404 



Prof. J. S. Macdonald. 



as is shown by a comparison of the data 



(1) 22, 32, 42, 44, 49, 70, 76 

 with the values deduced from the formula 



(2) 22, 32, 41, 42, 48, 70, 73. 



The agreement is certainly least where the experimental data are necessarily 

 fallible. 



In reference to the influence of " rate " upon the cost of movement, and in 

 exact explanation of the nature of the formulae, it may be said at once that 

 the point of greatest importance lies in the fact that the cost per stride 

 is least at a certain intermediate rate of movement, and therefore also the 

 cost of progression is least at the same intermediate rate. In both of these 

 formulae that fact is placed in unusual prominence by the direct insertion of 

 this economical rate in a definite position of importance in the formulae. 

 The cost per stride in Douglas' case, that is to say, the value of HV _1 , 

 is least when V has the value 1-475, and in Briscoe's case the value 1*783. 

 Speaking of the particular value of V as in each case P, then the two 

 formulae have the resemblance shown below : — 



(b) Douglas H = 52-37 (PV)°- 380V , 



(c) Briscoe Q = 16"45 (PV) ' 260 v . 



'Nov is this the end of the resemblance, as may be seen from the considera- 

 tions stated below. 



Digressing a moment, but as briefly as possible, it may be stated as an 

 axiom that, with regard to every formula of the general type, Jl = x (?/V) 2V , 

 the value of V at which EV _1 is minimal is determined by the relation 



»V!(log e Vi + log e y+l) = 1. 



In this particular case P = Vi = y, and therefore 



2P(l0g e P + l0g e P+l) = 1, 



therefore z = l/[P(21o&P+l>]. (d) 



That is to say that, in this particular rigid formula, z is also a function of P, 

 and may be represented by P' ; and this is exactly true in the two formulae 

 •given : in the one case 0*380 has this relation to 1'475, and in the other 

 - 260 to l - 783. The present resemblance between the two formulae is 

 therefore seen in the fact they may be both written as follows : — 



<7>) Douglas H = 52-37 (PV) P ' V , 



(c) Briscoe Q = 1645 (PV) P ' V . 



If it could be shown, then, that 52 - 37 in the one case, or, as it may be 

 termed, T in formula (5), is also a function of 1*475, and the same 



