258 



SCIENCE. 



[N. S. Vol. IV. No. 87. 



the text-books and an introduction of his- 

 torical and utilitarian ideas. Mathematics 

 is a tool to be studied for its uses, rather 

 than for its logic or for discipline that it 

 can give ; hence let its applications be incul- 

 cated frequently and not be systematically 

 kept out of view. If the student gains the 

 impression that his mathematical exercises 

 are merely intended to train the mind his 

 interest and his progress will usually be 

 slow. If, however, he learns what mathe- 

 matics has done in the past, how it joins 

 with mechanics to explain the motions of 

 the distant planets as well as to advance 

 the material prosperity of man, there arises 

 an interest and a zeal that helps him to 

 overcome all difficulties. 



The great advantage of numerical exer- 

 cises in all branches of pure and applied 

 mathematics, and the deplorable lack of 

 good preparation in arithmetic, have been 

 expressed by many educators. In numer- 

 ical computations the average engineering 

 student is weak in spite of the numerous 

 exercises in his practical work. To remedy 

 this defect better instruction in arithmetic 

 is demanded in the common and high 

 schools, while in engineering colleges the 

 teachers of mathematics should constantly 

 introduce numerical work and insist that it 

 be done with a precision corresponding with 

 the accuracy of the data. 



Next in importance to mathematics comes 

 mechanics, the science that teaches the laws 

 of force and motion. In most institutions 

 the rational is separated from the applied 

 mechanics and often taught by the mathe- 

 matical department. Probably less im- 

 provement has resulted in the teaching of 

 rational mechanics during the past quarter 

 of a century than in any other subject. 

 That mechanics is an experimental science 

 whose laws are founded on observation and 

 experience is often forgotten, and the formal 

 logic of the text-books tends to give students 

 the impression that it is a subsidiary branch 



of mathematics. The most interesting his- 

 tory of the development of the science is 

 rarely brought to the attention of classes, 

 and altogether it appears that the present 

 methods and results are capable of great 

 improvement. 



It should not be overlooked, however, 

 that in recent years the so-called absolute 

 system of units has been introduced into 

 mechanics and is now generally taught in 

 connection with physics. Here the pound 

 or the kilogram is the unit of mass, while 

 the unit of force is the poundal or the dyne. 

 Although this system possesses nothing that 

 is truely absolute, it has certain theoretical 

 advantages that have commended its use, 

 notwithstanding that no practical way of 

 measuring poundals has been devised except 

 by the action of the force of gravity on the 

 pound. Engineers have continued to em- 

 ploy the pound weight as the unit of force, 

 and the calculations of the physicist must 

 be translated into the units of the engineer 

 before they can be understood. The stu- 

 dent of rational mechanics thus has the 

 difficulty at the very outset of two systems 

 of units, and great care should be taken 

 that each be thoroughly understood and the 

 relations between them be clearly appre- 

 ciated by application to many numerical 

 problems. In view of these and other dif- 

 ficulties and of the novelty of the subject in 

 general, it appears that some engineering 

 colleges do not give to rational mechanics, 

 as much time as its importance demands. 



Physics in some colleges is taught by a 

 course of five or six exercises per week, ex- 

 tending over a year, while in others the 

 elements are required for admission and 

 the regular course is correspondingly 

 abridged. The marvelous development of 

 electrical theory and practice has naturally 

 tended to make this the most important 

 topic in the course, sometimes indeed to a 

 material abridgment of mechanics, acoustics, 

 thermodynamics and optics. Considering 



