TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 5 
In certain cases the surfaces in contact may approximately be represented 
by lines, as in what Professor REuLEAvux calls 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 podtnts 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 machinery, considered 
dynamically, is the application of energy, or, in more popular language, power 
to the performance of useful 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 resistance 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 jomt, 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 element relatively to the first. This condition will 
hereafter be frequently referred to, and will, for brevity, be spoken of as the 
condition that the bearing pressure shall make the stated angle with the joint. 
§ 6. Driving Element and Resisting Element—Driving Link and Resisting 
Link.—The source of power in a machine is often contained in a single element, 
which is usually so combined with the others as to exert equal and opposite 
forces in two directions, and only in two directions. The steam ina cylinder 
of a steam engine affords one example of this kind of element, which will be 
called a driving element. If the directions of the equal and opposite forces 
exerted by the driving element lie in the same straight line, the power tends 
VOL. XXVIII. PART I. B 
