Not many examples involving a technical knowledge of engi neering, physics, or chemistry have been inserted. Few young students understand examples of this kind without considerable explanation, and thus it seems better to refer the pupils to the more specialised text-books dealing with calculus (for instance, those of Perry, Young and Linebarger, and Mellor), which contain many examples of a technical character. For learners who can afford but a minimum of time for this study the essential articles of a short course are indicated after the table of contents.