HYDRODYNAMICS. 



559 



the area of the floatboards ought to be much greater 

 than the section of the current, and before one float- 

 board leaves the current, the other ought to have fairly 

 entered it. This construction may be employed with 

 advantage in deep rivers that have but a small velocity. 



Bftanfs Undershot H'keel. 



This wheel, invented by Mr Besant of Brompton, is 

 constructed in the form of a hollow drum, to resist the 

 admission of water ; but its principal peculiarity con- 

 sist! in the arrangement of the floatboards in pairs on 

 the periphery ot the wheel. Each floatboard is set 

 obliquely to the plane of the wheel's motion, and the 

 corresponding floatboard is inclined at the same angle, 

 but in an opposite direction, the plane of the wheel bi- 

 secting the angle formed by the two floatboards. The 

 acute angle which the one floatboard forms with its cor- 

 responding one i* open at the vertex ; but one of the 

 floatboards extends beyond the other. By this construc- 

 tion, the resistance from the tail water is diminished ; 

 but so far as we know, the machine has never come 

 into use. See Ferguson's Lectures, vol. ii. 



Horizontal Water WheeU. 



Horizontal water wheel* differ in no respect from 

 common undershot wheel* except in the circumstance 

 ;' their extremities being placed vertically. The mill 

 coarse i* constructed nearly in the same manner for 

 both. The principal object of thi* form of the water 

 wheel U to save machinery, by placing the mill-stooe 

 directly on the vertical shaft of the wheel The water 

 wheel mutt therefore more with a very great velocity, 

 so a* to enable the mill-stones to perform their work. 

 The water is turned into a horizontal dim-lion before 

 it strikes the floatboards, which may be either vertical 

 or inclined to the radius, a* in undershot wheel*. 



Horizontal wheels are often constructed so that the 

 floatboard* have a very great inclination to the radius. 

 In thi* case, the water i* not turned into a horizontal 

 direction, but is made to rtrike the floatboard* perpen- 

 dicularly, as in Fig. 9. where AB i* the wheel, MN the 

 mill-course discharging it* contents perpendicularly 

 upon the floatboard C, which ought to have a surface 

 more than twice the area of the section of the stream. 

 In thi* construction, the maximum effect will be pro- 

 duced when the velocity of th*> floatboards i* not les* 



t!un i , where A i* the height of the (all, and 

 2 sin. a 



a the angle which the direction of the fall makes with a 

 vertical line. But since this quantity increase* a* the 

 sine of a decrease*, we may diminish the angle a, and 

 thus increase the velocity of the floatboards, to suit the 

 nature of the work to be performed, without lessening 

 the maximum effect, which cannot be done in vertical 

 wheel* where a determinate velocity i* necessary to 

 produce the greatest possible effect. See Ferguson's 

 Lecture i, vol. ii. Appendix. 



In the southern department* of France, the float- 

 bond* arc made of a curvilineal form, so a* to present 

 a concave surface to the stream. This construction is 

 MI. shewn in Fig*. 10, 11, where AB i* the wheel, CD the 

 vertical shaft, and m, n the concave fluatboards. The 

 Chevalier Borda remarks, that in theory a double effect 

 i* produced when the floatboard* have Um form ; but 

 that the advantage is not so great in practice, from the 

 difficulty of making the fluid enter and leave the course 

 in a proper manner. They appear, however, lobe de- 

 cidedly superior to those in which the floatboard* arc 

 flaw, a* the water acts by its weight as well as by its 



Horizon Ul 



Water 



Wheels. 



Leslie's ho- 

 rizoutal 

 wheel. 

 Figs. 1J, 

 13. 



Wheels 

 with tpiral 



rt.n!-,irds. 



impulsive force. The ratio of the effects in the two 

 cases, with five or six feet of fall, is nearly as 3 to 2. An 

 advantage may be gained by dividing the current, and 

 throwing it in separate portions upon different float- 

 boards. See Leopold's Thealrum Mach. General. 



A different kind of horizontal wheel, invented by 

 Mr Robert Leslie, which works by the tide upon the 

 principle of a smoke jack, is shewn in Figs. 12, 13. 

 This machine, which is shewn in a vertical section in 

 Fig. 12, and in a horizontal section in Fig. 13, consists 

 of a circular box or drum op, widened at top into ano- 

 ther circular drum AB, two parts of which, GO and 

 1-1 , are made to open and shut, as shewn by the dotted 

 lines. When the tide moves in the direction OE, the 

 part GO shuts into the position GH, and admits the 

 water upon the wheel ; but when the tide returns, GH 

 assumes the position GO, and EF shuU into the dotted 

 position E /", and admits the water to the wheel. The 

 axis EF. Fig. 12, stands vertically, and has the vanes 

 m, H fitted upon it like those of a smoke jack. The wa- 

 ter enters at O, and at F/" when the tide returns, de- 

 scends in the direction of the arrows, acts by its im- 

 pulse and its weight on the oblique vanes m, n, and, af- 

 ter turning the wheel about its vertical axis EF, escapes 

 at the aperture P, or P when the tide return*. 



Wheelt nilk Spiral Footboards. 



IN some of the southern provinces of France a coni- 

 cal horizontal wheel with spiral floatboards is frequent- 

 ly used. It has the form of an inverted cone, with a 

 number of spiral floatboards winding round its surface, 

 so as to be nearer one another at the mailer or lower 

 end of the cone, than at the larger or upper end. When 

 the water has acted upon these floatboards by its im- 

 pulse, it descends along the spirals, and continues to 

 drive the machine by its weight. A drawing of this ma- 

 chine will be seen in Ferguson's Lecture*, vol. ii. App. 



Or Robison describe* another wheel with spiral float- 

 board*, which was moved by a screw. " It was," he 

 says, " a long cylindrical frame, having a plate stand- 

 ing out from it about a foot broad, and surrounding it 

 with a very oblique spiral like a cork screw. This was 

 plunged about Jlh of its diameter (which was about 

 IS feet), having it* axis in the direction of the stream. 

 By the work which k was performing, it seemed more 

 powerful than a common wheel, which occupied the 

 MOW breadth of the river." 



For farther information on the subject of undershot 

 wheel*, we Pilot, Mem. Aead. Par. 1729, 8vo. p. 359 i 

 Desagu tier's Experimental Philatophy, vol. ii. p. 42+ ; 

 Du Petit Vandin, Mem. del Sonant Etrantrers, torn. i. ; 

 IVparcieux, Mrm. Acad. 1754, p 614; Fabre Sur let 

 Maekinei Hvdranlijur. p. 55 ; Bossut'* Traile /////.- 

 rfroArMMSfiK, vol. i. chap. xiv. xv. p. 482 ; vol. ii. chap, 

 xviii. edit 1796 ; Maclaurin's Fluxiont, $ <X>7. p. 728 ; 

 1-ambert, Nan. Mem. de f Aead. Berlin, 177 A, p. 63 ; 

 Smeaton'* Experiment* on Millt ; Borda, Mem. Acad, 

 Par. ; Leopold's Theatrmm Machi*. General. ; Reperto- 

 ry of Arti, vol. i. p. 385 ; Ferguson'* Lectures, vol. ii. 

 App. ; and Dr Robison'* Syttem of Mcch. Philotophy. 



SCCT. III. On Brest! Wheels. 



\ breast water wheel is a wheel in which the water orea>: 

 ii delivered at a point intermediate between the upper 

 and under point of a wheel with AoatbonrcR It i- ge- 

 nerally delivered at a point below the level of the 

 axis, a* in Fig. I, but sometime* at a point higher 

 than the level of the axis, as in Fig. 9. On breu< 



Reference 

 M worki oa> 

 undenhot 

 wheel". 



