CHAP. V.] MOMENT OF ROTATION PARALLEL FORCES. 4:5 



pole distance o P. Thus h'h^ = f H A , H i = -| B b , and 

 H h = 7i h' + h' i = f M b + | /Mf+M*. 



The application of the method when the crank is not at right 

 angles to the shaft, as also when the crank is double, and gener- 

 ally in the most complicated cases, is equally simple and satis- 

 factory. Our space forbids any more extended notice of these 

 applications, and we must refer the reader to Der Constructeur, 

 by F. Reuleaux, Braunschweig, 1872, for further illustrations 

 and applications of the method to the solution of various practi- 

 cal mechanical problems. 



42. Continuous Loading Load Area. Thus far we have 

 considered only concentrated loads. But whatever may be the 

 law of load distribution, if this law is known, we can represent 

 it graphically by laying off ordinates at every point, equal by 

 scale to the load at that point. We thus obtain an area bounded 

 by a broken line, or for continuous loading, by a curve, the 

 ordinates to which give the load at any point. This load area 

 we can divide into portions so small that the entire area may 

 be considered as composed of the small trapezoids thus formed. 

 If, for instance, we divide the load area into a number of trape 

 zoids of equal width, as one foot one yard, etc., as the case may 

 be, then the load upon each foot or yard will be given by the 

 area of each of these trapezoids. If the trapezoids are suffi- 

 ciently numerous, we may consider each as a rectangle whose 

 base is one foot or one yard, etc., as the case may be, and whose 

 height is the mean or centre height. The weight therefore for 

 each trapezoid acts along its centre line. We thus obtain a 

 system of parallel forces, each force being proportional to the 

 area of its corresponding trapezoid, and equal by scale to the 

 mean height or some convenient aliquot part of this height. 

 We can then form the force polygon choose a pole ; draw 

 lines fr-om the pole to the forces ; and then parallels to these 

 lines, thus forming the string or equilibrium polygon ; and so 

 obtain the graphical representation of the moments at every 

 point. 



Since, however, the polygon in this case approximates to a 

 curve, that is, is composed of a great number of short lines, the 

 above method is subject to considerable inaccuracy, as errors 

 multiply in going along the polygon. 



This difficulty can, however, be easily overcome. 



Thus we may divide the load area into two portions only, and 



