308 On the Energy expended in Propelling a Bicycle. 
-we do not believe them to be worth publishing as we had not adequate appliances for 
measuring fractions of a second of time, which would have been necessary to give 
the observations a satisfactory amount of accuracy. ‘The method, however, is good, 
and as we have found that other practical difficulties can be overcome, it would 
probably be worth repeating* these observations with the assistance a chronograph. 
The first apparatus which we made for furnishing indicator diagrams was attached 
at the top of the right hand lever of the bicycle. The link which trammels the 
top of the lever was removed and a spiral spring substituted for it, which was 
compressed when the right foot acted on the pedal. To the lever a vertical flat 
board was fastened to carry the paper on which the diagram was to be produced ; 
and the diagram was drawn by a pencil connected with the inner end of the spring. 
Thus the pencil was relatively at rest and the diagram paper was moved past it in 
two directions—in the are of a circle corresponding to the up-and-down motion of 
the lever, and radially corresponding to the force applied. ‘The apparatus is 
represented in Pl. 89, Fig. 2, and the diagram it produced in Figure 3. This may 
be called the crude indicator diagram from which the true indicator diagram 
represented in Figure 4, Pl. 40 has to be derived. 
This was accomplished by hanging known weights on the pedal to represent the 
pressure of the foot, and moving the wheel round so as to get the lines corresponding 
to known forces exerted on the pedal. The successive dotted lines of Pl. 39, Fig. 3, 
were in this way drawn, when one, two, three, four, five, stones were successively 
hung on the treadle. In the reduced indicator diagram (PI. 40, Fig. 4) these become 
parallel equidistant lines, and are the dotted lines of that figure. Horizontal 
distances in Figure 4 would be strictly proportional to the forces applied by the 
foot if it had acted vertically, but if the foot acts obliquely the force as registered 
in this way may be somewhat greater than the actual force exerted. Hence the 
energy as indicated in this way might slightly exceed the true value, though, as 
the result proves, it has done so either not at all or but little. It was chiefly to 
detect and avoid this possible error that the second series of indicator diagrams 
described below was undertaken, contrived so that the indicated energy must fall 
somewhat short of the true value. A comparison of the two series shows that any 
such excess or defect is small in either series. 
To return to Figure 4, Plate 40. Vertical distances on Figure 4 have been made 
proportional to the nett vertical distances through which the foot descends. This 
was accomplished by the help of Figure 5 which represents the oval curve through 
* We have since made these observations, see the Addendum to this paper, page 314. 
+ By the net descent of the foot is to be understood the distance through which the foot would descend 
if the spring were not compressed. The additional distance through which the foot descends, owing to 
- the compression of the spring, represents additional energy exerted by the rider on the down stroke, 
which, however, the spring restores to the foot on the up stroke, when by its resilience it assists the 
lifting of the leg. It accordingly is not work done on the bicycle and should not be counted in. 
