20 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[January, 



niU- it will be gn-ntpst where most needed — for iiistunce, when a light 

 su|)eistniclure is lieddeil in clay, in a northern climate. 



'I'he (listribntion of (he weight ol the engine on S wlieels, instead of 

 throwing three-lifths or more on 2 wheels, is therefore intimately con- 

 neeteil \\ ith the conliiiuance of a cheap superstrnclure, which has been, 

 ane will be, even with the present engines, extensively nsed in many 

 parts of the coimtry, where capital and good mechanics are scarce and 

 timlier and axe-men abnndant. Owing to the increased deflection of 

 the wooden rail there will of coiu'se be a loss of power, bnt this, even 

 now not verv important, will be reduced one-half by the distribution 

 of the weight on all the wheels, besides which the only fear is, that 

 full loads will only too seldom be obtained for the lightest class of 

 engines, bnilt on this principle, even with grades of from 40 to GU feet 

 per mile. 



I have been informed by my friend Mr. E. F. Johnson, (the other 

 engineer alluded to in a preceding paragraph) that a trial of this new- 

 engine has been made, and that it appears to work well. Time and 

 ex])eriencc can however alone develop its powers, expose its defects 

 and give unerring proof of its general and successful adoption. But 

 sn])posing, what is most unlikely, that this experiment should lead to 

 no useful result, we have still the S wheeled engine of Messrs. East- 

 wick and Ihirrison (or Mr. H. R. Campbell?) which is capable of 

 ih-awing \W tons nett up an inclination of GU feet per mile, and wliich 

 will be less injurious to the su])erstructure than the ordinary S or '.) 

 Ions English or American engine. 



An extremely interesting and still more useful experiment may very 

 easily lie made with the engine of Messrs. E. & II., or still better, with 

 that of the Messrs. titevens. Remove the couplings so tliat the engine 

 may act by the adhesion of one pair of wdieels only, and ascertain the 

 maximum load without slipping the wheels ; then couple 2 pair of 

 wheels, repeat the experiment and the increase of load will show the 

 value of the improvement of Messrs. E. & H. With the S wheeled 

 engine, 4 such experiments should be made, by which the advantages 

 of this mode of construction would be determined with considerable 

 accuracy, and all requisite information afforded on this vital, and 

 hitherto much neglected principle, of working by the adhesion of 

 more than '2 wheels. 



The successful introduction of engines with the weight distributed 

 equally on, and acting by the adhesion of 8 wheels, would form an era 

 in the hisloiy of railways in tlie United States, second only, to that 

 which determined the general question of the practicability of loco- 

 motion by steara — in other words, that which gave its present im- 

 portance to this unrivalled mode of comniunication. 



ON THE DRAUGHT OF CARRIAGES AND ON SECONDARY 

 FRICTION. By M. Dupuit, C. E. 



(Translated from the French.) 



1. Draught of Carriages. 



By allowing wheels of diameters varying from 4 feet to 7 feet to 

 run down an inclined plane, and by measuring the spaces run over on 

 horizontal ground, by virtue of the fall, we find that they are propor- 

 tional to the scpiarc roots of the diameters, and height of the fill, 

 whatever may be the weight or breadth of the tire. From this we de- 

 rive the four following laws : — 



The draught is proportionable to the jiressure; 



independent of the breadth of the tire; 



independent of velocity ; 



in inverse ratio of the sijuare root of the diameter. 

 These four laws are the same as established by the author of this 

 paper in his Essay on the Draught of Carriages, published in ls37, 

 and which lie had found by means of a simple dynamometer. The 

 three last are completely in contradiction to those whicdi M. Morin 

 deduced from the experiments made with his <lynainometrical ap- 

 paratus. 



2. Secondary Friction of Rolling. 



The resistance which opposes the rolling of a body is nothing 

 more than the molecular action, wdiicli fakes place on contact. This 

 reaction, always equal to the pressure, passes by the normal when the 

 boily is at rest, and advances in front by a certain quantify 5 when it 

 rolls; it therefore resists the rolling with a power marked F5. 



Following up this single property of solid bodies, of being an assem- 

 blage of molecules in eipiilibrium, we arrive at the following expres- 

 sion of the friction of rolling : 



which gives all the properties of this resistance in friction with one 

 of them. If we follow up that of being proportional to the pressure, 

 which is not denied by any one, we rediscover the three other laws 

 pointed out above, wliiidi establishes a mutual confirmation of the ex- 

 periments and the theory. The friction of rolling being an immediate 

 consequence of the imperfect elasticity of bodies, we may, by its proper- 

 ties, ascertain those of elasticity ; wdience we deduce the following: — 

 When we subject the surface of a body to pressure, we obtain under 

 this pressure a certain instantaneous sinking t', which reduces itself at 

 last to a slight impression f, when the pressure ceases. This impres- 

 sion f is proportional to the square root of the definitive sinking «'. 



g 



The friction of rolling is proportional in the relation of in such 



l/ ('• 

 a way that it is determined by two coefEoients which define the elas- 

 ticity of a body. For want of these two coefficients we may substi- 

 tute two others. Knowing 1st, The friction of iron upon iron, and of 

 iron upon marble, we may deduce immediately from it the friction of 

 iron upon copper. Thus for twenty surfaces, forty coetlicients would 

 be enough to determine 3S0 to which their combinations two by two 

 would give rise. 



When two curved surfaces roll one ujion another, the result of the 

 molecular action, eqnal to the pressure, no longer passes in the direc- 

 tion of the normals, but parallel in the direction of the velocity, at a 

 distance, proportionable to the square root of the product of the rays 

 or radii of curve, divided by their sum or ditlerence, accordingly as 

 they are both convex or one of them concave. 



This formula resolves all the problems relating to the calculation of 

 the resistance to roUing, and it is capable of numerous practical ap- 

 plications. 



3. Action of Wheels upon Roads. 



Although the draught is to a certain point the expression of the de- 

 rangement of the materials of the road, it is quite inaccurate to con- 

 clude therefrom that the degradation is proportional to the draught. 

 By keeping the roads constantly •ven, which is always possible, the 

 passages are divided uniformly on the whole pavement;* then the small 

 displacements which they occasion destroy each other. Besides in a 

 number of cases the result of the passage of a carriage is to produce 

 an improvement. In a good system of road making, the roads are 

 never degraded, whatever may be the traffic, they are only worn. It 

 cannot be a question, in a road law, of having good or bad roads, but only 

 of spending more or less for their maintenance. Every restriction of 

 the freedom of a road is to the carriers a cause of increased expence, 

 greater than the saving which might be made in the expences of keep- 

 ing up the roads. 



v/ 



2R V«L4/2K/' 



PAPERS ON ARTESIAN WELLS. 



Obserralions undertaken for the purpose of estimating the height to which 

 the IVaier might rise in the H'^ell lured in the Jjbattoir de Grtnelle, 

 1)1/ M. Walferdin. lltad before the Academic des Sciences. 



The water w Inch springs up from Artesian sources does not always 

 rise above the level of the soil, sometimes it is several yards lower, 

 and in this case it is brought to the surface by mechanical means ; 

 sometimes it reaches it ; and at other times it rises more or less above 

 the surface. That as it is well known depends upon the dift'erence of 

 height at wdiich the water arrives across permeable strata, between 

 the impermeable strata which contain it, and that of the point at 

 which they ascend. 



I have considered that in the advanced state of the borings at Gre- 

 nelle, that it might be useful to compare the heiglit at which are 

 filtered the waters which form the supply which is sought under the 

 Paris basin, and that of the surface of the soil at Grenelle. 



If, by ascending the natural slope which the waters follow to the 

 surface of the earth, we seek the chalk boundary in the southwest di- 

 rection, we find it cease in the neighbourhood of Troyes. Then the 

 gault marls and clays which the bore now crosses at Grenelle succeed 

 the chalk, and at about eleven miles from Troyes, near Lnsigny, the 

 green sand appears, and forms the orifices by vvhicli the waters begin 

 to filter. 



The height at wdiich the waters thus penetrate the sands being near 

 Lusiguv, 13:") or 140 yards above the level of the sea, and that of the 

 surface at (irenelle'4U yards only, it follows that when the bore 

 reaches the layer of water at Paris, that the water will rise sensibly- 

 above the surface. 



* It must be remembered that M. Dupuit is talking of French roads. — Ed- 



