84 



NATURE 



[March 29, 1917 



natural period (T,) this energy (except for the loss in 

 extending- the muscles and in the ground) is conserved 

 by the action of gravity. 



and the power required is 



If P— Ca is the maximum power available (where 

 Ca represents loss from muscular extension), then — 



or, putting Ti=/To, 



Crt_ i -p- 



Fk;. I.— AA, motion of body (assumed uniform); BB, trace on ground of 

 r-ght femur (produced) ; B'B', trace on gr.und of left femur (produced) ; 

 FF, position of right foot ; FT', position of left foot. 



For any other period (Tj) an amount of energy 

 equal to 



''(tt'-t^') 



has to be expended four times in each pace, twice for 

 acceleration and twice for retardation. 



As a numerical example, assume that P — Co is 

 i/io h.p., or 55 ft. -lb. per sec, also that (as given 

 above) T„ = i-35 sec. 



The weight of each leg is about 30 lb. (so that m—\ 

 nearly). The length of the leg being 3 ft., and that of 

 the pendulum of 1-35 sec. period 148 ft., then, since 

 each half pace=i-5 ft., 0/1-5= 1-48/3, <^'' = 074 ^^^ 

 nearly. 



Thus T,,^ 7 ^'=2'46 -^ — = 3 nearly, 



" ^Tv'hnd- 79x0-55 ^ ■" 



whence p = o-6 nearly. 



Thus the speed of walking at which i/io h.p. is 

 consumed in acceleration would" be about 5 miles per 

 hour, or rather more. 



This is on the assumption that all the conditions 

 can be represented by one simple harmonic term. 



The actual motions ' in walking, however, are repre- 

 sented in Figs. I and 2, and some work must be done 

 in bending the knee joint. The details of this motion 

 vary considerably in different individuals, but in all 

 cases the work required would reduce the maximum 

 walking speed to something a little under 5 miles per 

 hour, which, as a fact, is about the limit for hard 

 walking. 



Although the above estimate rests on nothing except 

 common knowledge and casual observation, the result 

 gives a high probability to the assumption that mus- 

 cular inefficiency, i.e. the loss of work in accelerating 

 and retarding their own masses, sets the limit to the 

 speed at which they can be worked. 



A. Mallock. 



Fig. 2. — AA, positions of hip joints ; KK, positions of right knee; K'K', positions of left knee 

 FF, positions of right foot ; K'F', positions of left foot. 



Thus for both legs, in each complete period, the 

 amount of energy to be supplied by the muscles is 



STT^ma 



\4^ T^'j' 



Gravitation and Thermodynamics. 



Dr. Todd (Nature, March i) suggests that when 



one gravitative mass approaches another it acquires 



heat. This might occur when, as is usually (but not 



always) the case, the body moves up the gradient of 



potential ; for then the energy of 



field displaced by the body would 



increase. 



There is one development of the 

 above speculation which is not ex- 

 plicitly mentioned by "J. L. " 

 (Nature, March 15), though it may 

 have been inferred. Suppose two 

 cases : (a) A metal disc is in a 

 vertical plane at the earth's sur- 

 face. If it be started spinning on 

 a horizontal axis through its centre 

 the descendmg half warms and ex- 

 pands, the ascendini"- half cools and 

 contracts, there will arise a turn- 

 ing moment, and the disc will 

 now continue to spin of itself pro- 

 vided the friction 's small enough. 

 (b) The extreme top and the extreme 

 bottom of the disc will be cold and hot points respec- 

 tively, so that if metal brushes be applied there, we 



1 In the diagram, for the sake of simplicity, the motion of the body is 

 taken as being uniform. This is not strictly correct, but the difference from 

 uniformity is small. 



NO. 2474, VOL. 99] 



