NATURE 



\_yune lo, 1880 



ingly crystals of quartz, phenakite, tinstone, and hyacinth 

 (zircon), were placed in a tube and experimented on. 



" The only crystals that gave definite results were tin- 

 tone and hyacinth. A small crystal of the former mineral 

 glowed with a fine yellow light, which was extinguished 

 almost entirely when the long diagonal of the Nicol was 

 perpendicular to the axis of the crystal. 



" Here, therefore, the plane of polarisation of the 

 emitted light was parallel to the axis of the crystal, and 

 here it is again the quicker, though in this case (of an 

 optically positive crystal) it is the ordinary ray Mhich 

 corresponds to the light evoked by the electric stream. 



" So far, then, the experiments accord with the quicker 

 vibrations being called into play, and therefore in a 

 negative crystal the extraordinary and in a positive 

 crystal the ordinary is the ray evoked. 



" A crystal of hyacinth, however, introduced a new 

 phenomenon. In this optically positive crystal the 

 ordinary ray was of a pale pink hue, the extraordinary 

 of a very beautiful lavender-blue colour. In another 

 crystal, like the former from ExpaiUy, the ordinary ray 

 was of a pale blue, the extraordinaiy of a deep violet. A 

 large crystal from Ceylon gave the ordinary ray of a 

 yellow colour, the extraordinary ray of a deep violet hue. 



" Several other substances were experimented on, 

 including some that are remarkable for optical proper- 

 ties, among which were tourmaline, andalusite, enstatite, 

 minerals of the augite class, apatite, topaz, chrysoberyl, 

 peridot, garnets of various kinds, and parisite. So far, 

 however, these minerals have given no result, and it will 

 be seen that the crystals which have thus far given out 

 light in any remarkable degree are, besides diamond, 

 uniaxal crystals (an anomaly not likely to be sustained by 

 further experiment) ; and the only conclusion arrived at 

 is, that the rays whose direction of vibration corresponds 

 to the direction of maximum optical elasticity in the 

 crystal are always originated where any light is given out. 

 As yet, however, the induction on which so remarkable a 

 principle is suggested cannot be considered sufficiently 

 extended to justify that principle being accepted as other 

 than probable." William Crookes 



ON THE LAW OF FATIGUE IN THE WORK 

 DONE BY MEN OR ANIMALS 



T^HE Rev. Dr. Haughton, of Trinity College, Dublin, 

 -'- has recently brought to a conclusion a series of 

 papers on Animal Mechanics published in \\it Proceedings 

 of the Royal Society. The ninth of these papers was 

 appointed the Croonian Lecture for the present year, and 

 the tenth paper closes the series. 



The most important subject involved in these papers is 

 the experimental determination of the law that regulates 

 fatigue in men and animals, when work is done, so as to 

 bring on fatigue. 



Many writers, such as Bouguer, Euler, and others, have 

 laid down mathematical formula;', connecting the force 

 overcome with the velocity of the movement ; but these 

 theoretical speculations have never received the assent of 

 practical engineers. 



X'enturoli points out a method of observations and 

 experiments which would serve to determine the form of 

 the function which expresses the force in terms of the 

 velocity, after which a few carefully planned experiments 

 would determine the constant coefficients ; and he adds 

 that " such a discovery would be of the greatest usefulness 

 to the science of mechanics, upon which it depends, how 

 to employ, to the greatest possible advantage, the force 

 of animal agents." 



Dr. Haughton believes that he has found the proper 

 form of this function, by means of experiments, and sums 

 It up m what he calls the Law of Fatigue, which he thus 

 expresses : — 



The product of the total work done by the rate of luork 

 is constant, at the time when fatigue stops the work. 



If W denote the total work done, the law of fatigue 

 gives us — • 



dW 

 dt 



U/2 



W'. 



const. 



= const. 



(I) 



The experiments made by Dr. Haughton from I875 to 

 iSSo consisted chiefly in lifting or holding various weights 

 by means of the arms ; the law of fatigue giving, in each 

 case, an appropriate equation, with which the results of 

 the experiments were compared. When the experiments 

 consisted in raising weights on the outstretched arms, at 

 fixed rates, the law of fatigue gave the following expres- 

 sion — 



{w + a)hl^A (2) 



where w, n, are the weight held in the hand, and the 

 number of times it is lifted, ^ is a constant to be deter- 

 mined by experiment, and a another constant depending 

 on the weight of the limb and its appendages. 



The equation (2) represents a cubical hyperbola. 



The useful work done is represented by the equation — 



-'' = (^ (3) 



This denotes a cuspidal cubic, and the useful work is a 

 maximum, when w = a, or the weight used is equal to 

 the constant depending on the weight of the limb and its 

 appendages. 



\\'hen the weights were lowered as well as raised at 

 fixed rates, and no rest at all permitted, the law of fatigue 

 became — 



w(i + 8V=) 



A 



(4) 



where ;/, /, are the number and time of lift, A is a constant 

 depending on experiment, and /3 is a constant involving 

 the time of lift (t) at which the iiiaxiniiim work is done. 



Equation (4) denotes a cuspidal cubic. 



When the weights are held on the palms of the out- 

 stretched hands, until the experiment is stopped by- 

 fatigue, the law becomes — 



{w^a)H = A (5) 



where / is the whole time of holding out. 



This equation denotes a cubical hyperbola. 



The La7u of Fa/igue seems, in itself, probable enough,, 

 but of course its real value depends on its agreement with 

 the results of experiment. 



If W denote the total work done and R the rate of 

 work, the law becomes, simply — 



W X R = const (6) 



If different limbs, or animals w-ere used, each working in 

 its own way, and under its own conditions, the Law of 

 Fatigue would become — 



WR= U\ R^ + W„ R, + JF^ R^ + &c . (7) 

 and the problem for the engineer would be, so to arrange 

 the work and rate of work of each agent employed, as 

 to make the useful work a maximum, the work both 

 useful and not useful, in all its parts, remaining subject 

 to the conditions imposed by equation (7). 



In using equation (5) in his concluding paper, detail- 

 ing the results of experiments made on Dr. Alexander 

 Macalister, Dr. Haughton treats a as an unknown quantity, 

 and finds from all the observations its most probable 

 value to be — 



a= 5-68 lbs. 

 This result was compared with that of direct measure- 

 ments made on Dr. Macalister himself, and indirect 

 measurements made on the dead subject, from all of 

 which Dr. Haughton concluded the value of a to be — 



