This will give the first position _-o -o_, of the centre line of the link. As the rocker-pin must always be in the centre of the link, it is obvious that the point at which the centre-line of the link intersects the arc in which the rocker-pin oscillates must be the position of the centre of the rocker-pin. With this determined the position of the valve can easily be located. [52] This is usually the radius of the link but in some cases either a longer or shorter radius is taken to draw the link. In the following explanation it is assumed that the link is drawn with this radius, or from the centre of the axle. Of course if a greater or lesser radius is used, due allowance must be made therefor. [Illustration: _Fig. 125._ Scale, ³⁄₄ in. = 1 foot.] In order to represent the link at any other point of the stroke, say after the piston has moved four inches, the position of the crank must first be laid down. To do this, allowance must be made for the irregularity due to the angularity of the connecting-rod, which was explained in answer to Question 54. From the centre of the axle, a circle, _C D_, whose diameter is equal to the stroke of the piston, is first drawn, which will represent the path of the crank-pin. A horizontal centre line, _E F_, should also be drawn through the centre of the axle and the centre of the cylinder. The intersection _o_ of this line with the path of the crank-pin will be the position of the latter at the beginning of the stroke. If from this point a distance, _o o_, be laid off on the centre line equal to the length of the connecting-rod,[53] it will give the position of the wrist-pin at the beginning of the stroke, so that from this its successive positions for each inch of the stroke can be laid off. From its position after the piston has made say four inches of the stroke as a centre, and the length of the connecting-rod as a radius, if the path of the crank-pin be intersected at -4, the point of intersection will represent the position of the crank-pin at four inches of the stroke. The distance from _o_ to -4 is equal to 44 degrees of the whole circle. The eccentrics, being attached to the axle, of course move the same number of degrees that the crank does, and therefore, in order to determine their position when the crank has moved any distance, it is only necessary to move them as many degrees as the crank has. This can be done very easily by extending the radii of the eccentrics, when they are in the first position, until they intersect the path of the crank-pin at _c′_ and _d′_. By stepping off from the latter points of intersection a distance _c′ c‴_ and _d′ d‴_, equal to _o_ -4, which the crank has moved, and then drawing other radii from the two points _c‴_, _d‴_, their intersection, _c″ d″_, with the path of the eccentrics will represent the position of the centres of the eccentrics when the crank is at -4. Having determined the position of the eccentrics,