14 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



of a rate bearing one of a few limited simple relations to the 

 " pendular rate." 



It seems to be the case, then, that interesting rates of 

 walking are all referable to the " pendnlar rate " of the limb, 

 and I have no doubt that the " economical rate " has the same 

 reference. There are definite reasons for saying so, but they 

 are, unfortunately, complicated. Perhaps it is sufficient to 

 say that dividing the formula for the expenses of Douglas 

 " when walking on the grass at Oxford," by the formulae 

 which give these variations in step as found in the Webers" 

 data, the result is a general expression for the cost of walking 

 per step taken which has a minimal value, and exhibits, there- 

 fore, a point of maximum economy, which coincides with the 

 step taken at the " pendular rate." As I have said, this is 

 probably not true of every case, but it is probably a variant 

 of a more general statement also dependent upon the pendular 

 rate, which is more generally true. 



It now remains for me to apologise for the inconclusive 

 nature of my statement, and for the arid character of the series 

 of data* by which it has been reinforced. However, there is 

 one conclusion that perhaps may be drawn, namely, that 

 sufficient has been said to show that the expense of movement 

 is probably always capable of exact, and by no means distant, 

 statement, and that the method of statement is being more or 

 less energetically attempted. I may be pardoned for reiterating 

 my opinion, that Sherrington's revelation of the replacement 

 of one whole movement by another and the consequent view 

 that " rest " is, in essence, a movement, form probably the 

 key to the right system of accounts. Up to the present this 

 accountancy, and a real approach to " economy," have been 

 greatly embarrassed by undue attention to " rest." 



♦These data are published in the Proc. Boy. Soc, B, Vol. LXXXIX, 

 pp. 394-410. 



