92 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



(428.) 

 Principle 

 of greatest 

 advantage 

 in water- 

 wheels. 



(429.) 

 Power of 

 adaptation 

 of the tur- 

 bine. 



the inner surface of the moveable cylinder is all but 

 in contact with the circumference of the fixed cylin- 

 der. Further, water under a greater or less hydro- 

 static pressure, and moving with the consequent velo- 

 city, is introduced at the centre of the fixed cylinder, 

 and conveyed to its circumference by channels of a 

 peculiar form constructed by means of vertical parti- 

 tions or guides of continuous curvature, from which 

 the water is discharged against float boards within 

 the external cylinder, which are also curved, but the 

 curvature is turned the other way so that the parti- 

 tions in the first cylinder are where they terminate 

 nearly perpendicular to the internal surface of the 

 moveable or second cylinder where they commence. 

 These latter partitions or float-boards terminate ex- 

 teriorly in a direction nearly tangential to the outer 

 cylindric surface where the water emerges. 



The hydraulic principle of greatest possible advan- 

 tage to which these Turbines are made as nearly as 

 possible to approximate is this, that the water shall 

 enter the moveable apparatus without shock, and shall 

 quit it without velocity, being simply left behind by 

 the wheel as it escapes from it. Since both these con- 

 ditions cannot absolutely be fulfilled, the first part of 

 the condition is left imperfect. Some secrecy is, I 

 believe, still maintained as to the forms and dimen- 

 sions of these machines ; but their actual efficiency 

 has been most thoroughly tested by means of De 

 Prony's Friction Dynamometer 1 by Colonel Morin, a 

 most competent authority. His experiments leave no 

 doubt of the admirable qualities of these machines. 

 In particular, the useful effect compared to the theo- 

 retical effect represented by the fall of water expended 

 rises higher than probably in any other hydraulic 

 machine, being under favourable circumstances about 

 eighty per cent. Now water-wheels moved princi- 

 pally by the shock of the fall seldom, in the most 

 advantageous conditions, realize thirty-five percent., 

 often not seven per cent. This superiority of action 

 of the Turbine is due entirely to the approximation 

 which it gives to the theoretic condition above men- 

 tioned of perfect efficiency. 



But what is not less striking in the performance 

 of this machine, is the variety of circumstances under 

 which it acts advantageously ; however great may be 

 the variation in the size and velocity of the wheel, the 

 height of fall, and the power disposable. Turbines 

 have been made of as small diameter as 2 feet with the 

 enormous fall of 350 feet, making 2300 revolutions 

 per minute. They work with nearly equal advantage 

 (relatively to the power expended) whether the supply 

 of water be small or great. They may be completely 



drowned or buried under water to a considerable 

 depth without any sensible variation in their effi- 

 ciency, thus preventing any inconvenience from floods. 



It is remarkable that, with these manifest advan- (430.) 

 tages, the Turbine has been so sparingly introduced at 

 least in this country. No doubt the first establish- 

 ment of it is attended with considerable expense. 



M. PONCELET, an active and intelligent officer of (431.) 

 Genie, and member of the Institut, is favourably M - Ponce- 

 known by his hydraulic observations and inventions, Jf^i^ 

 as well as by his skilful investigation of the effects breast- 

 of machines, and his excellent works and memoirs wheels. 

 on several subjects. He has investigated with much 

 patience and geometrical nicety the form and dis- 

 charges of spouting fluids, and was one of the first 

 to improve materially the ordinary water-wheels, by 

 introducing a kind of breast-wheel (which thirty-five 

 years ago was scarcely known in France) in which 

 the water is conveyed without shock into compart- 

 ments on the descending side, from which again it 

 was allowed to escape with all its acquired velocity 

 spent, or nearly so. The efficiency of these wheels is 

 equal to about two-thirds of the power expended. 

 Before the Turbine had been finallv improved by M. 

 Fourneyron, M.Poucelet had invented an engine on 

 the same principle, in which the water enters at the 

 circumference of the horizontal wheel, and is deli- 

 vered at the centre. 



I am aware how imperfect this section remains as (432.) 

 a history of Hydrodynamics. But I must again Capillary 

 refer to special articles on the subject, the plan of attraction 



the Dissertation not admitting of farther detail. As and ^ 

 nothing material has been added to the doctrine of place. 

 Capillary Attraction since the publications alluded 

 to in Sir John Leslie's Dissertation (although M. 

 Poisson has written a treatise on the subject), I will 

 for the sake of compression not enlarge upon it. I 

 do so with the less regret, because I cannot regard 

 the excessive mathematical illustration which it has 

 received as altogether justified by the certainty and 

 due appreciation of the physical principles involved, 

 such as can alone give to applied mathematics their 

 distinctive value. The theory of Laplace, so far 

 as it was based on novel grounds, was anticipated 

 by Dr Young, and gave rise to several controversial 

 articles by that most eminent philosopher, of which 

 an account will be found in Dr Peacock's Life of 

 Young, pages 199-210, as well as a most excellent 

 review of the subject of Capillary Attraction, which, 

 indeed, by its candour and completeness, supersedes 

 anything which I should have felt disposed to say 

 on the subject. 



1 Gaspard de Prony, born in 1755, was an eminent engineer, especially in the department of hydraulics, and the author of a 

 voluminous work entitled Nouvelle Architecture Hydraulique , but his originality was not great enough to authorize his being 

 placed among the leaders of his age. His simple invention of the Frein Dynamometrique, or friction dynamometer, is the one 

 by which perhaps he will be longest remembered. It consists of an iron collar with tightening screw, which may be clasped 

 on a horizontal wooden arbor connected with uniformly revolving machinery. A lever, to which a weight may be applied, is 

 attached so as to form part of the collar. The clasping screw being moderately tightened, the collar and lever are of course 

 carried round by the machinery until a weight is applied sufficient to check the velocity, and to generate an amount of friction 

 which is in fact the useful effect of the machine for that velocity, and which is determined by the momentum of the weight over- 

 come in one second. De Prony was a most amiable man, and died in 1839, in the 84th year of his age. 



