1841.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



30.5 



This premised, when Mr- Parkes refers to tlie average velocity of 

 the whole trip, to value the pressure in the cylinder, as that velocity 

 is 20 miles per hour, and as the vaporization at the same time is GO 

 cubic feet of water per hour, he finds, for tlie ratio of the volume of 



1478 X 20 

 the steam expended to the volume of water, — -— =r 492-7. Con- 

 sequently, recurring to the table of the relative volumes of steam under 

 different pressures, he obtains for the corresponding total or absolute 

 pressure 5t)-06 Hi. per square inch; and deducting the atmospheric 

 pressure, he obtains for the effective pressure, 4 1-95 tti. per square 

 inch. 



But to show that this mode of calculating, from the average velo- 

 city, can only lead to error, let us suppose that, by reason of the divers 

 inclinations of the portions of the railway, the first 15 miles liave been 

 traversed in half an hour, and the other 15 miles in an hour, which 

 still makes 30 miles in an hour and a half; as 30 cubic feet of water 

 will have been vaporized in the first half hour, or during the passage 

 of the first lo miles, and GO cubic feet of water during the next hour, 

 or in the passage of the last 15 miles, it is plain that the volume of 



1478x 15 

 the steam will have been respectively in each of those times — = 



1478 X 15 



739 first, and afterwards = 3G9-5. Whence results, ac- 



uO 



cording to the table, that the effective pressure of the steam will have 

 been successively 21-62 and (J2-9.'> Iti. per square inch. 



Thus, during the first half hour the effective pressure will have been 

 21-02 It). ; during the second half hour it will have been G2-95 It;., and 

 during the third again (i2-9.">it). Consequently, taking account of the 

 time during which the pressure has had these respective values, it is 

 plain that the mean effective pressure in the cylinder will really have 



21-62 4- 62-95 + G2-95 ^ . , , 



been :, =:r. 49-1/ It), per squire inch, and not 4 1 95 



o 



lb. per square inch, as given in Mr. Parkes's calculation ; which, by 

 the fact, supposes all the portions of the tri^i to have been performed 

 in equal times. In this case, therefore, which has nothing in it but 

 what is very ordinary, there would be an error of 7-22 tb. per square 

 inch out of 41-95; that is an error of more than i on the effective 

 pressure of the steam. It is evident that the calculation, such as Mr. 

 Parkes makes it, is exact only for portions of road composed of one 

 inclination, or travelled with nni/onit velocity, and that it cannot apply 

 to the total passage of a line composed of different inclinations. For 

 further elucidation on this head, we refer to chapter XVII., relative 

 to inclined planes, of our Treatise on Locomotive Engines, 2nd edition, 

 and to chapter XII. of the same work, in which all the experiments 

 considered by Mr. Parkes are calculated. 



2nd. We have just shown the first error which Mr. Parkes intro- 

 duces, as a fundamental basis, in his calculation of the pressure of the 

 steam in the cylinder. But he does not stop there. In the table of 

 experiments on the vaporization of the engines (Treatise on Locomotive 

 Engines, page 175 of first edition, and page 253 of second edition), we 

 have given tue average velocity of the engines during each trip ; and that 

 velocity is obtained simply by dividing the whole distance performed, 

 by the time employed in performing it, as is seen in the table in ques- 

 tion. It would be natural then for Mr. Parkes, who, as has been said, 

 is satisfied with average velocities in his calculations, to take those 

 which are given in the table ; but instead of that, he augments almost 

 all the velocities about ^. Thus, for instance, the Vulcan, which tra- 

 velled 29-5 miles in 1 hour 17 minutes, and whose average velocity in 

 consequence was stated to be 22-99 miles per hour, had, according to 

 Mr. Parkes, a velocity of 26-90 miles per hour. The velocity of the 

 Vesta rises from 27-23 to 31-60 miles per hour, and so of the others 

 ("table viii., col. 10 ; table xiii., col. 9 ; table xvi., col. 2). The critic 

 falls into this new error because, in the Treatise on Locomoli re Engines 

 (page 324 first edition, and page 311 second edition), in speaking of 

 fuel, it is said that, when the engines ascend without help the inclined 

 planes of the Liverpool and Manchester Railway, the surplus of work, 

 thence resulting for them, equals, on an average, the conveying of 

 their load to ^ more distance, and Mr. Parkes logically concludes from 

 this that the velocity of the engine must be by so much increased (pages 

 86, 112). So that if an engine perform 1 mile in 4 minutes, ascending 

 a plane inclined -^, which renders nearly five-fold the work of the 

 engine, it would follow, from this calculation, that the velocity would 

 not have been 15 miles per hour, but 15 X 5 =r 75 miles per hour, 

 since the quantity of work done would have been five-fold ! Mr. 

 Parkes's error proceeds from his having applied to the velocity a cor- 

 rection which refers only to the !Dor/: done, and, as a consequence, to 

 the corresponding consumption of fail. 



But on examining what effect results from this substitution of the 

 imagined velocity of Mr. Parkes for the observed velocity, it will be 

 remarked that whenever an engine is obliged to ascend without help 

 one of the inclined planes of the Liverpool and Manchester Railway, 

 it exerts at that moment, as we have said, an effort five times as great 

 as upon a level, and draws its load less rapidly. One would deem it 

 then allowable to conclude, that the average pressure of the steam in 

 the cylinder must be augmented, since during a certain portion of the 

 trip, the effort required is greater, and that the useful effect per unit 

 of time must be diminished, since during the same time the useful load 

 is drawn at less velocity. But no. Mr. Parkes's calculation, by aug- 

 menting, then, the apparent velocity of the engine, demonstrates that, 

 in this case, the average pressure in the cylinder becomes on the con- 

 trary much less, and that the useful effect becomes much greater. So 

 that the error committed produces itself here in the two opposite 

 ways. 



With these elements JVIr. Parkes establishes the /i/o't of his cal- 

 culations and tables, to the very end of his paper (table viii., col. 10; 

 table ix., col. 19; table xiii., col. 9 ; table xiv., col. 2 : table xvi., col. 2); 

 and as, to augment the evil, this pretended correction is made only on 

 one portion of the experiments, namely those in which the engines 

 were helped up the inclined planes, without being made in the other 

 cases, there results an inexplicable confusion in all the calculations. 

 Thus, it happens that Mr. Parkes's determination of the volume and 

 pressure of tlie steam consumed by the engines (table ix., col. 26, 29), 

 the horse power produced per cubic foot of water vaporized, or the 

 quantity of water employed to produce one horse power (table x., col. 

 44, 45, 49, &;c.), the momentum generated per pound (table xiii., col. 

 1 1, 12 ; table xiv., col. 9, 10, 1 1), and all the consequences thence de- 

 rived are in every way erroneous. 



To show by a particular example, the fallacy of the results to which 

 Mr. Parkes has been led by this wholesale and faulty way of calculat- 

 ing, we need only refer to the two experiments of the Flhy, which he 

 extracts from our work on locomotive engines. He pronounces, " with 

 certainty," (page 12s), these two experiments to be erroneous, as ex- 

 hibiting an engine performing more work at 23 than at 215 miles per 

 hour, in the ratio of 2 1 to 19. Now, to arrive at this conclusion, Mr. 

 Parkes first takes the velocity of the engine, not at 18-63 and 19-67 

 miles per hour, as given from actual observation, page 175 of the first 

 edition, and pages 253 and 392 of the second edition of our Treatise 

 on Locomotive Engines, but at 21-79 and 23 miles per hour (table xiii., 

 col. 3). Secondly, in comparing the work done in the two trips, he 

 does not take into account that the first of the two trips has been made 

 from Manchester to Liverpool, and the second on the contrary from 

 Liverpool to JIanchester. But there is a general rise of the ground 

 from Manchester towards Liverpool, and from that circumstance, the 

 gravity opposes more resistance in that direction than in the contrary 

 one. Thus it happens that a less train carried on the line from Man- 

 chester to Liverpool, may require from the engine, a greater quantity 

 of labour than a heavier train carried in the opposite way. In effect, 

 Ijy referring to pages 5ul and 504 of the second edition of our work 

 on locomotives, it will be found that in the two experiments under con- 

 sideration, the work done by the Fluiy, in carrying the two loads of 

 43-8 and 51-16 tons, besides tender, from Manchester and from Liver- 

 pool respectively, to the other end of the line, was 



13-S tons, from Manchester to Liverpool, equal, 



gravity included, to - - - 1964 tons to 1 mile. 



5 1- IG tons, from Liverpool to Manchester, equal, 



gravity included, to - - - 1837 tons to 1 mile. 



We see, therefore, that when we take an account, as we ought to do, 

 and as Mr. Parkes has not done, of the surplus of labour caused by 

 gravity, the work required of the engine is in reality more in the first 

 case than in the second, although the load itself is less. Consequently 

 the engine ought to have accomplished the second trip in less time or 

 with a greater average velocity than the first, which in fact it did, and 

 which had led Mr. I'arkes to pronounce with such " certainty" the 

 experiments to be erroneous. 



This example shows that the calculation of Mr. Parkes, made with 

 an erroneously averaged and exaggerated velocity, in which, more- 

 over, he omits the gravity on the inclined planes, the resistance of the 

 air, the friction of the engine, and all the other resistances really op- 

 posed to the motion, leads him to a very inaccurate measure of the 

 work performed by those engines ; and this refers to the whole of the 

 results obtained, table ix., col. 29 — 32; table x., col. 41 — 50; table 

 xiii., col. 11, 12; table xiv., col. 9, 10, 11; table xvi., &c., and also to 

 his comparison of locomotive and stationary steam engines, which we 

 shall notice further on. 



3rd. After having calculated very exactly, as we have shown, the 



pressure of the steam in the cylinder, Mr. P.irke3 compares the result 



, which he has obtained, with the total pressure on the piston resulting 



2 T 



