^Iarch 29, 191 7] 



NATURE 



83 



organs of a plant are not in mere haphazard 

 positions, but that they occupy definite positions 

 in relation to one another; and that the whole plant 

 is a " living-, breathing, feeding, energy-producing 

 organism." The student is thus led on by easy 

 steps to the clear conception of modification of 

 organs, and of homologies ; and is thus furnished 

 with a clue by which to solve riddles presented 

 by an apple, a cocoanut, the corm of a crocus, 

 seeds, buds, flowers, etc. Practical work enters 

 largely into the scheme ; and by means of ques- 

 tions and exercises the attention of the pupil is 

 frequently directed to the wild plant life of the 

 countryside in a way that is entirely admirable. 

 ^\'e cordially commend the book to all teachers of 

 elementary botany. O. H. L. 



Poverty and its Vicious Circles. By Dr. Jamieson 

 B. Hurry. Pp. xiv4-i8o. (London: J. and 

 A. Churchill, 191 7.) Price 55. net. 



Dr.' Hurry has, in a previous volume, discussed 

 the vicious circles of disease. He now enters the 

 domains of sociology and economics and deals 

 with poverty in a similar manner. "Poverty" he 

 defines as the condition of a person who lacks the 

 necessaries for subsistence and efficiency, and a 

 " vicious circle " is the process by which a pri- 

 mary disorder provokes a reaction which 

 aggravates such disorder. In the ordinary course 

 of economic law the reaction provoked by a social 

 disorder tends to arrest such, disorder, but when 

 a vicious circle becomes established the usual 

 --equence is modified, and the reactions which 

 -should be beneficent are the reverse and intensify 

 the disorder. As an instance of one of Dr. 

 Hurry's vicious circles we may quote that asso- 

 ciated with malnutrition : Poverty leads to mal- 

 nutrition ; this begets debility, which causes 

 diminished earning capacity, and this accentuates 

 the poverty. 



The vicious circles of p>overty are discussed 

 under twenty-two headings, and a chapter is 

 devoted to "artificial circles," e.g. when injudi- 

 cious relief aggravates the poverty it seeks to 

 remove. The " effects of vicious circles " and the 

 ''breakinj^f of vicious circles" form the subject- 

 matter of succeeding chapters. 



The book is largely made up of quotations 

 from official reports and from standard authors, 

 and as an outline of the complex subject of 

 poverty should be of considerable value to the 

 student of sociology and economics. It is 

 illustrated with five plates. 



Determitmcion de la Latitud par Alturas Abso- 

 lutas, Circunmeridianas , Meridianas e Igudlcs 

 de dos Estrellas. Por Carlos Puente, Astro- 

 nomo. (Madrid : Bailly-Bailliere, 1917.) 

 After a short introduction, four chapters of this 

 short manual describe the methods of finding the 

 latitude from altitudes observed outside the meri- 

 dian, from circummeridian altitudes, from meri- 

 dian altitudes (this is the longest chapter), and 

 from two different stars observed at the same 

 altitude when the time is known. Each chapter 



NO. 2474, VOL. 99] 



is divided into two parts, the first giving the 

 necessary formulae, the second and longer part 

 showing how the method is carried out in prac- 

 tice, describing the various instruments (sextant, 

 theodolite, transit circle) and explaining how the 

 instrumental errors are found. Lastly, some 

 auxiliary tables are given. The little book should 

 prove useful to astronomical beginners and 

 travellers. 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible jot 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond 'X'ith 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



Muscular Inefficiency and Possible Speeds of Walking. 



I\ walking over a level surface, were there no mus- 

 cular loss or imperfect elasticity in the ground, the 

 only work to be done would be that required to start 

 the body and limbs at the walking speed, which work 

 might be recovered when stopping. Thus any energy- 

 expended in walking on the level is due either to work 

 taken up by the ground, or lost by muscular ineffi- 

 ciency. (Air resistance may be neglected at walking 

 speeds.) 



That there is, for each individual, a certain speed 

 at which walking involves a minimum effort is well 

 known ; and it seems probable — in fact, almost certain 

 — that this depends on the natural period of the leg 

 about the hip joint. By frequent trials I have found 

 that in my own case this period is about 1-35 sec. so 

 that, since there are two steps to each complete period, 

 the natural number of steps per minute would be 

 about 88 ; assuming further that each p>ace is equal to 

 one yard (which is very nearly correct in my own 

 case), the natural speed of walking is 5280 yards, or 

 three miles per hour. 



In walkinjj at this pace the accelerations of the 

 masses are effected by gravity. 



A pendulum giving 44 beats per minute is 1-46 ft. 

 long, and this corresponds verj' fairly with the equiva- 

 lent length of a leg which measures 3 ft. from hip 

 joint to the sole of the foot, taking into account the 

 distribution of mass. 



At this speed the only work required is that lost in 

 the muscles or expended on the fjround. At any other 

 speeds the muscles are called on to accelerate or retard 

 the various parts, and such work is apparently not 

 j recoverable. I do not know of any experiments on 

 I this ]X)int, but it would be of interest to examine 

 whether, for instance, the muscular effort required to 

 move a body, with a given velocity against a force, 

 is the same as would have to be expended in prevent- 

 injij acceleration when the force is in the direction of 

 motion ; or, in other words, whether for equal motions 

 the muscular effort required to cause acceleration is 

 the same as that required to prevent it. 



Assuming for the moment that it is, it is possible 

 to calculate the greatest speed at which walkinef is 

 possible, the speed, namely, at which the mere accelera- 

 tion of the masses absorbs the whole work of which 

 the muscles are capable. 



If. as the simplest supposition, the motion of the 

 leg be represented by the harmonic motion of a mass 

 m. with period T and amplitude a, then — 



The energ>- is t1^^"'. When the period is the 



