August 28, 1890] 



NATURE 



423 



The diameter of a cricket-ball is nearly 3 inches, and 

 its weight 5"5 oz. The value of a for its motion is there- 

 fore 327 feet. Partly on this account, but more on account 

 of its lower speed, a cricket-ball has its path much less 

 affected by resistance than is that of a golf-ball. If we take 

 its maximum initial speed as 130, the initial resistance is 

 only about i"6 times its weight ; while for a golf-ball it 

 rises to about 28-fold its weight. Their momenta are 

 nearly equal, being about 45 and 50 respectively. But 

 their kinetic energy is very different in the two cases, 

 being 90, and 390, foot-pounds respectively. This, again, 

 is in full accord with every-day experience. In the simple 

 vernacular of the cricketer, a well-struck golf-ball would be 

 characterized, at least for the first fifty yards or so of 

 its course, as a "hot" one indeed ! 



The article may fitly close with a few remarks on 

 another very prevalent fallacy : — viz. the belief that a 

 golfer continues to guide his ball with the club long after 

 it has left the tee. How any player who has ever 

 "jerked" a ball (and who has not ?) could maintain such 

 an opinion is an inscrutable mystery. But it is a physical 

 fact, established by actual measurement, that when a 

 block of wood weighing over 5 pounds is let fall on 

 a golf-ball (lying on a stone floor) from a height of 

 \ feet, the whole duration of the impact is less than 

 I 250 of a second. When it falls from a greater height 

 the duration of impact is less. But if the elastic force 

 which made the block rebound had been employed 

 to move the golf-ball itself, whose weight is only 

 [ID of a pound, (or 1/50 of that of the block) the 

 operation would have occupied only 1/50 of the time ; 

 say the 1/12,500 of a second. In the case before us we 

 are dealing with much greater speeds, and therefore with 

 still smaller intervals of time. It is with \<tx\X.i!o\&instants 

 like these that we are concerned when driving a golf-ball. 

 The ball has, in fact, left the club behind, before it 

 has been moved through more than a fraction of its 

 diameter. 



Another way in which this important point can be made 

 plain to anyone is as follows : — When two bodies impinge, 

 the whole time of the mutual compression is greater than 

 that which would be required to pass over the space of 

 linear compression with the relative speed, but less than 

 twice as great. And the time of recoil is greater than 

 that of approach in the ratio i : e : — where e is the " co- 

 efficient of restitution " which, with hard wood and gutta- 

 percha, is about 06 when the relative speed is very great. 

 Hence the whole time of impact between the club and 

 the ball is that in which the club, moving at 300 feet per 

 second, would pass through about four times the linear 

 space by which the side of the ball is flattened. 



P. G. Tait. 



THE WORKING EFFICfENCV OF SECONDARY 

 CELLS. 



UNDER this title a paper was contributed, at the 

 recent meeting of the Institution of Electrical 

 ICngineers at Edinburgh, by Prof. Ayrton and Messrs. 

 Lamb, Smith, and Woods, which contains some con- 

 siderable additions to our knowledge of the subject of 

 secondary cells. The cells on which the tests were made 

 were of the 1888 E.P.S. type, and were charged and dis- 

 charged at the maximum working currents, these being 

 kept constant in value by hand and automatic regulation. 

 In the most important series of tests the limits of volts 

 employed was 24 volts for charge and i "8 volt for dis- 

 charge : it was found that a lower limit than this led 

 to detrimental actions in the cells, with loss of active 

 material. 



The advantages of a constant current are that it is a 

 nearer approximation to practical working conditions, 

 and that the calculations are much simplified : in fact, the 

 ampere efficiency is got by simply multiplying together 

 the ratio of the charge and discharge currents and the 

 ratio of the times occupied in charging and discharging. 

 The true (or watt) efficiency was found by plotting time 

 readings of the P.D., and taking the ratio of the areas of 

 the curves thus drawn : this, multiplied by the ampere- 

 efiiciency, is the required true efficiency. 



The first important point brought out in the paper is 

 the importance of the resuscitating power possessed by 

 accumulators. In an early set of tests, made on well- 

 charged cells, the authors found a quantity efficiency 

 of over 100 per cent, with correspondingly abnormal 

 watt efficiency, and this, although the tests occupied 

 five days, from which they conclude that, " if accumu- 

 lators be well charged up before being tested, five days' 

 continuous alternate charging and discharging with the 

 maximum currents allowed by the manufacturers fails to 

 give the normal working efficiency." 



Since these results were so unsatisfactory, some method 

 of avoiding drawing on a previous store had to be adopted. 

 Some experimenters secured this condition by running 

 down a cell, and then leaving it short-circuited for some 

 time. In the present series of experiments the required 

 condition was fulfilled as follows : the cells were con- 

 tinuously charged and discharged with regularity until 

 the successive charges occupied exactly the same time, 

 and successive discharges did also. When the cells 

 arrive at such a " steady state," it can evidently be taken 

 that no drawing on a previous store is taking place. It 

 was, then, under these conditions that the experiments 

 were made. 



As such a long series of experiments would entail much 

 labour in keeping the current constant, an automatic 

 regulator was devised to effect this, together with further 

 automatic devices for breaking circuit when the P.D. 

 reached any predetermined value, and for telling the time 

 when such break occurred. The authors state that these 

 apparatuses worked to within h per cent, of the supposed 

 limits. Throughout the investigation D'Arsonval instru- 

 ments were adopted, and by suitably suspending the 

 movable coil, the calibration curve was absolutely a 

 straight line. In these further tests the same instrument 

 was used for measuring volts and amperes, the requisite 

 alteration of circuit being made by a rocking commu- 

 tator. The volts were read frequently, and curves of 

 P.D. plotted. With this apparatus and measuring in- 

 struments, the curves given below for steady state of 



NO. 



1087, VOL. 42] 



charge and discharge between limits of 2-4 and 16 volts 

 per cell were obtained. 



From these curves efficiencies of 98*3 per cent, for 

 current, and 865 per cent, for energy, were obtained. 



