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 pretending to insist on their absolute right to the title; they may be called sciences of the second or third order, or by their usual names; they employ scientific methods, and treat by their means special regions of investigation; within these they have reached by degrees an independence which has made necessary their separation, from the more general sciences.

First comes the study of machines in general, looked at in connection with the work they have to do. This is known in Germany under a number of somewhat vague titles, as general or descriptive, special and theoretical "Maschinenlehre." In its general form it deals, descriptively, with the whole of existing machines,—it teaches , and thus affords us a glance at their manner of growth. It proceeds teleologically in the fullest sense of the word, seeking always to refer everything to the special object for which the machine was constructed. Its methods of classification are made as general as possible. At present a complete descriptive, or really general treatment of machinery in this way, is hardly possible on account of the enormous number of existing machines. To be really general only classes and types can be treated of. Quietly adapting itself to the every-day wants of the learner the study thus becomes specialised,—single classes are taken up and treated singly in detail. Along with the construction of each special machine its is also, for the most part, considered, that is, the nature of the sensible forces which come into action and the motions to which they give rise are examined, and deductions are drawn in regard to the most suitable way for turning these forces to account. This method of treatment is therefore based also on existing machines, but differs from the former in not only describing their arrangement and purpose, but in examining also how they can best be arranged in order to carry out the given purpose. In Germany at present it is for the most part rightly grasped and comprehended, the machine itself being taken as both the end and the beginning of the problem. The French, however, have not always freed themselves from the idea that the machine occurs merely as an illustration—an example—in Applied Mechanics; if this idea were right, however, it is clear that all other applications of Mechanics should be treated in the same way. If,—coming somewhat nearer to the heart of the matter,—the