5GO 



HYDRODYNAMICS. 



HUM-' 

 \Vhecl. 



PLATE 

 CCCXXI. 

 Figs. 1, . 



Smexton'i 

 breast- 



wheel. 



Improved 



hreast- 



wrteel. 



Effect of 

 breast- 

 wheels. 



Comparison 

 of water 

 wheels. 



nil). 



wheels, buckets are never employed, but the floatboards 

 are fitted accurately, with as little play as possible, to 

 the mill course, so that the water, after acting upon 

 the floatboards by its impulse, is retained between the 

 floatboards and the mill-course, and acts by its weight 

 till it reaches the lowest part of the wheel. 



A breast wheel, as constructed by Mr Smeaton, is 

 represented in Fig. 1, where AD is a portion of the 

 wheel, MN the canal which conveys the water to the 

 wheel, MOP the curvilineal mill course accurately 

 fitted to the extremities of the floatboards, and c d the 

 shuttle moved by a pinion a, for the purpose of regu- 

 lating the admission of water upon the wheel. 



An improved breast wheel is shewn in Fig. 2. The 

 water is delivered on the wheel through an iron gra- 

 ting a It, and its admission is regulated by two shuttles 

 c, d, the lowermost of which, d, is adjusted till a suffi- 

 cient quantity of water passes over it; while the other, 

 c, which is generally moved by machinery, is made to 

 descend upon d, so as to stop the wheel. 



According to Mr Smeaton, " the effect of a breast 

 wheel is to the effect of an undershot wheel, whose head 

 of water is equal to the difference of level between the 

 surface of water in the reservoir, and the part where it 

 strikes the wheel, added to that of an overshot whose 

 height is equal to the difference of level between the 

 part where it strikes the wheel, and the level of the 

 tail water. 



M. Lambert observes, that when the fall of water is 

 between 4 and 10 feet, a breast water wheel should be 

 erected, provided there is enough of water ; that an un- 

 dershot wheel should be used when the fall is below 4 

 feet, and an overshot wheel when the fall exceeds 10 

 feet. He recommends also that when the fall exceeds 

 10 feet, it should be divided into two, and two breast 

 wheels erected upon it. These rules are not of great 

 value. The other results of Lambert's investigation, 

 will be found either in his Memoir, or in Ferguson's 

 Lectures, Appendix, vol. ii. 



Comparative effects of Water Wheels. 



M. Belidor very strangely maintained that overshot 

 wheels were inferior to undershot ones. It appears, 

 however, from Smeaton's experiments, that in overshot 

 wheels the ratio of the power to the effect is nearly as 3 

 to 2, or as 5 to 4, whereas in undershot wheels the ratio 

 is only as 3 to 1 ; from which it follows, that the effect 

 of overshot wheels is nearly double of the effect of un- 

 dershot wheels. The Chevalier de Borda has concluded 

 that overshot wheels will raise through the height of the 

 fall a quantity of water equal to that by which they are 

 driven ; that undershot wheels moving vertically will 

 produce ^ths of this effect ; that horizontal wheels will 

 produce a. little less than \ of it when the floatboards are 

 plain, and a little more than ^ when they are curvilineal. 



SECT. IV. On Wheels Driven by the Reaction or Covn- 

 terpressure of Water. 



s The first mills which were driven by the reaction of 

 water were called Barker's mill, and sometimes Parent's 

 mill. We are not acquainted with the nature of M. 

 Parent's claim to the invention ; nor .can we determine 

 whether the priority is due to him or to Dr Barker. 

 Dr Desaguliers, who seems to have been the first per- 

 son who published an account of the machine, describes 

 it as having been invented by Dr Barker. " Sir George 

 Savile says, he had a mill in Lincolnshire to grind corn, 

 which took up so much water to work it, that it sunk 



his ponds visibly, for which reason he could not have 

 constant work ; but now, by Dr Barker's improvement, 

 the waste water only from Sir George's ponds keeps it 

 constantly to work." 



Dr Barker's mill is shewn in Fig. 3. where CD is a 

 vertical axis, moving on a pivot at D, and carrying the 

 upper millstone m, after passing through an opening 

 in the fixed millstone C. Upon this axis is fixed a 

 vertical tube TT communicating with a horizontal tube 

 AB, at the extremities of which A, B are two apertures 

 in opposite directions. When water from the mill- 

 course MN is introduced into the tube TT, it flows 

 out of the apertures A, B, and by the reaction or coun- 

 terpressure of the issuing water the arm AB, and conse- 

 quently the whole machine, is put in motion. The bridge- 

 tree a b is elevated or depressed by turning the nut c at 

 the end of the lever c b. In order to understand how thij 

 motion is produced, let us suppose both the apertures 

 shut, and the tube TT filled with water up to T. The 

 apertures A, B which are shut up, will be pressed out- 

 wards by a force equal to the weight of a column of wa- 

 ter whose height is TT, and whose area is the area of the 

 apertures. Every part of the tube AB sustains a similar 

 pressure ; but as these pressures are balanced by equal 

 and opposite pressures, the arm AB is at rest. By 

 opening the aperture at A, however, the pressure at 

 that place is removed, and consequently the arm is 

 carried round by a pressure equal to that of a column 

 TT, acting upon art area equal to that of the aperture 

 A. The same thing happens on the arm TB ; and 

 these two pressures drive .the arm AB round in the 

 same direction. This machine may evidently be applied 

 to drive any kind of machinery, by fixing a wheel upon 

 the vertical axis CD. 



In the preceding form of Barker's mill, the length 

 of the axis CD must always exceed the height of the 

 fall ND, and therefore when the fall is very high, the 

 difficulty of erecting such a machine would be great. 

 In order to remove this difficulty, M. Mathon de la Cour 

 proposes to introduce the water from the millcourse, 

 into the horizontal arms A, B, which are fixed to an 

 upright spindle CT, but without any tube TT. The 

 water will obviously issue from the apertures A, B, in 

 the same manner as if it had been introduced at the top 

 of a tube TT as high as the fall. Hence the spindle 

 CD may be made as short as we please. The practi- 

 cal difficulty which attends this form of the machine, 

 is to give the arms A, B a motion round the mouth of 

 the feeding pipe, which enters the arm at D, without 

 any great friction, or any considerable loss of water. 

 This form of the mill is shewn in Plate CCCXXI. Fig. 

 4. where F is the reservoir, K the millstones, KD 

 the vertical axis, FEC the feeding pipe, the mouth 

 of which enters the horizontal arm at C. In a ma- 

 chine of this kind which M. Mathon de la Cour saw 

 at Bourg Argental, AB was 92 inches, and its diameter 

 three inches ; the diameter of each orifice was 1J. inch, 

 FG was 2 1 feet ; the internal diameter of D was two 

 inches, and it was fitted into C by grinding. This ma- 

 chine made 115 turns in a minute when it was unload- 

 ed, and emitted water by one hole only. The machine, 

 when empty, weighed 80 pounds, and it was half sup- 

 ported by the upward pressure of the water. This im- 

 provement, which was published in Rozier's Journal de 

 Physique for January and August 1775, appeared about 

 20 years afterwards as a new invention of Mr Waring's 

 in the Transactions of the American Philosophical So- 

 ciety of Philadelphia, who was probably not aware of 

 the labours of M. Mathon de la Cour. 



Water 



Wheels. 



PLATE 

 CCCXXI. 

 Fig. a 



mem on 

 Barter's 

 mil) by M. 

 Mathon de 

 la (.'our. 



Fig. 4. 



