vi PRACTICAL MATHEMATICS 



lying principles and methods, and this familiarity can only be 

 obtained by steady practice. It is unfair to a student to give 

 him as a standard form 



n+l 



and then expect him to use it as a formula to integrate any func- 

 tion which might resemble it, or by some means reduce to it. 

 This might be working along the line of least resistance, but it 

 is not educational : neither is it to the best interests of the student. 

 to whom sound work in Differentiation and Integration is an 

 absolute necessity. 



The work in Section III consists of the Mathematics involved 

 in those problems more or less familiar to the technical student, 

 and before this work should be attempted it is essential that the 

 work in the two previous sections should be fully grasped. 



I have devoted a chapter to the study of Interpolation and the 

 best way of dealing with tabular values, and I have endeavoured 

 to put this part of the subject in a reasonable form. The method 

 of Harmonic Analysis given in Chapter XXII is the one I have 

 found from experience to be best adapted to class work. 



The examples are numerous, and have been chosen in accor- 

 dance with the text. The answers are given, and these have been 

 carefully checked ; but it is possible, as may be expected when 

 dealing with such a number, that errors might occur, and I should 

 be grateful to any teacher or student drawing my attention to 

 them if such is the case. 



H. LESLIE MANN. 

 June 1915. 



