236 
OF THE PARTS OF 
[sect. VII. 
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- =—~ = 
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,