28 



HYDRAULICS. 



ing, has but one point in which its whole 

 moving force is concentrated, and which 

 point must be stopped, if it is required 

 to make the pendulum stop instantly, 

 in a completely dead manner, or with- 

 out communicating vibration or a strain 

 on any one part in particular. This 

 point is called its centre of oscillation. 

 So likewise in a stick or sword: if it is 

 desired to strike the most powerful 

 blow that can be given by such a wea- 

 pon, it must not be made with the point 

 nor near the hand, but at a certain dis- 

 tance between the two, where the point 

 of percussion exists ; and this, if the 

 stick is of equal size and weight through- 

 out, will be at two-thirds of its length 

 from the centre upon which it turns, or 

 the hand that wields it ; but if it tapers, 

 or becomes lighter at the end, the point 

 of percussion will be moved nearer to 

 the hand. The same reasoning applies 

 to water-wheels, and indeed to all other 

 wheels and bodies in circular motion ; 

 for if such a wheel had no rim or peri- 

 phery, its arms might be considered as so 

 many sticks whirling round one common 

 centre. But having such a rim, which 

 is of considerable weight in respect 

 to the arms, the point of percussion, or 

 of greatest effect, (which, in revolving 

 bodies, is called the centre of gyration^) 

 will be moved further from the centre 

 to near the external weight or rim ; and 

 in the circle described by these points 

 should the power be taken, in order to 

 equalize the strain upon every part of 

 the water-wheel as well as its shaft. 

 Placing cogs, therefore, on one of the 

 rings of a water- wheel, or using a driving 

 wheel of the same diameter as itself, is 

 an injudicious application, as thereby 

 the natural momentum of the wheel will 

 be considerably checked ; and, on the 

 contrary, if too small a driving wheel 

 is used upon the w T ater-wheel shaft, 

 the outside of the water-wheel will have 

 a constant tendency to run faster than 

 its central part, which will be very likely 

 to break its shaft. 



To ascertain the circle of gyration in 

 a water-wheel, its radius must be taken, 

 and the weight of its arms, rim, shroud- 

 ing, and float-boards, as well as the 

 weight of water acting upon it. Thus, 

 for example, in a wheel twenty-four feet 

 diameter, the arms of which weigh two 

 tons, the shrouding and rim four tons, 

 and the water in action two tons ; call 

 the weight of the rim R, which must be 

 multiplied by the square of the radius, 

 and the product be doubled, because the 



rim exists on both sides of the centre, 

 when the new product may be carried 

 out. Next, the weight of the arms called 

 A, must be multiplied by the square of 

 the radius, and be doubled and earned 

 out as before. Then the weight of the 

 water in action called W, must be mul- 

 tiplied in like manner and carried out, 

 without doubling, because the water 

 only acts on one side of the wheel. Then 

 double the weight of the rim and the 

 arms, and add the weight of the water to 

 them, which will give a sum by which 

 the sum of the former products carried 

 out are to be divided ; and the square 

 root of the quotient so obtained, will be 

 the radius of the circle of gyration, or 

 circle of greatest power ; and putting 

 down the foregoing operations in figures, 

 they will assume the following form : 

 R = 4 Tons x!2 2 = 576x2= 1152 

 A =2 Tons x 12*= 288x2= 576 

 W=2Tonsxl2 2 = 288 



2016 



2x4 + 2 + 2 = 



= 126, 



the square root of which, 11.225 feet, 

 will be the radius of the circle of gyra- 

 tion. The heavier the rim and load of 

 water are in respect to the arms, the 

 nearer will this circle coincide with the 

 size of the wheel; while, if they are 

 light, it will approach nearer the centre : 

 but power may always be safely derived 

 from a water-wheel, at about one-fourth 

 of the radius from the circumference. 



The power from a water-wheel ought 

 likewise to be taken as nearly as pos- 

 sible at the point that is opposite to 

 where the water is producing its greatest 

 action upon the wheel; otherwise a great 

 and, in some cases, very unequal strain 

 will be thrown upon different parts of 

 its shafts and bearings, and such a one 

 as, if it does not cause their fracture, 

 w r ill require unnecessary strength in 

 them, and cannot fail to produce waste 

 and unequal wear of the brasses or other 

 bearings upon which they are supported. 

 Thus, for example : let it be supposed 

 that the power is communicated from 

 an undershot- wheel, as at (Jig. 17.) by 

 a toothed-w T heel, or pinion, placed di- 

 rectly under the main shaft upon which 

 that wheel turns : then, since the power 

 of the water acts under the bottom of 

 the wheel a little lower than where the 

 power is taken from, it will be evident 

 that both the strains will be on the under 

 side of the shaft without any thing above 

 to balance them ; and as the power de- 

 rived is in most cases nearly equal to 



