1816.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



307 



the first and third terms of his formula had been proved by the labours of 

 preceding investigators. 



After some further observations, Professor Willis closed the discussion 

 by remarldns on ihe reciprocal action of the pistons as a fruitful cause of 

 resistance aiRl loss of power. 



[It remains only to give our own opinion on the result of JMr. Russell's 

 labour. On a subject of such great moment to the engineer, a general 

 account of the deductions to be made from the arguments employed in the 

 discussion cannot fail to be acceptable, ^^e must begin then by according 

 to Mr. Russell the merit of having approached tlie subject in a philoso- 

 phical spirit. He says that his conclusions are the results of a great 

 number of careful experiments, but he does not dogmatise upon them. On 

 the contrary, he tells us plainly, that his formula has been suggested for 

 want of a better. M'ith respect to the '' remainder" term, which consti- 

 tutes the novelty of his results, he rather asks whether it may not repre- 

 sent physical facts, that asserts that it actually does so. This is precisely 

 the language of a. true student of science. AVhile, however, we feel that 

 Mr. Russell has made a step in the right direction, we unhesitatingly deny 

 that his formula will account even appreximately for the resistance to 

 trains. There appear snIHcieut reasons Un- questioning tlie accuracy of 

 each of the three terms of his expression. The last (C in) makes the axle- 

 friction independent of the velocity; whereas it depends materially on the 

 velocity, as we will show. Mr. Russell says that the friction of the axle 

 is proportional to the pressure, and he evidently takes it (or granted that 

 the only pressure is a vertical one, namely the weight of the carriage. 

 This looks very like an error of principle, for it is obvious that if no hori- 

 zontal pressure acted on the axle, the wheel would not move forward. 

 The wheel is subject to two retarding lorces, — Ihe action of the rail on its 

 periphery, and the action of the air on its whole surface. Now, these 

 forces both depend on the velocity of the train, and their sum is equal to 

 the accelerating horizontal force on the axle ; on the principle that when a 

 body is moving uniformly its accelerating and retarding forces are equal. 

 The pressure, then, on the axle is a function ()f the velocity, and conse- 

 quently the axle-friction also depends on the velocity. It may be further 

 observed, witli respect to the retarding for'ce on the circumference of 

 (he wheel from the rad, that it is made up of three parts — rolling friction 

 on the tire, iatei'al friction on the flange, and concussion at the joints of 

 the rails. The efl'^ ct of all these probably, or at all events of the latter of 

 them, depends materially on the velocity, and also greatly aifecls the pres- 

 sure, and consequently the friction, on tlje axle. 



Next, with respect to the term (Api;-), Mr. Russell here assumes that 

 the whole resistance of the atmosphere varies as the square of the velocity 

 of the train. Now it seems certain, that whatever law represents the re- 

 sistance to the front of the train cannot apply to the wheels; for the latter 

 rotate as well as move forward. The action of the air on them difl'ers so 

 greatly from its action on the rest of the train, that the resistance must be 

 expressed by dilferent functions of the velocity. Moreover, the symbol r 

 ought to express not the actual velocity of the train, but the relative velo- 

 city of the irain and tlie wind. For if the wind and the train were both 

 moving in the same direction, with the same velocity, the resistance on the 

 bodies of the carriages would he zero. And lastly, whatever function be 

 adopted ought to l)e a discontinuous one, for this reason : if the wind 

 moved faster than the train, it would urge the train forward and be changed 

 from a retarding to an accelerating force. In this case, v (the relative 

 velocity) would be negative ; but i-^ would still remain positive, which it 

 ought not to do. This contingency ought to be provided against. We 

 know that the expression for the motion of a projectile in air is discoQ- 

 tinuoiis : the resistance during the ascent of the projectile is not the 

 same function of the velocity as during the descent. 



Lastly, in the term Bmw, it is assumed, without sufficient data, that all 

 the other resistances besides those of the air and at the axles, vary as the 

 velocity simply. We may decide wiib absolute certainty, that this cannot 

 correspond to physical fads. The concussion of the joints, for instance, is 

 more likely to depend on the second than Ihe first power of the velocity. 

 It is shown in Moselpy's Engineering (p. 59-1-C), that when a body in mo- 

 tion impinges directly on a body at rest, the mutual pressure at any period 

 during impact is expressed by certain quantities, which represent the 

 hariJness o' the materials, multiplied by the product of the mass of the 

 moving body into the square of the velocity. There are many other in- 

 gredients of the calculation for which it would be difficult to prove that 

 they vary as the velocity simply. It may be also observed, that Mr. Rus- 

 sell's formula frequently did not agree with his own experiments. In 

 about a dozen cases tiiere was an analogy; but the coincidence seems 

 purely accidental, and it would be easy to invent a score of different 

 formuliie which might be supported by similar comparisons. — [Editor (J. E. 

 and A. Journal.] 



A paper on Imjirovcmcnts in Sttam Engines, by Mr. Lamb was read. 

 One object ol Ihe paper was to suggest an improved method of ** blowing 

 off." It was found by experiment that the scales which formed the concre- 

 tion in boilers weri> bojed on the surface of the water when boiling, and 

 that they were not precipitated to the bottom till ebullition had ceased. 

 Mr. Lamb proposed to take advantage of this circumstance by putting the 

 blowing otf pipe near the surface of the water. The subject of the next 

 paper was 



The INIenai and Conway Tubular Bridges, 



The subject was illustrated by a large number of diagrams, sections, 

 and "working drawings; a view of Ihe Menai Bridge with two long and 



two shorter spans was shown, and on the table was a large model of the 

 bridge which it is proposed to erect over the Conway before the Menai 

 bridge is commenced. The model of the Conway bridge shows a single 

 span ; the abutments are two massive towers rising to about twice Ihe 

 height of the tube ; the sides of the tube have a series of cruciform aper- 

 tures for the admission of light and air. 



Mr. Fairbairn commenced by detailing the course of the experiments 

 which had been made to ascertain the strongest form of the tube. The 

 tube generally gave way on the upper side, and it was first attempted to 

 strengthen it by making the top plate of corrugat- 

 ed irou. This being found insufficient, the next 

 proposition was that the top of the tube should 

 contain long tubes between two horizontiil plates ; 

 the form of the section being that represented 

 in the accompanying diagram. This form was 

 afterwards modified by making the top with rect- 

 angular cells or compartments, and a model of 

 this form was made one-sixth the dimensions of 

 the proposed bridge ; that is to say, of one- 

 sixth the length, breadth, and height, and with 

 plates rolled as nearly as possible to one-sixth 

 the thickness of those intended to be adopted. 

 The following diagram represents the section of the model at the middle, 

 and also of the Conway Bridge for which the dimensions will be as fol- 

 lows : — 



14'. S" 



[Section of the Conway Bridge at the middle.] 



Dimensions. 



Hsight outside 



*• inside 

 Breadth outside 



" iuside 



Thickness of side plates 



