THE ECONOMY OF MOVEMENT. 11 



valuable. One may conclude that in reference to this particular 

 movement of cycling the search for ; " economy " must be 

 made with an eye upon the work that is to be accomplished 

 by the movement, up to a certain amount of work lightness is 

 economical, at an intermediate range (work of ^ Horse Power 

 approximately) lightness, or weight, is of no consequence, 

 beyond that weight is economical. 



Xow, having in this way ascertained the factor by which 

 work had to be multiplied, that is to say, knowing the 

 " efficiency " available, it was possible to remove the cost 

 of work from other statements of the expense of cycling, and 

 that even at any other rate of movement, so long as the amount 

 of the work done upon the " brake " had been measured. One 

 of my subjects had, in the interests of this operation, cycled 

 at rates of many different values along the whole available 

 scale of rate such as he could maintain uniformly for the dura- 

 tion of an experiment. Eliniinating from his total expenses 

 the cost of work performance I was able to present the cost of 

 movement at every such rate, and found the effect of rate to 

 be complicated, more complex, for example, than mere propor- 

 tionate increase with increase of rate, but continuous, so that 

 it could be expressed in a single mathematical formula, modified 

 in each case only by insertion of the particular rate then 

 observed. Now the nature of this variation with rate is such 

 as at once to show that movement is most economically per- 

 formed in this case, not at the slowest rate of movement, but 

 at a certain intermediate rate. In " cycling " movement, at 

 all events, there is a certain " economical rate " of movement, 

 which may readily be ascertained by experiment, and which, 

 in my opinion,, is capable of general statement applicable to 

 even' kind of subject. Further, the expense of all other rates 

 of movement may be assessed from the expense of this inter- 

 mediate " economical rate." Xow, if this is true, there is the 

 view that the cost of " cycling," and all similar motion and 

 work, mav be laid down in a hard and fast fashion, and that 



