Feb. 4, 1875] 



NATURE 



277 



results cannot be obtained. The mean of ten determinations 

 gave, for my right arm, a = l"SO kgr. The mean of twenty 

 determinations likewise gave a. ~ 1-50 kgr., with a probable 

 error of O'OI kgr. Calculating from (6) the values of /Ffor the 

 different values of i;', and co-ordinating these two quantities, and 

 it is plain that the function is hyperbolic. It was found that W 

 did not vary inversely as (w + o), or as any power of this quantity.* 

 The equation 



(ui + ajAii- 



(7). 



was then assumed, where c and v are'constants to be determined. 

 From this we readily have 



log. (?;' + l"5) + log. n = k — Z'log. w, 

 which is of the form 



y = k - v.x, 

 where y and .v can he calculated from the observations. Co- 

 ordinating these values oi y and .v, and the curve is found to be 

 linear, and we find v, as the change in y for each unit of change 

 in .r, to be 2'007. Hence Eq. (7) becomes 



(w ^a)h7i = ~ (S). 



Calculating now the values of a and c by the method of least 

 squares, we find c = 4261 and a = I '52. The difference be- 

 tween o (calc.) and a (obs. ) is only i -3 per cent, of o(obs. ) Solving 

 (8) for n, and substituting the proper values, and we have n 

 (calc), as given in Table II. d n is the difference in per cent, of 

 n (obs.) Column e is the probable error of 11 (obs.), also in per 

 cent. The comparison between n (calc. ) and n (obs.) is shown 

 graphically in Fig. 3, the observations being represented by the 

 small circles. 



Soon after arriving at Eq. (S), Prof. Haughton's book came to 

 hand, containing his reduction resulting in Eq. (5). As already 

 shown, this equation does not represent my later and more accu- 

 rate observations. In order to test the matter still further, ex- 

 perimentally, the following experiments were made : — 



1. I lifted my right arm from a vertical to a horizontal (// = 

 071 cm.), the experiments being conducted exactly as in the case 

 of those given in Table II. The arm was lifted 2,oco times 

 without feeling any appreciable exhaustion. According to (5), 

 when w — o, complete exhaustion should occur when « = 1,000. 

 According to (8) it should occur when n = cc. 



2. A weight, 'ill = o'5 kgi., was lifted in the same manner, 

 and the arm allowed to drop with the weight during the inter- 

 val of rest, as in case of my earlier experiments. It was thus 

 lifted 1,500 limes with very httle exhaustion. According to (5) 

 complete exhaustion should occur when n — 400. According 

 to (8) K should be 12,000. This would make the total time of 

 exhaustion 8 hours and 20 minutes. The total mechanical work 

 would be 16,800 kgr. metres. The daily labour of a working 

 man is about 100,000 kgr. metres. From estimates based upon 

 this fact, and from the slight fatigue felt in the second experi- 

 ment, I am convinced ths.t my arm, at its mean strength, could 

 work for 8J hours at the above rate, if the experiment were con- 

 ducted as described above, care being taken to eliminate the 

 fatigue caused by standing on the feet, &c. It would, how- 

 ever, be a highly dangerous experiment. 



It will be remembered that each value 01 n (obs.) in Table II. 

 is a n.eaii of ten indej endent determinations. It occurred to me 

 to co-ordinate tlie originally observed values of n with the daily 

 determination of strength c. The result was most instructive. 

 Each value of w gave a curve which is really parabolic, but 

 which — since one of these curves {-o = 5 'o) was taken as a unit 

 in which to represent the others — appeared here as a straight line, 

 or very nearly so, with exception of those which had been before 

 rejected in calculating the constants. The reason for the great 

 value of n for w = 2'5 (Table II.) is thus apparent. 



This at once opened up a new field — the relation of strength 

 to work. In the investigations here the strength is de- 

 termined by a spring balance, so arranged that the arm is 

 held horizontally and the strain exerted upwards. Calling s the 

 reading of the dynanometer, and the strength is (w + a).t Co- 

 ordinating, for the different weights used in Table II., the 

 strength with the work done before exhaustion, and we have for 

 each value of ic a curve which is apparently parabolic, intersect- 



• The equation (:.' + ") ^' « = t^^ . ^)->-6-> ^^'i^^ represent the observations, 

 but it is a highly improbable relation 



1 (i + u) IS rcilly ihe highest tension attainable by the muscle in exerting 

 a uniformly accelerated force, with a uniform velocity tfirough the space 

 moved over by the hook of the dynanometer. 



ing the axis of abscissa (strength) at a point just inside the 

 point where s + a. — w -^ a* As to diminishes, the curves in- 

 crease in steepness with great rapidity. Eq. (8) shows the relation 

 between the points on each of these curves, which correspond to 

 nry mean strength. 



This opens up a way of estimating the statical work ol a 

 muscle, a problem which has been in view from the outset. We 

 will take as the unit of statical work, the kilogram-second, or the 

 work done by a muscle in sustaining for one second a strain of 

 one kilo, exerted at right angles to its line of contraction. If 

 now the same weights be used in exhausting the horizontally 

 outstretched arm, we shall have by co-ordinating the work (in 

 kgr.-sec.) with the strength, a system of curves as in the case of 

 dynamical work. Accurate values of the constants for these 

 curves have not yet been obtained, and we therefore will not 

 discuss them further here. For each weight, co-ordinate the 

 dynamical with the statical work, and it is readily seen that the 

 relation between them can be made out, so that — given the total 

 energy of a muscle in kgr. -sec. with any weight, and we can calcu- 

 late thedynamicalwork in kgr-metreswhich thissame muscle could 

 do with this same weight. I intend to determine as accurately as 

 possible the values of the constants in the cases heretofore dis- 

 cussed in these papers. I shall also thus investigate the effect of 

 variation of the angle of elevation of the arm on the dynamical 

 and statical w^ork, including the case of statical work where the 

 angle of elevation is zero : also the dynamical work, where the 

 strain on the muscles is continuous, and (i) where the strain on 

 the muscles (a weight) is constant, and the velocity of motion 

 uniformly varied ; (2) where the velocity is constant, and the 

 weight uniformly varied ; and (3) where both weight and velocity 

 are constant. Making in this latter case, v = 0, and we have the 

 case of statical work. The apparatus necessary for this inves- 

 tigation has been already devised. Feank E. NlPHEii 



SCIENTIFIC SERIALS 



Ztitschrift der Oesterreichischen C-esdhchafi fiir Meleorologie, 

 Dec. 15. — To this number Dr. Prestel contributes an article on 

 lines of cirrus as a means of foretelling storms. Storm signals 

 he presumes to be inadequate for warning sailors of an approach- 

 ing gale. He has compared during last year the indications of 

 cinous streaks with the weather shown by the charts to be pre- 

 valent on each day when his observations were made. From all 

 the instances in which the streaks were well developed, he 

 comes to the conclusion that the currents of the upper air do 

 not follow the law of Buys Ballot ; that is, that in the region of 

 cirrus the air has neither a cyclonic nor anticyclonic movement, 

 but streams from the point of highest pressure in the area of 

 high pressure to the point of lowest pressure in the area of low 

 pressure. — Herr Koj pen, having remarked the tendency of 

 cyclones to follow closely upon one another, gives a table for 

 Northern Russia of the intervals which most commonly separate 

 them. Of 107 cyclones, occupying 393 days in the territorj', 

 33 per cent, came in less than twenty-four hours after their pre- 

 decessors ; 32 per cent, after an interval of one day ; 19 per cent, 

 aher two or three days ; 19 per cent, alter four, five, or six days ; 

 and iS per cent, alter seven, ei^ht, nine, or ten days. — The 

 observations of MM. Fautrat and .Sartiaux, by which it appeared 

 that more rain fell within than withe ut the forest of Halatte, are 

 objected toon account of the disturbing influence o( wind, which 

 blows less stoiigly at the one position, six metres above tree-tops, 

 than at the other, fifteen metres above the plain. 



Keale Isiituio Lombardo. Rendiconti : vol. vii. fasc. ix., xi. — 

 The first paper is On variations in the temperature of Milan, by 

 Giovanni Celoria. Meteorological observations were commenced 

 at the Observatory of Brera in 1 763, and have been carried on 

 without intermission, and show regular and irregular variations. 

 The maximum temperature follows the culmination of the sun, 

 and shows an oscillation in time of seventy minutes, being at 

 2h. 4m. in January and at 3h. 14m. in July. The minimum 

 temperature in summer is eight minutes before the rising of the 

 sun, and in winter forty-nine minutes before sunrise. This varia- 

 tion is less at Milan than elsewhere. The author follows Dove 

 in dividing the year into seventy-three periods of five days each. 

 There are two periods of medium temperature in the year, April 

 15 and 16, and October 18 ; 179 days are colder and 186 hotter 



• My left arm is about five-sixths the 'strengih of the right. Each 

 varies greatly from day to day. Several ether persons, the length of whose 

 bones approximated my own, have been experimented upon. The co-ond- 

 nated values of work and strength are continuous with my own. 



