2 ;6 APPLIED SCIENCE 



the higher pairs, and we may even conceive a class of joint 

 which requires only points of the elements to be in contact, as 

 where a sphere is pressed against a plane. In connection with 

 geometrical diagrams, the word 'joint' will be applied to points 

 round which intersecting lines may be said to turn relatively to 

 one another. Geometrical joints of this kind will generally be 

 designated by a single capital letter. 



4. 'Definition of a Complete Machine. The object of ma- 

 chinery, considered dynamically, is the application of energy, 

 or, in more popular language, power, to the performance of use- 

 ful work, and the name complete machine may be given to any 

 combination of elements so joined that the energy developed in 

 one element, or between two elements, is, by the relative motion 

 of the elements, enabled to do useful work in overcoming a re- 

 sistance exerted either by one element or between two elements. 

 A complete machine is self-contained, and the internal] action 

 between its parts can change neither its momentum nor its 

 angular momentum. Most actual machines have one portion 

 fixed relatively to the earth, which then becomes part of one 

 element of the machine. 



5. Lines of Bearing Pressure. The elements of a complete 

 machine are so held together at the joints by the forces which 

 are in play when the machine is in action, that each element of 

 the machine occupies a determinate position relatively to all the 

 others, and presses against its neighbours at each joint with a 

 force determinate in magnitude, direction, and position. A given 

 position of the parts does not necessarily imply constant forces 

 at the joints, but it does imply a determinate relation between 

 the forces at the joints. A line indicating the direction and 

 position of the equal and opposite resultant forces at a joint will 

 be called a line of bearing pressure. In consequence of friction, 

 a line of bearing pressure where it cuts the joint, must, when 

 the machine is in motion, make an angle with the common 

 normal to the surfaces equal to the angle of repose, or angle of 

 which the tangent is equal to the coefficient of friction for 

 the surfaces at the joint, and must be so inclined that the 

 force exerted by the one element on the other has a tangential 

 component directly opposed to the sliding of the second ele- 

 ment relatively to the first. This condition will hereafter bo 



