathematics for engineering students 

 should have two objects (1) to develop an 

 engineering mind, and (2) to develop 

 mathematics as an instrument of research 

 for the engineer. I came to these conclu- 

 sions at that time as a result of inquiries 

 made of graduates of several institutions, 

 who were in engineering practise, and of 

 their employers. From the latter, I have 

 had the statement that it is inadvisable to 

 place a man in the higher positions in engi- 

 neering who has not had a good mathe- 

 matical training, especially, in the cal- 

 culus, which, they assert, develops those 

 modes of thought which are necessary to 

 the engineer. 



I wish to call your attention to the fact 

 that the fifty-four hours of analytical 

 dynamics credited to Rose Polytechnic In- 

 stitute on this chart are spent on applied 

 calculus. There is a regular course of 

 one hundred and forty-four hours in 

 Rankine not mentioned here, which is 

 given by my colleague, Professor Gray. 

 In applied calculus we take up problems 

 which require the use of the calculus, such 

 as motions in constant, elastic and central 

 fields, the bending of beams, the twisting 

 of shafts, problems in electricity, in chem- 

 istry, etc. We take problems gathered 

 from all sources, text-books, magazines, 

 engineering professors, and discuss them in 

 the class-room, with special reference to 

 the analysis and its mode of application. 



By Edward V. Huntington, Assistant 

 Professor of Mathematics, Harvard Uni- 

 versity. 

 I desire to call attention to the fact that 



besides the analogy of mathematics as a 

 tool or instrument, there is also the perhaps 

 more significant analogy of the mathe- 

 matician as the discoverer of quantitative 

 relations which already exist in the prob- 

 lems themselves. Logarithmic relations 

 between varying quantities, for instance, 

 are not dragged into the problem from 

 some artificial tool-chest, but are already 

 present in the problem, and are analyzed 

 out of the problem much as the precious 

 metal is analyzed out of the ingot by the 

 metallurgist. The practical mathema- 

 tician is simply a scientist specially trained 

 to perceive the quantitative aspects of 

 physical phenomena. 



By Donald F. Campbell, Professor of 

 Mathematics, Armour Institute of Tech- 

 nology. 



"We have had a number of good ideas 

 set before us in the last two days — ideas 

 which we ought to make an effort to 

 crystallize. I think that the present time 

 is the psychological moment to have a com- 

 mittee appointed to draw up a report on 

 mathematics for colleges of engineering. 

 This report perhaps might be in the nature 

 of a symposium, but it would be especially 

 valuable if it considered in detail the sub- 

 jects which should be emphasized in a 

 course in mathematics for engineering stu- 

 dents. These, however, are merely sug- 

 gestions. I would not hamper the com- 

 mittee in their deliberations by outlining 

 any particular course which they should 

 pursue. The only condition which I would 

 impose is that the committee be representa- 

 tive enough that all of us can look towards 

 their report with the utmost confidence. 



I would move that the chairman be em- 

 powered to appoint a committee of three, 

 these three to increase their number to 

 fifteen, chosen from among the teachers of 

 mathematics and engineering and the 

 practising engineers, these fifteen to con- 



