306 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Oct. 



duction in this country ; but he had no doubt it would make its way, ]nrti- 

 cularlv if it could be combined with I'auvelle's system. — J. Lobb, Ksq., 

 Mayor of Southampton, wished to ask a question relative to the applicabi- 

 lity of FauTelle's plan to tlie boring of the Southampton artesian well 

 They had got to the depth of 1 ,200 feet with a bore of G inches in diameter- 

 and the expense had been nearly 20,000/. ; this system, however, seemed to, 

 diminish the expense of boring in an extraordinary manner; and lie wished 

 to ask if it could be applied to the present boring at the Southampton Com- 

 mon .' — Mr. ViGNoi.Lts, as an engineer, had no hesitation whatever in 

 saying that it conld be applied without dilliculty. If they wanted force to 

 send the water down tlie tube, they might use a steam-engine. — Dr. RoBi>r- 

 SON suggested that a deputation from the Section should go to the works of 

 the Southampton well, and inspect them. — Mr. J. Hill said that percussion 

 had long been used in this country. They had used that plan whenever they 

 came to hard substances in the Southampton boring. The rods were drawn 

 up by a windlass, and dropped down a foot or six inches ; and after the 

 material was loosened the rods were drawn, and the pulverized material 

 raised up by a cylinder. — Mr. Vignolles said this was different from the 

 Chinese system of percussion, where a rope was used, which saved the 

 trouble and loss of time in drawing the rods. The power required for 

 sending down the water on Fauvelle's plan was much less than might be 

 supposed. — The Marquis of Northampton suggested that a committee of 

 the Geological Section should be invited to accompany the committee from 

 this section. — Dr. Lankuster expressed his warm approval of M. Fauvelle's 

 plan, and his opinion of its applicability. — V conversation followed, in the 

 course of which Sir John Guest said tlie weight of a hollow rod, three 

 inches in diameter, and the iron a quarter of an inch thick, would be less 

 than that of a solid rod of an inch iliameter ; the weight would be further 

 lessened by the rod floating in water. 



Mr. Sharp read a paper on improvements in the construction of gas- 

 meters. 



Mr. RicARDu explained the construction of a machine which he had 

 used for registering the velocities of railway trains. An eccentric is keyed 

 on to one of the carriage axles and gives reciprocating motion to a rod 

 which turns a ratchet-wheel by engaging with each of its teeth in succes- 

 sion. By these means, a drum, provided with a paper for indicator-dia- 

 grams, is made to revolve with a velocity proportional to that of the train. 

 A separate part of the machine contains the mechanism of a common- 

 clock, attached to which is a tracing pencil, which moves with a velocity 

 proportional to the clock's rate of going. Consequently, the diagrams 

 register the velocity of the trains for every period of time during the tran- 

 sit of the train. 



IttsisTANCE to Railway Trains. 

 This paper was of considerable iinportaace, and we are the more glad to 

 have the opportunity of expressing an opinion respecting the formula 

 proposed, because it is the same as that of which Mr. W. Harding re- 

 cently gave an account before the Institution of Civil Engineers. 



Mr. Scott Russf.ll commenced by briefly reviewing the labours of those 

 who had gone before him in the in\e.'!tigation of the subject. The report 

 on the experiments, instituted at the instance of the British Association, 

 concluded by observing that tlu' results were so anomalous, that uo satis- 

 factory law could be deduced from them. He had undertaken a large 

 series of experiments, but only collected those on which he could place 

 perfect reliance. The trains varied in size from one one to fourteen car- 

 riages. Mr. liusseil thcu exhibited his results in three columns of figures ; 

 the first column showing the velocities iu miles per hour, the second the 

 resistance experimentally determined in ijouuds per ton weight of the 

 train, the third the resistance determined by I'.is formula. 



It would be seen from the second coltimu that it was not very easy to 

 elicit a law : the resistance was very variable with respect to the vt-locity ; 

 for instance, in certain cases the resistance actually appeared to diminish 

 as the velocity increased. The old theory had been that the total resist- 

 ance was about 8 lb. per Ion, and remaiued constant at all ordinary veloci- 

 ties. It had been found, however, that this theory was quite untenable. 

 The next iiuiirovement was to add for the resistance of air a term varying 

 as the square of the velocity. This, however, was still iusuflicient to re- 

 present the experimental results. He was therefore iuduced to propose a 

 modification of the formula, which be by uo uieens asserted lo be theoreti- 

 cally correct, nor did it exactly coincide with the experimental results ; but 

 which, however, came nearer to them than did any of the old formula", and 

 might be used till a better one was discovered. 

 Mr. S. Russell's formula is — 



R = Api-'-' + Bwii-f C ;« 

 where K is the total resistance, A the area of the front of the train, >■ the 

 velocity, m the weight of the train ; B, ;), aud C empirical constants. The 

 last term of this equation represented the resistance from the trie t Ion of 

 the axles. The value of C, as determined by the experiments of M ood 

 and llip llritish Association, appeared to be six pounds per ton, so that 

 the whole of the resistance = times the number of tons weight of the 

 train. The next element of resistance was that of the air, which ilepended 

 rather on the surface exposed than on the weight of the train. The greater 

 number of experiments under this head were few and inapiilicable. 

 Smeatou's were made by observing the rotation of thin disks, which pre- 

 sented no analogies to the present case. It ajipeared, however, to be 

 pretty clearly established that the total resistance could be deduced from 

 multiplying the area of the front of the train bv the square of the velocity, 



and by multiplying this quantity again by a certain empirical constant, 

 which he had represented by p. 



After deducting these two resistances, namely, A p t = and C hi, there 

 Btill remained a considerable residue, which indeed was, in many cases, 

 more than half the resistance determined experimentally. Now the 

 general appearance of this residue was, that it was a quantity varying as 

 the velocity multiplied by the mass of the train ; and therefore v being the 

 velocity of the train, m its mass, and B a constant, B m v represented the 

 remaining term of the expression for resistance to trains. 



The whole argument turned on this question — Does the expression hmv 

 represent with sufficient accuracy the residue, after substractiug from the 

 total resistance, as experimentally determined, the theoretical quantities 

 for friction and resistance of air? In answer to this question, Mr. Russell 

 proceeded to exainiue the two columns of figures before him, one of them 

 showing the theoretical, the other the practical, resistance. In many 

 cases, the accordance was very exact: in others, he confessed, there were 

 great discrepancies. There were anomalous results in both columns of 

 figures ; for instance, in the column of experiments, the resistance to the 

 the train at 3i miles was actually less than it was at 31 miles. In fact, 

 there were frequent iustances iu both columns of the resistance diminish- 

 ing when the velocity increased : the resistance at a given velocity was 

 often no greater than, and often less than, the next less velocity. 



Mr. Scott next considered the physical causes which would account for 

 the new term. A most important element of resistance was the concussion 

 sustained fay the wheels of the carriages as they passed over the joints of 

 the rails. This concussion produced a noise aud vibration of the earth, 

 which was sometimes perceptible at extraordinary distances. It was fre- 

 quently so great as to derange the position of the rails, aud was a constant 

 cause of wear and tear of the road. This was one most important ele- 

 ment of his new term. Another was the lateral abrasion of the flanges of 

 the wheels against the rails — this abrasion representing, of course, a loss 

 of force. Another loss was occasioned by the vertical movement of the 

 carriage.s on their springs, which was, from the imperfect elasticity of the 

 springs, equivalent to a loss of vis cica. There were other elements of his 

 " remainder" or new term, but these were the principal. In conclusion, 

 Mr. .Scott Russell stated that all the experiments were not his own ; that 

 some of them were the previous property of the Biiti?h Association, made 

 on trains descending inclines by their own gravity. The dynamometer 

 %vhich he had employed was an excellent one, made by Morin ; it was 

 placed between the tender and the first carriage. He exhibited the dia- 

 grams which had been actually drawn by this dynamometer, aud which 

 were traced in red ink by a camel's hair brush. 

 The following is the table referred to : — 



Velocity in Sliles Resistance by experiment Kesistance by for- 



per liour. in lbs. {)er ton. uuila in lbs per ton. 



h hi) i-T 



14 12 « 13'9 



■Ji) 16-5 157 



;il 



33 

 34 



3.5 

 .11) 

 37 



3:i 



41 

 4.1 

 4fl 

 47 

 50 

 .'■I 

 ■<X 

 t>l 



25-4 

 227 

 2?7 

 17-3 

 22.4 

 25-.5 

 18-2 

 31-6 

 19'6 

 21-0 

 23-3 

 33-1 

 36-3 

 23-0 

 421 

 54-8 



Dr. RoiiiNsd.N said that though great credit was due to Mr. Scott Rus- 

 sell for putting the invetlii;ation in an improved form, there were still seve- 

 ral elements of resistance which he thought ought to be taken into con- 

 sideration. He then proceeded to write on the diagram-board a formula, 

 of wdiich each term explained some kind of resistance, which he explained 

 as he wrote down the corresponding expression. The loss from concus- 

 sion at the joiuts should vary as (velocity)^. The resistance to the motion 

 of the wheels, regarded as separate bodies acted on by the air, was two- 

 fold ; aud arose, first, from their rotation, secondly, from their longitudi- 

 nal motion. The one resistance would vary as the velocity ; the other, as 

 the square of the velocity. In like manner, the resistance from the air lo 

 the carriages themselves was composed of two terms; the one representing 

 the resistance to the front of the train, the other lo its sides. 



Mr. Sraup thought that Jlr. .Scott Kussell ought to have taken into ac- 

 count many contiugencies w bich occurred in practice, such as the efl'ect of 

 curves in the railway. The axlc-fnction was far greater in some carriages 

 than in others. 



Blr. l.'oiititis confirmed the latter statement : be had constantly observed 

 that the w heels of carriages were out of their proper place, and consider- 

 ably inclined to the axle. In many cases which he had examined, the 

 divergence from the perpendicular was so great, that the resistance must 

 have been enormous. The learned professor did not, however, appear 

 aware that Mr. Russell's formula applied lo the resistance of the train 

 only, indepeiideully of the engine : nor did he seem to have a very clear 

 idea of the line of argument pursued, for he look occasion during the dis- 

 cussion to obserie that Mr. Russell had proved everything experimentally, 

 aud that " he had not taken anylhiug for granted," whereas he had taken 

 for granted an integral point of his argument, namely, that the accuracy of 



