78 LECTURES TO SCIENCE TEACHERS. 



I presume you are acquainted to a certain extent with the 

 ordinary method of studying "pure mechanism;" the method 

 originated by Monge (1806), developed in Willis' well-known 

 Principles of Mechanism (1841) and made popular to a 

 great extent by Prof. Goodeve's capital little text-book 

 and others. Each mechanism is studied for and by itself, 

 in general by the aid of simple algebraic or trigonometric 

 methods, and is spoken of in reference to a certain " con- 

 version" of motion which occurs in it. Thus we have the 

 conversion of circular into reciprocating motion, the con- 

 version of reciprocating into circular, &c., and simple formulae 

 express certain relations between the motions of two or more 

 moving points. In this way we know something important 

 about a great number of mechanisms, and arrive at many 

 results which are both useful and interesting. Some things 

 are still left wanting, however ; and these things may be 

 summed up in this way : 



(1) We notice at once that we have taken the mechanism 

 as a whole. We do not analyse it in any way whatever, 

 and therefore, 



(2) We have scarcely any knowledge of its relations with 

 other mechanisms, or (what is quite as important) of the 

 various forms which one and the same mechanism may take. 

 We shall see presently how extraordinarily various these forms 

 are. We have never a general case with special cases 

 derived from it ; each case is treated by itself as a special 

 one. Then 



(3) 'The mechanism is studied in general from a point of 

 view which gives us only the conditions of the motion 'of 

 two points in it, or two portions of it, and is then left. 

 The kinematic conditions of the mechanism as a whole 

 remain absolutely untouched. 



In such a mechanism as that of an ordinary steam-engine, 

 for instance, we study the relative motions of the guide- 

 block and the crank, or I ought perhaps to say of the axes 

 of the crosshead and of the crank-pin. We thus know the 

 motions of two points in the rod which connects those axes, 

 the "connecting-rod," but we leave the motions of all its 

 other points untouched. It may, of course, be said that 

 these others are of much less practical importance. This is 

 true to some extent, although their practical importance is 

 greater than might be supposed at first. But in any case 



