354 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[October, 



pared the common forms of merchantmen and other ships. The class of 

 fast-sailing yachts and cutters was treated in the same way, the object always 

 being the determination in given circumstances of the method of giving 

 such a form to a ship as shall enable her to pass through the w ater with the 

 least resistance, the greatest velocity, and of course the smallest expenditure 

 of force, power, and money. The methods of drawing these vessels through 

 the water, varied with the scale on which the experiments were made. Those 

 on the smallest scale were drawn by a weight arranged i;i such a manner as 

 to supply a uniform force through any given distande — and on the largest 

 scale, the experiments were made on the sea by means of powerful towing 

 vessels. In this way the experiments were made on a wide range of magni- 

 tudes, both as regarded the vessels themselves and the sheet of water on 

 which they were propelled, an element of resistance not always sufficiently 

 taken into account. The resistance was accurately measured by dynamo- 

 metric apparatus of great accuracy, through which the moving force was 

 communicated to the vessel; the velocity being determined, in certain cases, 

 by a peculiar apparatus designed for this purpose, and in other cases by in- 

 struments for measuring and marking time with accuracy. After the obser- 

 vations had been reduced by independent calculators, and not till then, were 

 they made the subject of special examination, with reference to any theory; 

 and thus it was conceived that the greatest amount of authenticity had been 

 secured. The author then proceeded to give to the meeting a number of 

 specimens of the results which the experiments afforded, such as he knew 

 were likely to interest those members of the section who were acquainted 

 with the principles of naval construction. He demonstrated a remarkable 

 law, by which it appears, that each velocity has a corresponding form and 

 dimension peculiar to that velocity ; and he showed, in a variety of diagrams, 

 the means of constructing such forms. To show bow much influence form 

 alone, without any other element or dimension, affects the question of re- 

 sistance, he adduced the following as one of the most important experiments. 

 Four vessels were taken, having all the same length, the same breadth, the 

 same depth, the same area and form of midship section, and all loaded to 

 the same weight, displacement, and draft of water. The only difference 

 being in the character of the water-lines ; No. 1 being of the new form in- 

 dicated by these experiments as that of least resistance ; No. 3 the old form, 

 very nearly the reverse of the first ; No. 2 intermediate between them, and 

 No. 4 intermediate between No. 1 and No. 2. The following table shows 

 the result of the comparative trial : — 



These c'.iffcreiices showed how much might be gained, everything else being 

 equal, by the adoption simply of judicious form in the construction of the 

 water lines of a ship. The vessel No. 1 was constructed on the wave-line; 

 the methods and rules for which he proceeded to explain in diagrams, too 

 numerous for our space to admit. But we hope the speedy publication of 

 the report itself may soon remedy this omission. 



Mr. Perry observed that the position of the paddle-wheels in steam vessels 

 was an important subject, which required to be determined, especially as 

 different opinions were entertained by practical men whether the paddles 

 should be nearer to the stern or to the head of the vessel. 



The Marquis of Northampton remarked on the importance of these expe- 

 riments, which lud been carrietl on by the British Association. The results 

 would possibly produce a change in the naval architecture of every country 

 in the world; and if the British Association had done nothing else than 

 carried out these experiments, anil attained those important results, all the 

 efforts they had made would have been amply rewarded. 



Mr. J. Taylor observed that these experiments had been carried on for five 

 years, and that the late Sir J. Uobisou, who had been associated with Mr. 

 Russell in their prosecution, had watched over them with great anxiety till 

 within a short period of his death. The Association had expended £850 in 

 making these experiments, and now came the question, what was to be done 

 with the valuable body of information that had been collected ? It ought 

 not to lie idle on their shelves, but ought to go forth to the public; and the 

 best manner of accomplishing that would be a subject of consideration for 

 the Council. 



Mr. Russell said, that with regard to the position of paddles, the subject 

 had been already taken up by the government, and some practical results 

 might shortly be expected. In conducting the experiments for the British 

 Association, Sir J. Robison and himself having satisfied themselves as to 

 the correctness of their system, they had endeavoured to get it introduced 



without exciting opposition. The experiments were made in a ship-building 

 country, and ship-builders every now and then borrowed the forms of the 

 boats that had been found to move the fastest through the water, and thus 

 they had been gradually introduced. The Flambeau, which was built on the 

 Clyde in 1839, on one of the experimental lines, beat a vessel of greater 

 length, though having but 75 h.p. against 120. In smooth shallow water 

 the vessel on the old construction was a match for the Flambeau, but in a 

 deep and heavy sea the experimeutal vessel beat the other by two miles an 

 hour. There had been since constructed in that part of the country a whole 

 class of vessels built of that form. The Great Britain had the wave water- 

 line ; and the Vanguard, which made her passage last week from Dublin to 

 Cork in two hours less time than bad ever been previously accomplished, 

 constructed by the same builder who had made the models for the British 

 Association experiments. 



Elasticity of Materials. 



" Experiments to prove that all Bodies are in some degree Inelastic, and a 

 Proposed Law for estimating the Deficiency." By E. Hodgkinson, F.R.S. 



Mr. Hodgkinson said it was a principle generally acknowledged in the 

 present day, and employed by those who have written on the subject of elas- 

 ticity, that, when bodies are acted upon by forces tending to elongate or 

 compress them in a small degree, the changes produced are in proportion to 

 those forces; and that equal extensions and compressions are produced by 

 equal forces. That this principle is true, so long as the change produced in 

 bodies is very small, is not to be doubted ; aud as regards extensions it is the 

 basis of the irly investigations of Jacques Bernouilli on the elastic curve ; 

 of ilooke who was it* anther (Theory of Springs, Phil. Trans., 1666,); 

 Maiiotte, Leibnitz (I>- Resistentia Solidorum, 1684). With respect to elas- 

 ticity, it was adopted in the profound inquiries of Euler on the strength of 

 columns, which were corroborated by Lagrange (Berlin Memoirs); and with 

 respect both to extensions and compressions, it forms the basis of the calcu- 

 lations on the strength aud elasticity of bodies in the principal theoretical 

 and practical works on mechanics of the present day ; as the Mecanique of 

 Poisson, and the works of Whewell, eie. — the practical treatises of Navier, 

 Poncelet, Tredgold, Barlow, Moseley, &c He hoped, however, to convince 

 the section that this principal does not operate alone in the resistance of 

 bodies subjected to tension, or to compression, or to both. He hoped, too, 

 to show the law which the clemeut, not considered by writers, nor generally 

 known to exist, is subject to. This element is a defect of elasticity, or a set, 

 to which all bodies made to undergo a change of form, however small, seem 

 to lie liable, The defect here mentioned was known to exist only when the 

 body had been strained with a considerable force, or such as to be equal to 

 one third, or upwards, of the breaking weight. But the experiments which 

 he ^ould adduce would show that the defect commences with the smallest 

 changes of form, and is increased according to the square of the extension, 

 or compression, or of the weight. Thus, if e represent the extension or 

 compression which the strained body had undergone, and a e the force which 

 would have produced that extension or compression if the body bad been 

 elastic, the real force necessary to produce this change, e, will be 

 1. thi n the former b> a quantity, b e-, representing the defect of elasticity. 

 Hence the force req'iii' 1 to produce a change, e, is a e — b e 2 , where a and b 

 Bl i taut quantity . He bad found this law to obtain when the change 

 in the bod; rose from extension or compression alone, but when 

 the change arose both from extension and compression, as in the flexure of a 

 rectangular body, the force of a fibre was to that due to perfect elasticity, as 

 a i — h i- to a x ; or it was equal to ax— I x;- where X was the height ap- 

 plied, and a b constant quantities, as before. In proof of these statements, 

 Mr. Hodgkinson mentioned that having remarked, in his experiments made 

 for the British Associa' m on the subject of hot and cold blast iron, that the 

 elasticity of bars broken transversely was injured much earlier than was 

 generally assumed, he paid particular attention to this circumstance in his 

 future experiments, and had bars so formed that he could separate the elas- 

 ticity of extension from that of compression ; by these bars, which were 

 very long and of small depth, he perceived that one-fiftieth or one-eightieth 

 of the breaking weight was sufficient to injure the elasticity. He mentioned 

 the matter to his friend Mr. Fairbairn (who was associated with him in the 

 inquiry), soon after he had made the discovery ; and Mr. Fairbairn's subse- 

 quent experiments made to determine the strength of rectangular bars of 

 iron, from all parts of the kingdom, were conducted in the same manner as 

 Mr. Hodgkinson's bad been; the deflexion and quantity of set, or defect of 

 elasticity, from each weight being always observed. Mr. Fairbairn's experi- 

 ments were on bars cast one inch square and five feet long, and were made 

 with the utmost care; Mr. Hodgkinson has, therefore, adopted their results 

 with respect to the " set," and taking means both from Mr. Fairbairn's re- 

 sults and his own on the same sort of bars, he has sought for the relation 

 between the weights and the mean sets from those weights, these sets being 

 the deflexions or deviations from the original form of the bar, after the 

 weights have been removed. To ascertain the relation above, Mr. Hodg- 

 kinson has curves described from the results of the experiments, making the 

 sets the abscissae, and the weights the ordinates ; and the similarity in ap- 

 pearance of these curves to the common parabola, led him carefully to exa- 

 mine whether they were not in reality represented by that curve. The exa- 

 mination was successful — the parabola was the curve ; and the mean results 



