
TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 713 
distant 7, from the crosshead B; also let & be its radius of gyration about B. 
Then the first component mentioned above, or F, is 
M dz 
Gi ae 
and acts through G parallel to the path of the piston. 
The second component, F,, is 
Mi, (0? 
ye 
and acts along the line of the rod towards B. The third component, F;, is 
M1, (ae 
a Ge) 
and acts at right angles to the rod through the centre of the percussion H, which 
2 
is at a distance = from B. 
0 
These three forces may be most conveniently compounded by shifting F; to G, 
and introducing a couple whose moment is F,-HG, or 
MW(e—2) 20 I @&0 
ig | ee ae 
where I is the moment of inertia of the rod about G. 
Forces equal and opposite to those components form the several parts of the 
whole resistance to acceleration, and when these are combined with the weight, 
the resultant is the whole load on the element. (See § 27, page 30, Trans. 
RS.E., vol. xxviii.) This composition is effected graphically, and a single force 
is obtained acting through G, which has then to be shifted parallel to itself to 
; ; : I #0 ; : “ 
such a distance as to give rise to the moment aaa This process gives a single 
force of determinate magnitude and position, as the load on the element in each 
position of the engine. 
The following tables show the component parts of the acceleration and force 
in the cases which have been actually examined. In Table I. the connecting- 
2 
rod is 41” long, and its mass is 34 lbs. ; / is 20’, and = is 34:08 inches. In 
0 
Table II. the connecting-rod is 28" long, and its mass is 28 lIbs.; d, is 14”, and 
2 
E is 25°32 inches. In both cases the crank radius is 8’, the mass of the piston 
and piston-rod 46 lbs., and the speed is one revolution per second, whence 
da 
ya 
