1839. 



THE CIVIL KNCilNKKK AND A U( I IITI-XTS JOURNAL. 



.383 



111 offering llicse few aiul liuiitei observations on a small part of tlie uiiper 

 Clyde, I regret exceedingly that it lias not been in iny power at jireseiit to 

 bring luuler review the iiuprovemeut of tbe lower water-basin of tbe Clyde, 

 from the Jamaica-street Bridge to Port-Cilasgow ; the natnre of the wide 

 expanse of the tidal estuary, as well as the narrow parts ; the eanse of the 

 formation of the sandbanks and shoals opposite Port-Glasgow and Greenock; 

 the basin of the Leven, the Cart, and the Kelvin, and their influence on the 

 slii|) channel. And as regards the upper Clyde, I more particularly regret 

 not Ijeing able to give the souudiugs, levels, nature of the bottom of the river, 

 and the form of its bed, according to the various strata ; the limit of tbe high 

 floods, and those of low water, during summer and winter ; the mode of se- 

 curing the sides of tlie river when deepened ; the area of the dry basin of 

 the Clyde; the quantity of water falling within it in a year; the average 

 daily (piantity passing through it at the city of (ilasgow ; the quantity of 

 alluvium held in suspension by its waters ; the limit to wiiicli the sea-water 

 reaches, and ceases to be sensible to the taste ; the mean liych'aulie depth at 

 numerous places. These are subjects highly instructive to the engineer in 

 devising pUins for the improvement of estuaries, rivers, and harbours situated 

 witliin them. I hope I shall be able, at no distant period, to submit to the 

 trustees a detailed report upon the dry and water basins of the Clyde. Those 

 basins will be found the most interesting in Scotland, whether as regards 

 their physical structure, the immense and almost inexhaustible mineral 

 wealth which they contain, or their capability of improvement in the tidal 

 navigation, combined with the probable connecting ramifications of railways. 

 All those matters are intimately connected and blended with the rising com- 

 luercial prosperity of the city of Glasgow, its port, and its river. 



I am obliged to bring under your consideration, tlie great and pressing 

 necessity which exists of affording immediate accommodation to a large class 

 of steamers, built or now building, and which may require to be furnished 

 with engines. My feeUng on this subject is so great, that I cannot refrain 

 from hoping, that this branch of mechanical industry will receive at the 

 hands of the river trustees, all that protection to which it is so justly entitled, 

 forming, as it docs, a branch of national industry, not only highly creditable 

 to Scotland and to the genius of her people, but whicli employs thousands of 

 her mechanics — diffusing wealth among numerous classes, and calling into 

 full activity that peeuUar mechanical and inventive power, which has ex- 

 tended the fame of this land and its iuhal)itants through the most remote 

 and distant regions of the earth. 



This accommodation for steamers of tbe largest class ought, as soon as 

 possible, to be afforded, although it should only consist of a simple exca- 

 vation on the side of the earthen bank of the Clyde, bordered with a small 

 cheap wharf, constructed of home-grown timljer ; and this might be done 

 below the present quay walls, without interfering with the present shipping 

 accommodation, situated at the lower reaches at tbe entrance to the Harbour. 



William B.yld. 

 Glaxffow, 30M Jul;/, 1839. 



ON RAILWAY CONSTANTS. 

 By Dr. L.\rdxer, L L.D. 

 Jbntracf of a Paper " On Railway Cotistantx, and Resutance of Air to 

 Railway Trai)iA-,*' read at the last Sessioius of the Britiafi .hsociatioii held 

 at Birmin/jliam, for w/iich tee are indebted to the utile reports of tlie 

 " Atltenteum.^' 



At the Liverpool meeting of the Association, in the autumn of 1837, an 

 inquiry was undertaken by Dr. Lardner, in connexion with some other mem- 

 bers of the Association, with a view to determine the mean numerical value 

 of what were called Railway Constants by analogy to similar numerical 

 quantities in other branches of science and art. Constants is a technical 

 name given to certain quantities, more especially in astronomical and phy- 

 sical science, which enter largely into general calculations. As an example 

 of these, may be mentioned, the height through wliich a body falls in a 

 second of time ; tbe length of a seconds pendulum ; the ratio of the eireum- 

 ference of a circle to its diameter, and so on. A project of a magnificent 

 kind was formerly suggested by Mr. Babbage, for the determination of the 

 mean numerical values of the " Constants of NatMe and .4rt." Among 

 these quantities w-hich enter railway calculations, that which is of the greatest 

 practical importance is, the number by which is ex])ressed the proportion 

 which the tractive power, necessary to move loads on a railway, bears to 

 the weight of the loads it moves. The great importance of this will he 

 readily perceived, if it be considered that such is in fact in a great degi'ee 

 the ratio of the cost to the work done. Accordingly, the first point to 

 which this inquiry was du-ected was, the solution of that problem. 



The resistance opposed by a raUway train, to tbe power which draws it, 

 arises from several causes; 1st, the friction or attrition of tbe axles of the 

 wheels in their bearings ; 2nd, the rolling friction of the tires of tbe wheels 

 upon the rails ; 3rd, the resistance of the air to the train moving through 

 it. These are all the causes which produce resistance in the train moved. 

 But independently of these, there are resistances peculiar to the engine, 

 arising from the friction, or attrition of the various parts of tbe machinery 

 which are in motion, and which suffer a pressure or .strain, depending on 

 the resistance of the load drawn ; also tlie re-action of the steam, escaping 

 from the blast pipe on the other side of the piston, and other similar causes. 

 But to simplify the inquiry in the (irst instance, the resistance of the engine 



was put aside, and the investigation was directed exclusively to tbe resist- 

 ance of the train. Various methods presented themselves for testing this. 

 Tbe most direct method was the application of an instrument called a dyna-c 

 moineter in front of the train, by which the train could be drawn, and which 

 would afford a direct measure of the force with which it was so drawn. 

 This method, however, was subject to several objections. It was found 

 that tbe surface of rails, commonly regarded as level, were really subject to 

 variations of inclination through small distances, which produced upon the 

 dynainometer suihlen jerks, which caused its index to play between such 

 extreme limits as to render it imjiossible to arrive at any useful mean of 

 its indications. Besides this, if such an instrument were used to estimate 

 the resistance of a train, moving with any considerable speed, it must neces- 

 sarily be placed between the engine and the train, and would therefore show 

 only a modified eft'ect of tlie atmospheric resistance ; inasmuch as the engine 

 would have already encountered and removed a portion of that resistance 

 before the instrument could be atfected by it. Numerous experiments were 

 nevertheless made with siicli instruments, and it was not abandoned luitil 

 its failure was rendered practically manifest. Another method occurred to 

 Dr. Lardner for determining that portion of the resistance which is due to 

 friction, by attaching to an engine such a load as the engine is capable of 

 moving, at a slow uniform velocity, up a given inclined plane, ami then 

 taking the same load to a more steep ineUned plane, and detaching from it 

 as many waggons as would en.ible it to move up the steeper inclined plane 

 at the same slow speed as that at which it moved up the less steep inclined 

 plane. Under these circumstances it might be safely assumed, that the 

 absolute resistance to the engine would be in both cases the same, and the 

 difference of the gravity of the two inclined planes would, in such a case, 

 by the aid of mathematical principles, and by formula?, which Dr. Lardner 

 eonstiiicted, give the resistance due to the waggons detached in passing from 

 the less to the more steep inclined plane. This method would be attended 

 with the advantage of giving a result, in a great degree, free from the atmo- 

 spheric resistance, and therefore would furnish a near approximation to the 

 value of the friction, properly so called. As the motion would be slow, and 

 a part of the train would be in front of the waggons detached, the atmo- 

 spheric resistance would necessarily have but a very slight effect. As no 

 opportunity, however, presented itself of executing experiments upon this 

 principle, lie did not occupy the time of the Section in enlarging upon it. 



After much consideration, he arrived at the eouelusion, that the method 

 of investigation which was calculated to give the most satisfactory results 

 as to the resistance of railway trains was, by observing their motion down 

 steep inclined planes. This method bad been already practised, and its 

 principles wdl he easily rendered intelligible. If a body be placed on a 

 steep iueliiied plane and allowed to descend it by the force of its gravity, its 

 motion down the inclined plane would be accelerated. If the causes of 

 resistance aflfecting the body were uniform in their effect,- and independent 

 of the velocity, then the motion of the body dowm the inclined plane would 

 be uniformly accelerated, just as a body falhng freely and perpendieiUarly 

 by gravity would, apart from the atmospheric resistance. By being uniformly 

 accelerated, is meant this, that the increase of velocity which takes place 

 every second of time is the same. Thus, whatever velocity is acquired by 

 the body at the end of the 1st second, having descended from a state of 

 rest, twice that velocity will be acquired at tlie end of the 2nd second, and 

 thrice that velocity at the end of the 3rd second, and so on. It is evident, 

 therefore, that a body, subject to such acceleration, would go on increasing 

 its speed without any limitation. .\s the intensity of the force of gravity 

 is exactly known, and as tlie effect produced in diminishing that intensity by 

 a plane of given inclination is a matter of easy and exact calculation, nothing 

 can be more certain than the computation of the motion which a body woidd 

 have down an inclined plane if that body were subject to no resistance. 

 Now, if it be subject to resistance, the comparison of its actual and observed 

 motion, with the motion which it would have, being subject to no resistance, 

 computed, as just explained, ought to supply means of determining the 

 amount of the resistance ; but to do so it is necessary to know, to a certain 

 extent, the law of the resistance which is in ojieration. 



The resistance arising from attrition or friction, whether it be of sm-faccs 

 rubbing one on another in the manner of a sledge, or rolling one on another 

 as the tire of a wiieel rolls upon a rail, or subject to the kind of attrition 

 which takes place between the axle of a wheel and its bearings, have been 

 all submitted to most elaborate and careful experimental inquiry ; and the 

 laws of the resistances, arising from these, have l)een fully and clearly de- 

 veloped. The question of friction was foniieiiy investigated by Coulomb, 

 Ximenes, Viiice, and others ; but recently a more extensive and valuable 

 series of experiments on the subject, than was ever before executed, ha•^ been 

 made, under the order of the French government, by M. Morin, and their 

 details made public. The results of these fully corroborate the laws which 

 had ah-eady resulted from the inquiries of the philosophers who before ex- 

 amined the subject, which laws are as follows : — 1st, the resistance arising 

 from friction, whether of rubbing or rolling, or that between the axle of a 

 wheel and its bearings, are, wiieu other tilings are the same, independent of 

 the velocity; 2nd, other things being tlie same, tlicse resistances are directly 

 proportional to tbe amount of pressure on the I'ubbiug surfaces, and inde- 

 pendent of the magnitude of these surfaces. To tlicse laws, taken within 

 practical limits, there can scarcely he said to be an exception. The extreme 

 cases which become exceptional, having no aiiplication whatever to the 

 present inquiry, it will not be necessary to regard tlicni. 



2 I 



