98 



NATURE 



{Dec. 2, 1875 



direction as that below ; and that the diminution of temperature 

 with increasing height was greater in clear than in cloudy 

 weather. This last result is in agreement with that of Herr 

 Hann, derived from observations taken at Praya West and 

 Victoria Peak. 



SOCIETIES AND ACADEMIES 



London 



Royal Society, Nov. 19. — " On some Elementary Prin- 

 ciples in Animal Mechanics. No. VII. The Law of Fatigue." 

 By the Rev. Samuel Haughton, M.D. (Dubl.), D.C.L. (Oxon), 

 r.R.S., Fellow of Trinity College, Dublin. 



The approximate law of muscular action, which I have called 

 the law of fatigue, is thus expressed : — " When the same muscle 

 (or groups of muscles) is kept in constant acti*n until fatigue sets 

 in, the total work done multiplying by the rate of work done is 

 constant." 



The following experiments, in illustration of this law, were 

 performed in Trinity College during the spring of the present 

 year. 



I instructed a number of medical students, chosen at random, 

 to raise dumbbells of varying weight, one in each hand, in the 

 transverse plane, with hands supinated, raising and lowering the 

 weights in equal times regulated by the beat of a pendulum. 

 This process was continued until the distress of the fatigue pro- 

 duced became intolerable, and the number of times each weight 

 was lilted was noted. The students were required to count 

 " one-two," in time to the beat ol the pendulum, so as to pre- 

 vent them from counting the total number of lifts of the weight. 

 Prof. Macalister assisted me in these experiments ; and one of 

 us counted the number of lifts, while the other compelled the 

 experimenters to observe the conditions of the experiment, which 

 were : — 



1. To keep time with the pendulum. 



2. To raise the weight in the transverse plane. 



3. To supinate the hands. 



4. To abstain from all bending of the knees or spinal column. 

 For each experiment I chose twenty students at random, using 



altogether about fifty different students ; and no individual was 

 experimented upon again, until an interval of forty-eight hours 

 had elapsed. The object of this arrangement was to avoid the 

 effects of " training." In my first Table I give the mean result 

 of twenty different students ; and in my second Table I have 

 selected one student, set aside for the purpose, and experimented 

 upon, once a week, so as to prevent the influence of "training." 

 Let W denote the total work done, and T the time of doing 

 it ; then, by the law of fatigue, 



=- = constant (i) 



If w be the weight held in the hand, and a be half the weight 

 of the arm, and n the number of times the weights are lifted ; 

 since the time of raising and lowering the arms is constant, n is 

 proportional to T, and the law of fatigue gives the formula 



(w -h o)^« = A (2) 



where A is an unknown constant. In the following Table I give 

 the values ot w and the mean value of n for twenty distinct 

 persons. The time of lift is in all cases 07ie second. 



Table I. — Mean of Twenty Experiments. 



The column containing the calculated values of « was obtained 

 from equation (2) by using the values 

 a — 3-50 lbs. 

 A = 4699. 

 These values were obtained by finding the value of a, which 

 renders A most nearly a constant, or 



8A 



= mmimum. 



This Table gives 7 lbs. for the mean weight of the arm of all 

 experimented on, a result which accoids with the known facts. 



In Table II. I give the results obtained from a single student, 

 as already described, each value of « being a mean of several 

 experiments, closely concurrent. 



Table II. — Air. Samuel Warren. 



The calculated values of n were found from equation (2), using 

 the values 



a =: 3-9 lbs. 

 A = 5737, 

 which were obtained from the principle of least variation of 

 A, or 



5A . . 



— = mmimum. 

 A 



In the accompanying diagrams I. and II., I have plotted the 

 cubical hyperbola represented by equation (2) ; and also the 

 several observations which lie sufficiently near the curve to justify 

 me in considering the law of fatigue to be a first approximation 

 to one of the fundamental laws of muscular action. I have else- 

 where * shown that the law of fatigue corresponds with other 

 experiments based on different data. 



If we consider the useful work only, we have from equa- 

 tion (2), 



useful work = wn = — ,. • • • • (3) 



[w + o)* 



This equation represents a cuspidal cubic, whose ordinate has 

 a maximum value, when w = a = half the weight of the arm. 



The foregoing observations are in accordance with this deduc- 

 tion, as may be seen from Table III. 



Table III.— Useful Work. 



It is to be observed, that in the foregoing experiments the 

 muscles in action were not allowed to rest during the whole time 

 of work. 



Linnean Society, Nov. 18. — Dr. G. J. Allman, F.R.S., 

 president, in the chair. —The following paper was read: — On 

 the organisation and systematic position of the Ornithosauria, 

 Part i., by Prof. H. G. Seeley, F.L.S. The different results ob- 

 tained by investigators who have written upon Pterodactyles, led 

 the author to propose a method of research in Comparative Ana- 

 tomy by which the true nature of these animals could be deter- 

 mined. It consists chiefly in an attempt to distinguish between 

 the characters which make animals members of a class of 

 Vertebrata, and the characters which make those animals mem- 

 bers of vertebrate ordinal groups. The class characters were 

 regarded as furnished by the soft vital organs, while the ordinal 

 characters are derived from the skeleton. This was illustrated 

 by an argument tending to show that since the form of brain, 



* " PrindpUs of Aniautl Mechanics " (London, 1873). 



