108 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



LApbil, 



raising the paddle-wheels out of tlie water, simultaneously with stopping the 

 enpines, an accurate result could not be arrived at. The screw propfller 

 fiftered greater facilities, as he believed methods had been devised for rais- 

 ing it out of the water. He was of opinion also, that unless the experiments 

 were tried in perfectly smooth water, they could not give accurate results, 

 on account of the dipping of the bow of the vessel, and the consequent 

 oscillation of the suspended sphere and rod, which would become a pendu- 

 lum. These were practical objections, which were raised in his mind, by the 

 difficulties he had experienced, in determining the raetliod of conducting his 

 own experiments, which were all tried upon vessels of considerable bulk and 

 tonnage. The mode he eventually adopted was, to try the vessel both light 

 and loaded. First taking all the float-boards off the paddle-wheels, and by 

 means of a steam-tug, of about 250 h.p., drawing the vessel through the 

 water, ascertaining the resistance at different velocities by means of a dyna- 

 mometer; then, by replacing the float-boards, varying tlie load, and conse- 

 quently, the immersed section of the vessel, and noting carefully all the re- 

 sults, he found an extraordinary uniformity in the amount of resistance by 

 similar forms at equal speeds. At first he conceived, that it would have 

 been necessary to reduce all the oscilUtions of the dynamometer, but he 

 found the motion was so uniform, that any ordinary instrument would suffice 

 for the purpose. He used an instrument, called I'itot's tube, for measuring 

 the velocity, and he had found it very valuable ; he might say almost unerr- 

 ing. It consisted of a vertical glass tube placed in the centre of the vessel, 

 through the bottom of which a hole of about half an inch diameter was 

 bored, to pass a metal tube, continuing for a distance horizontally beside the 

 keel, and terminating in a funnel-shaped mouth. When the vessel was at 

 rest, the water outside, and the column within the tube, stood at the same 

 level ; but in proportion as the velocity of the vessel increased, so the column 

 of water in the tube rose ; and by graduating the tube in accordance with 

 observed heights for given speeds, the results might be read off with great 

 facility and accuracy. Any undue amount of oscillation was prevented, by 

 contracting the area of ihe metal luhe at one spot, by a stop cock, which 

 was only opened when taking observations. He thought the method he had 

 described, combined with the use of Pilot's tube, was preferable to that pro- 

 posed by Mr. Heppel. 



Mr. Rennie concurred with Mr. Russell in his opinion of the proposed 

 method of experimenting. No subject was more difficult than the resistance 

 of fluids. It had occupied the attention of the most learned philosophers, 

 yet nevertheless the present state of knowledge of the subject was still very 

 imperfect. The true theory had never been discovered. Newton to whom, 

 after Galileo, the credit of the first pi-eci~e experiments was due, had also 

 given the first of the two theories, of which the least imperfect supposed the 

 body to le directly struck by each of tlie molecules in motion. The subse- 

 quent experiments of Bernouilli, Euier, Kobins, Borda, Bossut, De Buat, and 

 otheis, had shown the imperfection of that theory. 



The experiments of the French Academy, and the labours of Bouguet, 

 Clairbois, Duhamel, Don Juan, Chapman, Forfait, Attwood, Dupuis, Poisson, 

 and others,' had slied considerable light on the subject, and on that of the 

 stability of floating bodies; but no extended series of experiments was tried 

 in this country, until the question was taken up by Colonel Beaufoy, who in 

 1791 established a "Society for the Improvement of Naval Architecture," 

 under whose auspices he made, in the Greenland Dock, the elaborate experi- 

 ments, the first portion of which had been so munificently presented to the 

 scientific world by Mr. Henry Beaufoy.^ The society however sunk for 

 want of funds, and the experiments were eventually conducted and brought to 

 a conclusion, entirely at the expense of Colonel Beaufoy. A short notice of 

 them in Thomson's "Annals of Philosophy"^ induced the communication of 

 the results of a similar series of experiments, made by Messrs. Lagerbjelm, 

 Forselles, and Kallstenius for the Society of Ironmasters of Stockholm, at 

 the Fahlun mine, between 1811 and 1815. Owing to the combined circum- 

 stances of the Swedish language being but little cultivated in England, and a 

 want of mathematical attainments in those who did understand the lan- 

 guage, the Swedish experiments remained untranslated, until after Colonel 

 Beaufoy's decease. Mr. Henry Beaufoy then committed the book to the 

 Rev. Elijah Smith, of Sidney College, Cambridge, who learned Swedish and 

 completed the translation, as also that of Lagerhjelm's " Testamen Theorise 

 Resistentiae Fluidorum constituenda;." The results of these examinations 

 occupied ten years in their reduction, and yet but few practical results had 

 been obtained. The general deductions which appeared to he drawn were — 



Ist. The confirmation of the theory, that the resistance of fluids to pass- 

 ing bodies was as the squares of the velocities. 



2ndly. That, contrary to the received opinion, a cone would move through 

 the water with much less resistance with its apex foremost, than with its 

 base forward. 



3rdly. That the increasing the length of a solid, of almost any form, by 

 the addition of a cylinder in the middle, diminished the resistance with which 

 it moved, provided the weight in the water remained the same. 



1 See Bouguet, Traits dcs Navires ; Euler, Scienlije Navaliaj Clairbois, Architecture 

 Navale ; Dullaniel, ditto, ditto; Don Juan, Examen MarilLme; Chapman (Sweden), 

 Naval Architecture; Forfait, Traitc sur la mature des Vaisseaux; Attwood, Philosophi- 

 cal Transactions; Dupuis, G^omttrie Di^scriptive ; Poisson. Th^orie des Ondca ; D' Alcni- 

 bcrt and Bossut, Rechcrchea poui ia Societe des Experiences en Architecture Navale ; 

 I-ngerlijelm and Kallstenlua, Experiments for the Swedish Societyi Marestier, iVlemoire 

 sur lea Bateaux k Vupeur; Beaufoy, Nautical Experimenta. 



2 Beaufoy's *' Nautical Experiments. " Vol.1. London, 1834. 

 s Thomaon'a "AddqIs of Philosophy." 1814, 



4thly. That the greatest breadth of the moving body should he placed at 

 the distance of two-fifths of the whole length, from the how, when applied 

 to the ordinary forms in naval architecture. 



5thly. That the bottom of a floating solid should he made triangular; as 

 in that case it would meet with the least resistance when moving in the 

 direction of its longest axis, and with the greatest resistance when moving 

 with its broadside foremost. 



Such was a short summary of the labours of Colonel Beaufoy, to whom 

 the scientific world was deeply indebted. Mr. Rennie thought, however, 

 that errors had been fallen into, by not sufficiently considering the question 

 of the friction upon the sides of the various forms used in the experiments. 

 They were moreover tried upon masses of too small dimensions. 



The papers on the same subject in the archives of the Institution of Civil 

 Engineers, presented by Bidder, Carlsund, Telford, Palmer, and Macneill, 

 and those of Fairbairn and Colonel Page,' treated of experiments upon 

 larger vessels, and produced more practical results. 



■fhe great difficulty of separating the resistance from the friction, arose 

 out of the imperfect apparatus hitherto adopted. The balance of Coulombe, 

 and the pendulum, had been tried with doubtful success. Profiting by the 

 problem of the cylinder revolving in the vortex, in the Principia of Newton, 

 Mr. Rennie undertook a series of experiments in the year 1830, which were 

 published in the Transactions of the Royal Society, " On the Resistances of 

 solid Bodies in Air and Water. "^ The apparatus consisted of an upright 

 spindle of wrought iron, made to slide up and down in a frame, so as to be 

 plunged to any convenient depth in the water, or to revolve in air only, as 

 required. 



The iron discs of square, circular, and triangular forms, as well as the cy- 

 linders and globular bodies, all of the same areas, were moved through the 

 same spaces, and with the same velocities, in air and in water ; the results 

 were tabulated, and the conclusions arrived at were: — 



Ist. That the friction and adhesion were not as the surfaces, with slow 

 velocities; being in the ratio of 1 to 3, and diminishing rapidly with the 

 velocities, without observing any ratio. 



2ndly. Tliat the resistance of fans and globes of equal areas in air, was as 

 the squares of the velocities up to 8 miles per liour. 



3rdly. That the resistance of fans or discs with equal areas, was to globes 

 as 2 to 1. 



4thly. That the resistance of fans or discs to globes of equal area in 

 water, was to the globes as the squares of the velocities. 



5thly. That the mean resistance — 



Uf Circular discs in water"! , , ., ., u nA ,. i 



„ J- ■ i were to each other as the numbers 21 to 3, 



,, Square discs m water ^,/-i<»j,.o 

 " ,,f , 1 „ • , I 16 to 2, and 4 to 2. 

 „ Wooden balls in water J 



Of Circular discs in air 1 , u .i, »i, i o- . la 



I .., gj^i, other as the numbers 2^" to 18, 



, and 10 to 2. 



Of Circular discs in air 5 ^^^ ^^ ^^^ 

 „SqM,,refansma,r .. ^ 3, 

 ,, Wooden balls in air. . J ' 



Mr. Bidder doubted whether the question of resistance, or friction, could 

 be fairly tested by a cylinder revolving in a fluid, inasmuch as a rotary mo- 

 tion was imparted to a portion of the water, in the same direction as the 

 revolution of the cylinder. 



The subject was one of great interest, and to which he had devoted much 

 attention. Some years since he assisted Mr. Walker in a series of experi- 

 ments in the East India Dock, and he came to the conclusion, that it was 

 not possible to arrive at one law suitable for all cases. There were in reality 

 three cases to be considered : — 



First. The resistance due to displacement. 



Secondly. The resistance due to non-pressure. 



Thirdly. The resistance due to friction. 



As regarded the first case ; the resistance due to displacement included 

 that of the area of resistance of the water heaped up against the bows, 

 which augmented as the velocity increased. In such case he found, that 

 the increase of resistance was in a more rapid ratio than the square of the 

 velocity. 



In the second case ; that of non-pressure, occasioned by the filling up of 

 the channel in the wake, vacated in the passage of the vessel through the 

 water. In this case he found the resistance increased in a less ratio than 

 the square of the velocity. In Mr. Walker's experiments, boats were used 

 with bluff prows and with acute prows ; it was found that at a slight immer- 

 sion, and when drawn at a low velocity with the bluff prow foremost, there 

 was the least resistance ; but that when deeply immersed, all other condi- 

 tions remaining the same, there was the greatest amount of resistance. 



As to the third position. The formula of Du Buat with regard to fiiction 

 was found applicable ; as there was no distinction whether the vessel was 

 moving through the fluid, or whether the fluid was running over the bottom 

 of a river. In this case the resistance due to friction was as the square of 

 the velocity. 



IJossut tried a variety of experiments upon the angles of resistance, by 

 attacking to a rectangular parallelogram various shaped prows, at angles 

 varying from 168° to 12°, with the view of ascertaiuing the law of resistance 

 due to the angle of the plane meeting the water ; but he overlooked the con- 

 stant deduction necessary for the non-pressure due to the rectangular form 

 of the stern, which formed the largest portion of the resistance, and conse- 

 quently invalidated the deductions from the experiments. 



4 "Remarks on Canal Navigation." By \V. Fairhairn. 



5 Vide " Phil. Trans.," 1831, p. 423. 



evo. London, 1831. 



