
TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. GLE 
The necessary calculations and drawings for this paper have been made by 
my assistant Mr J. A. Ewine, to whom I am much indebted both for the 
accuracy with which the work has been done, and for the interest he has shown 
in adopting the novel method of investigation. 
The appendix contains data which will allow the reader to verify the results 
arrived at without going through all the calculations. 
This appendix has been drawn up by Mr Ewine. 
APPENDIX TO PART IL. 
On the Application of Graphic Methods to the Determination of the Efficacy of 
Machinery. 
To determine the forces required for the acceleration of the piston and con- 
necting-rod in each position of the engine, we must know the acceleration of 
the piston, and the angular velocity and angular acceleration of the connecting- 
rod. If AC be the crank, and CB the connecting-rod, and if AB be called 2, 
then “? is the acceleration of the piston ; and if the angle CBA be called 6, 
dt? 
do. 5 ae. @O. . 
q@ is the angular velocity of the connecting-rod, and gp is its angular acceler- 
ation. 

If the angle which the crank makes with AB be called a, = is the angular 
velocity of the crank. 
Then, calling the crank radius 7, and the length of the connecting-rod /, 
we have 
ret ee Nie cee a cities 
sim op = sn (-*) 
ag T COS @ da 
Ge. J? —?* sin 2a ” dt 
VOL. XXVIII. PART lII. 8 Zz 
