552 



SCIENCE 



[N. S. Vol. XXX. No. 773 



wooden troughs kept well painted with thin 

 coats of asphalt have given good satisfac- 

 tion. They are much to be preferred to 

 lead pipes, which continually give trouble 

 from clogging. In concrete construction 

 the writer has these troughs replaced by 

 trough-like depressions made in the floors 

 and lined with asphalt. Care should be had 

 to make these of sufficient capacity and fall ; 

 they are covered with slate or cast-iron 

 slabs. The vertical drains should be con- 

 structed of hard baked Akron tile or better 

 yet, chemical pottery, and the joints made 

 with cement or possibly with the same ma- 

 terial as the asphalt floors. These vertical 

 drains can either be in the elevator well or 

 in a square space in the wall, it being closed 

 with doors so that they too, are readily ac- 

 cessible. Individual traps and vents are 

 not needed in the various laboratories, but 

 the whole system should be effectively pro- 

 tected by traps in the basement. For sinks 

 the ordinary round stoneware wash bowl 

 may be used. This is made with an over- 

 flow, and instead of the usual brass fitting 

 at the bottom a porcelain tube two or three 

 inches long projects from it, carrying eye- 

 lets at the top on either side of the bowl. 

 The tube fits down into a piece of lead pipe 

 two feet long which empties into the trough 

 on the back of one line of desks. This lead 

 pipe is supported at the top by the eyelets 

 just mentioned. These pipes can then be 

 easily replaced by the janitor, the services 

 of the plumber not being needed. Each 

 laboratory should be provided with valves 

 so that the steam, water and gas can be 

 shut off from it without disturbing another 

 room. The gas valve should be placed 

 near the exit so that it can be closed nightly 

 and diminish the danger from fire. 



Augustus H. Gill 

 Massachusetts Institute op Technology, 

 March, 1909 



THE PRINCIPLES OF THE CALCULUS AS 



APPLIED IN THE TECHNICAL COURSES 



OFFERED AT THE UNIVERSITY OF 



ILLINOIS 



Considerable discussion has been aroused 

 in mathematical and engineering circles 

 by the publication in Science of the papers 

 presented at the symposium on mathe- 

 matics for engineering students held in 

 Chicago at the time of the joint meeting 

 of the American Mathematical Society and 

 the American Association for the Advance- 

 ment of Science. The committee appointed 

 soon after this meeting is now formulating 

 a course in mathematics intended primarily 

 for engineering students, and their outline 

 will undoubtedly be accepted as a syllabus 

 of the mathematics required by students in 

 technical courses throughout the country. 

 In this connection it may be suggested that 

 some notions as to the contents of such a 

 course might be obtained from an investiga- 

 tion of the various technical courses offered 

 at some university maintaining a school of 

 technology of recognized standing. It 

 would be of interest to know what prin- 

 ciples, say of the calculus, are actually used, 

 and how often, in a single complete course 

 or group of technical courses. Data on the 

 relative frequency with which these prin- 

 ciples are used might suggest the amount of 

 emphasis to be accorded each in a course of 

 mathematics for engineers. On the other 

 hand, such data should also suggest to the 

 teacher of mathematics those principles 

 which, though not emphasized in the appli- 

 cation, should constitute an important part 

 of any Avell-rounded course in the calculus. 

 The gaps to be thus filled become apparent 

 on investigating what principles of the 

 calculus are emphasized throughout the 

 technical courses actually offered. 



In this investigation I have considered 

 'the technical courses as offered in the col- 

 lege of engineering of the University of 



