406 



Prof. J. S. Macdonald. 



It is now useful to define T in terms of P, and a possible procedure is as 

 -follows : — 



Let T = 1-17/i, therefore (Douglas) m = 44*76, (Briscoe) m = 14-06. 



Let /j, = y"P z and therefore log /j, = log y + z log P, 



therefore (Douglas) 1*651 = logy + 0*1692, (1) 



(Briscoe) 1*148 = logy + 0*251 z. (2) 



Prom these equations 



z = -6*134, and log y = 2*687, 

 therefore also y — 486*5 = e 6 " 187 , 



therefore fi = ^-m/pe-m 



and T = 117a* = 1*17 e 6 * 187 /P 6 - ]34 . (g) 



Introducing this expression for T in the general equation 

 H* = ri7(e 6 - 187 /P 6 - 134 )(PV) p ' 7 , 



itherefore 0*426 H = |(e 6 " 187 /P 6-134 )(PV) p,vr . (h) 



The suggestion implied in the form (h) is obvious, and may be briefly 

 expressed by saying that the expression 



0*426 H = E' (|- mu 2 ) = } (mE') v?, (j) 



would represent a rational formula, in which E' was the reciprocal of the 

 efficiency in movement, also that there is some promise shown in (A) of a 

 final statement in this rational form. 



Under the impression that this promise is sufficient to permit immediate 

 ■examination of the formula from such a point of view, I shall venture to 

 speak of part of the formula as the possible " (?«E') " factor. 



The " (mE')" Factor. 

 An attempt to ascertain the relation between e 6 ' 187 yp 6-134 and the mass, 

 •and at the same time to express 1/P in terms of W, may be made very 

 simply by utilising the relation found in the case of the four cycling 

 •subjects, Q = 0-1094 W 1 ' 438 . It will be remembered that for both 

 Douglas and Briscoe, and therefore inferentially the cycling subjects, 

 Q = i-i6 v T 1+ ' 213VlogV . It is true there was a slight difference in Douglas' 

 ■case, but it was even then of minimal value, and there can be little 

 hesitation in applying the exact form of Briscoe's statement to the subjects 

 •examined under similar conditions. In their case, since V = 2, the latter 

 •expression becomes Q — T346 T 1 ' 128 , 



01094 W 1 " 438 = Q = 1*346 T 1 * 128 , 

 * Or Q. 



