236 OF THE PARTS OF [SECT. vn. 



Hence this rule : 



RULE v. The link divides the beam into two parts : divide the square of the 

 length of the central part by the length of the extreme part, or the length of the 

 parallel bar, and the quotient will be the length of the radius bar. 



7x7 49 

 This rule applied to the preceding example gives the radius bar = g- =-4 = 



9'80 feet, which differs only 0'08 from the other calculation. 



When convenience requires the rod to be attached to some other point between 

 D' and B, as in Fig. 1. it is still only necessary to make the radii inversely as 

 the segments D E, E B of D B, as in the preceding proportion, viz. 



DE:EB::AB:CD, 



since the track of G must be similar to that of E. 



And it may be observed, that as this ratio approaches to a ratio of equality, the 

 more accurate will be the motion, particularly if the beam and bars be fitted 

 parallel at half stroke ; so that the line of the piston rod may bisect the versed 

 sine of the half arc described by the end of the beam, or the horizontal distance 

 through which it vibrates. 



The calculation may be differently conducted by supposing A F to be the 

 radius of the beam, G' F' to be the extreme link or connecting rod, the other 

 link D B to remain unaltered, and supposing the piston to work from the point G'. 

 For on these suppositions the point G' will obviously describe a path exactly similar 

 to that of the point G ; hence we may proceed and calculate the length of the 

 radius bar C D, according to the common rules; and this method has the 

 advantage of taking into account the length of the stroke if required. 



With this arrangement, which is used for boat engines, the parallel bar 

 may be attached from the point D, and as is shown in Plate x. (B), Figs. 10 

 and 11, to which the above reasoning equally applies, the piston rod will then 

 be attached to a point G, in the connecting bar F H produced. In fact, the 

 parallel bar may evidently be fixed to the connecting bars at any distance from 

 the beam, without affecting the motion or the calculation of the parts : strength 

 and convenience are the principal considerations for its regulation. Suppose 

 Fig. 8, the parallel bar G D to be continued to m, so that its length G m may 

 be equal to the radius of the beam ; and the extremity m to be connected to 

 a bar A m equal and parallel to B D and F G. Then it is plain, that during the 

 motion the point m will oscillate over the small arc m n, centre A, of which the 

 horizontal chord m n is equal to the versed sine of the arc, described by the ex- 

 tremity of the beam. Let the combination be now divested of the beam A F, and 

 connecting bars B D, F G ; let the bar A m still work from the fixed centre A, 



