712 



NA TURE 



[June 3, 1922 



I believe that (2) is correct, for no energy is restored 

 when a contracted muscle is again extended either 

 b}'- the action of outside forces or by the contraction 

 of other muscles. 



(3) also is true, but in what way the leakage varies 

 with muscular stress is not known. It probably lies 

 between " as the force " and " as the square root of 

 the force," and in this note I shall assume the latter 

 hypothesis. 



If P, Pa, Pl are respectively the total power 

 developed and the powers lost by acceleration and 

 leakage, then, / and v being the force and velocity, 

 P =/v, Pa = A//^ and Pi. = B/^. 



The useful power is Pe = P-Pa-Pl, and the 

 Pa+Pi 



efl&ciency E = i 



Differentiating E with re- 



spect to / it will be found that the minimum of 

 Pa + Pl occurs when /= {^^ *. 



The constants A and B may be determined by the 

 conditions that, when the whole power is expended 

 in accelerating the limbs A=/o*P, where /,. is the 

 force which can be maintained at the greatest 

 practicable velocity, and B = P//Li', where /l is the 

 greatest average force which the muscles can apply. 



In the case of the bicycle I will assume (i) that 

 the gearing is 70 with a 7-inch crank ; {2) that the 

 power available is 40 ft. lb. per sec. (about 1/14 

 H.P.) ; (3) that the greatest speed attainable with 

 that power and in the absence of air resistance is 

 40 ft. per sec. (about 28 M.P.H.) ; and (4) that the 

 greatest average force which can be continuously 

 exerted on the crank is 30 lbs., from which it may 

 be deduced that A =5000 and B =24. 



These values were used in computing the curves 

 in Fig. I. 



The minimum of Pa + Pl is 12-5 ft. lbs. per sec, 

 thus leaving 27-5 ft. lbs. /sec. for useful work, which, 

 with the assumed length of crank and gearing, would 



n-. lbs. 120 Scale 

 sea 



Scale 1 2 ft 

 '''~ per sec. 



Fig. I. 



I is the hyperbola /"?./ = ? ; f'va lbs., v in ft. per sec. 

 II Pl, the power lost in acceleration of the limbs. 



III Pl, the power lost by leakage from the strained muscle. 



IV Pi+Pi, which has a minimum value of 12-5 ft. Ibs./sec. 



suffice to lift a load of 200 lbs. (weight of rider and 

 machine) up a gradient rather less than one in thirty. 

 Hence even with this gentle gradient it would pay to 

 ascend the hill obliquely, i.e. in a series of tacks. 



The Pa + Pl curve, however, is very fiat near the 

 minimum, so that a considerable increase of gradient 

 would not do much to diminish the efficiency. 



Whether the assumed maxima of speed and force 

 are anywhere near the truth I do not know, and it 

 would be interesting to have laboratory experiments 

 on these quantities. 



A. Mallock. 



9 Baring Crescent, Exeter, May 10. 



"G. B. M." 



I FIRST saw the late G. B. Mathews on June 4, 1884, 

 at the Queen's Hotel, Chester, when the staff of the 

 newly founded University College of North Wales was 

 appointed. He was chosen for the Chair of Mathe- 

 matics, and almost from that time we were linked 

 together in friendship as well as in our offices as 

 teachers of intimately related subjects in the same 

 institution. I well remember his youthful and strik- 

 ing yet attractive appearance. He was the senior 

 wrangler of the previous year, and came full of eager 

 enthusiasm for the teaching of mathematics and for 

 original mathematical work, and for ten years laboured 

 hard in the hope of founding something like a school 

 of mathematical study in North Wales. But alas ! 

 these hopes were dashed. Perhaps he was a little 

 impatient, and I certainly did my best to counsel him 

 to wait, and to find out the effect of the new Welsh 

 university on the studies of the place, but without 

 effect. The best of the Welsh students were at that 

 time attracted by the Neo-Hegelian philosophy, and 

 some of them, as seems to be the way of such students, 

 seemed not a little proud that their mental tendencies 

 were not mathematical. To this curious type of 

 intellectual pride Mathews referred eloquently in the 

 posthumous paper published in Nature of April 22. 



In that paper he lamented the revival of the falla- 

 cious arguments for the supremacy of the Latin-Greek 

 classics as an educational instrument ; but he in no 

 way undervalued classical culture, only he thought 

 that to an Englishman, the inheritor of a copious and 

 flexible language, and of a literature unequalled in 

 the past, a training in Latin and Greek was far from 

 indispensable, and might have its disadvantages. Cer- 

 tainly many classical people, tutors of colleges and 

 old-fashioned classical schoolmasters, often write Eng- 

 lish which can scarcely be regarded as a model to be 

 imitated, as any one can convince himself by reading 

 the prefaces and introductions to editions of classical 

 texts. He always thought Greek more important for 

 students of science than Latin. And truly the tech- 

 nical language of zoology and physiology, and in a 

 less degree that of physics, is much more exclusively 

 of Greek than of Latin derivation. 



Mathews had a knowledge of Latin and Greek as 

 minute and accurate as that generally possessed by 

 professional classical scholars. He wrote pure and 

 elegant Latin. I remember his amusing himself by 

 turning into Latin prose an original philosophical dis- 

 sertation which happened to come into his hands and 

 arrested his attention. I remember also some Latin 

 verses which he published anonymously and which 

 were much praised by a very eminent scholar. 



He wrote also charming English essays in the style 

 of Charles Lamb, of whom he was a great admirer. 

 These I fear are lost, but one of them, " On a cock-loft," 

 was a perfect gem, a charming piece of the most 

 natural and simple prose, somewhat after the manner 

 exemplified more recently by Kenneth Grahame in 

 his " Golden Days." He gave much time to Arabic 

 in later years, and it is to be hoped that his transla- 

 tions of Arabic poetry will ultimately be published. 

 I have seen some of them, which certainly seemed very 

 remarkable. His most valuable work was done in 

 mathematics, and this has been well appraised by a 

 mathematician who knew him well in later years. It 

 is, I think, a pity that the variety and strength of his 

 interests distracted him from mathematical work, and 

 prevented him, until it was too late to take it up again, 

 from finishing his work on the Theory of Numbers. 

 But in his Nature articles his extraordinary wealth of 

 knowledge and his keen and yet genial criticism must 

 have helped innumerable students. A. Gray. 



The University, Glasgow. 



NO. 2744, VOL. 109] 



