Mans Mechanical Efficiency in Work Performance. 405 



function as is 16 - 45, the T in formula (c), of 1783, then H would be a 

 function of P, Q also a function of P, and the functions would be identical 

 in character. This actually seems to be the case, as is shown incidentally in 

 the following method of dealing with the two formulas, which is of use later 

 in assessing values of P in additional individual cases (see (I), p. 407). 



(b) Douglas H = T(PY) P ' V = 52-37 (1-475 V)°' 380V , 

 therefore log H = 1719 + 0-380 V log V + 0-064 V, 



= 1719 (1 + 0-221 Y log V) + V log 116, 



therefore H = i-i6 v T 1+0 ' 221vl °g v . 



It will be seen that this new form of statement is permissible, inasmuch as 

 P p/ is approximately equal to 1*16, and because 



P' = 0-221 x 1719 = 0-221 log T. (e) 



(c) Briscoe Q = T(PV) P v = 16 45 (1-783)°' 260V , 

 therefore log Q = 1-216 + 0-260 Y log Y + 0-065 Y, 



= 1-216 (1 + 0-213 V log Y)+Y log P16. 



= (l + 0-213YlogY)logT + Ylogl-16. 



therefore Q = i-i6 v T 1+0-213V,o s v . 



This statement, similar to that given in the case of Douglas, is again also 

 permissible because P p ' is approximately equal to 1-16, and because 



P' = 0-213x1-216 = 0-213 log T. (/) 



Now when (e) is compared with (/), with an appreciation of the fact that 

 the quantities of heat dealt with in the two cases are in the ratio of 210/49 

 at the same common value for V, (Y = 2 - 667), also of the ease with which 

 it would be possible to adjust the small difference thus revealed without 

 modifying the formulas probably in any other way than to make them still 

 more applicable to the data than they are at present, it will be granted 

 that (e) and (/) reveal T as the same identical function of P. T may then 

 be written as P". It follows that the formulae are completely identical in 

 form, and may either be written as follows : — 



H or Q = P" (PY) P ' V = (P, V). 



The only difference, then, between' the cost of walking, on the one hand, 

 and the cost of cycling on the other, is to be sought in the different 

 magnitude of P in the two cases, and in either case the cost of movement at 

 every other rate, including that at the " economical rate," where this cost is 

 least, may apparently be anticipated after an examination of the cost at any 

 one definitely maintained rate. 



