408 



Prof. J. S. Macdonald. 



to ~W 2 1/4: as shown, it is extremely likely that in the fully extended dimension 

 of the body utilised in walking, P„, will be found rather related to that 

 function of the weight which is of so great comparative value in connection 

 with the linear dimensions of the body, namely, the cube root of the weight. 

 Considering the mass factor, e 6-i87p-6-i34 } w ith this possibility in mind, it would 

 seem as if under such circumstances the whole factor would become m 2 . This 

 view may be tested immediately, since it should be possible to calculate 

 Douglas' weight on the assumption that in his case fx, = (W 2 /^/) 2 . 



Thus p = ee-wp-e-m = t/1-17 = 44-76 (Douglas), 



therefore 44 - 76 = (W 2 /g) 2 and therefore W 2 = 65 - 6 kgrm. 



But since his weight is given in 1910* as 65 kgrm., the assumption 

 would seem to be reasonably justified. It is probable then that, whereas 

 P c = 4-8.8/ W 2 ' 252 , V w = 5-77/W 2 °" 32B , so that in Douglas' case the observed 

 value of T5 in the case of walking movement would probably correspond 

 with a value of VI in reference to cycling movement. 



The Velocity Factor (PV) p,y . 



In the case of " Douglas walking," it is possible to compare with some 

 interest the square root of the velocity factor on the one hand with the 

 actual horizontal velocity or rate of progression on the other, and perhaps 

 this is best done at first in reference to the most important " economical 

 rate " P, when the cost of stride is least. At the rate P per second, since 

 V = P, therefore (PV) P ' V = P 2PP ' = (P475) 1 ' 121 = 1-546 = (1-243)*. Again, 

 since the length of a stride is 0-837 metre, the horizontal velocity at the 

 rate P is 0-837 P, and is therefore 1-235 metres per second. For brevity, using 

 the term / in place of (PV)* P ' V , it is seen that there is no great difference 

 at this rate between v and /. 



In general, the relation between v and / is such that the line v inter- 

 sects the curve / at two points, where V = T5 and where V = T5 3 ; that 

 is to say that, at rates not very different from P and P 3 respectively, 

 v is equal to /. At intermediate values of V the horizontal velocity is 

 slightly the greater quantity, the maximal difference of 0-213 metre per 

 second being found at the rate P5 2 , that is to say, at a rate not very different 

 from P 2 . Beyond these points on either side of P and P 3 the curve rapidly 

 falls away from the line, so that / becomes much greater than v. 



In short, although v is not a tangent to /, yet v + 0*213 is such a 

 tangent at the point where V = T5 2 . There does not seem, under these 



* ' Journ. Physiol./ vol. 40, p. 235. 



