102 MATHEMATICS 



aims of the students, it is certain that either 

 an exclusive fixing of the attention upon the 

 abstract side of the subject, or a merely qualitative 

 observation of phenomena of motion and rest 

 without a precise study of their quantitative aspect, 

 will very materially diminish the advantages de- 

 rived from this fundamentally important study. 



The mode in which mathematical teaching 

 should be adapted to the needs of students of 

 Engineering Science has received much attention 

 during the last two decades. That much of the 

 mathematical teaching current in the Universities 

 and other institutions was too purely abstract in 

 character, and that too much time was spent on 

 an accumulated mass of details which obscured 

 the principles of the subject, to be suitable for 

 students whose primary aim was to learn how to 

 apply Mathematics, has been very generally ad- 

 mitted. The recognition of this has led to the 

 setting up of special courses of instruction and to 

 the production of numerous text books intended to 

 meet the needs of such students. Although un- 

 doubtedly much good work has been accomplished 

 in this direction there is distinct danger of an 

 excess in that revulsion against pure theory which 

 is exhibited in some of the current treatment of 

 what is known as practical Mathematics. It 

 cannot be too strongly insisted upon that a firm 

 grasp of principles, as distinct from the mere 

 processes of calculation, is essential, if Mathematics 



