4IO 



NA TURE 



[March 25, 1875 



Now, A (A 5), the difference of inclination which we 

 wish to find, as has been shown, 



. . , 77- A / 



and </) consists of /(5 - 6) + R, of which the former is 

 the ship's righting moment, and the second her moment 

 of resistance. 



Thus we can find R from the angular velocity, 6 from 

 the " curve of wave slopes," and & absolutely at the 

 beginning of the first interval and approximately at the 

 end of the subsequent time intervals. 



The difference between the exact ordinate length of the 

 two curves at /o and approximately estimated length at t^ 

 is applied by dividers to the line of abscissa, and hence 

 is obtained the value ol 6 - & and therefore the corre- 

 sponding ordinate gives f (6 — 6'). 



The sum of {6 - 6') and of R is taken as an ordinate 

 of the " force curve " at each point, and by connecting the 

 tops of these ordinates we have a close approximation to 

 the first segment of the force curve. The ordinate length 

 of </) being now obtained, some necessary correction being 

 made, if the line P^p be now drawn, the difference of its 

 tangential inclination from that of P^p represents with 

 close approximation (indeed, exactly, if the provisional esti- 

 mate has been judiciously made) the change of velocity 



which has ensued during Aj/, and a line parallel to Pf^p 

 will be the tangent to the curve of inclination at /,. Draw, 

 therefrom, b bas the tangent across the ordinate t■^ at such 

 a height that it shall intersect the previous tangent at the 

 middle part of AjA This height is the first approximate 

 value of the ordinate to the curve of inclinations at that 

 point. 



By carrying out this method the whole curve of in- 

 clinations is obtained. 



This description of Mr. Froude's paper is necessarily 

 very imperfect, through our being obliged to leave out the 

 small corrections, which without figures would be unin- 

 telligible. But it is sufficient to show his extremely neat 

 and simple way of drawing a curve which shall determine 

 a ship's absolute inclinations. 



The third paper was by Mr. B. Tower, on a method of 

 obtaining motive power from wave motion. He said that 

 this inquiry originated with Mr. Deverell, who came home 

 from the antipodes for the purpose of promulgating it. 

 Mr. DevereU's proposition was to suspend a heavy weight 

 on board a ship by means of springs, and to obtain mo- 

 tive power by the oscillation of this weight through a 

 distance not more than the height of the waves. It how- 

 ever appeared to Mr. Tower that since the centrifugal 

 force of wave motion in a vertical direction is alternately 



^i^ 



m 



m 



added to and subtracted from, the force of gravity thereby 

 causing a virtual variation of the intensity of that force, 

 the question might be broadly stated as follows : — 



Supposing the force of gravity to vary in intensity at 

 regixlar intervals, that is, to become alternately greater 

 and less than its normal amount, what is the best means 

 to obtain the maximum amount of energy from a given 

 weight oscillating under the influence of these variations ? 

 For example, supposing the force of gravity to be for three 

 seconds one-fifth greater, and for the next three seconds 

 one-fifth less than its natural intensity, and suppose that 

 v/e have a weight of five tons suspended by a spring, with 

 an infinitely open scale, so that the spring will continue 

 to exert a uniform upward force of five tons, no matter 

 how far the weight moves up and down, it is clear that 

 during the three seconds' interval, during which gravity is 

 one-fifth more than its normal intensity, the five-ton 

 weight will virtually weigh six tons, and will thus exceed 

 the upward force of the spring by a downward force of 

 one ton ; in the same way, when the force of gravity is 

 one-fifth less, the weight will only weigh four tons, and 

 the sprmg will then exert an unbalanced upward force of 



one ton. Now, as energy or power is defined as force 

 moving through distance, it is clear that the quantity of 

 energy or power to be obtained by this system will depend 

 on the distance through which this weight is caused to 

 move during each successive variation of gravity. Thus, 

 supposing that during the plus interval it moves down- 

 wards through one foot, and during the minus interval it 

 moves upwards through one foot, it is clear that during 

 each of these intervals it will exert a force of one ton 

 moved through one foot — that is, one foot-ton ; but if, 

 instead of one foot, it moves through ten feet, it will exert 

 ten times the power — that is, ten foot-tons ; or if it moved 

 through loo feet, it would exert loo foot-tons during each 

 interval of three seconds. 



The first experiments Mr. Tower made with a model 

 apparatus constructed on these principles showed him 

 that the best arrangement would be to put a weight 

 on the end of a revolving arm, whereby the centri- 

 fugal force of the wave motion might be utilised as well 

 as the rising and falling motion. 



The diagram shows the position of the vessel and of its 

 revolving arm at all parts of a wave ; the arrows show 



