652 MINING ENGINEERING 



these subjects. Each is an essential support to any superstructure 

 that he may desire to build in the future. 



Mathematics should include the differential and integral calculus, 

 the theory of probabilities, and the methods and criteria of approxi- 

 mations. A firm grasp of space-relations as developed in descriptive 

 geometry is peculiarly important in following geological structure and 

 vein-formations in the deeps of the earth. The mathematical work 

 should be made familiar by numerous applications to concrete cases 

 in which numerical results should be insisted upon. In this connection 

 it is particularly important that the engineer should be made to 

 realize that the most important part of his numerical result is the 

 position of the decimal point, and only after that, the value of the 

 first significant figure. Mathematical instructors too often neglect 

 this, to the engineer, most vital matter. The sense of it should be 

 made instinctive. It is much more important that mathematical 

 instruction should be thorough as far as it goes than that it should 

 feebly cover a large territory. The subject should be so thoroughly 

 mastered that it comes to fit the hand like a well-worn tool. 



No man is fit to teach mathematics to engineers who has not had 

 some experience in its applications either to engineering, to physics, 

 or to astronomy. For only such a man knows just what to emphasize 

 and what to omit, how to sympathize with, and how to inspire his 

 students. 



Men of prime ability in the mathematical faculty are absolutely 

 the first essential in any engineering school. It is wonderful how 

 difficulties melt away like wax in the fire with a really able mathe- 

 matical teacher. By such a teacher mathematics can be made as 

 interesting as a romance to the average man; while it is often regarded 

 as hopelessly difficult merely on account of the poor hands in which 

 it is placed. To make new discoveries in the field of mathematics 

 requires genius of a high order; but to master all the mathematics 

 necessary for the intelligent practice of engineering requires no 

 faculties beyond those of a logical mind, a certain power of imagina- 

 tion, and a reasonable degree of application. I have always found 

 that the students who do well in mathematics do well in everything 

 else that requires close thinking. 



Instruction in physics and in mathematics should go on side by 

 side; and the two courses should be so arranged that the mathe- 

 matical principles may be at once applied to physical problems of 

 a useful nature. The importance of actual numerical results should 

 be always insisted upon. The student should be trained in the arts 

 of observation and in inductive as well as deductive reasoning. He 

 should acquire practice in the theory of approximations and should 

 form the habit of judging or "weighing" his own results and of 

 checking them by independent methods. 



