188 APPENDIX. 



" regulate the velocity, and no calculation which shall exclude that element can possibly lead 

 " to the true result ; consequently the preceding formula cannot be exact. 



" This is why, in applying this formula to the case of an ordinary locomotive engine of the 

 " Liverpool Railway with a train of 100 tons, the velocity the engine ought to assume is found 

 " to be 734 feet per second, instead of twenty miles an hour, or 30 feet per second, which is 

 " its real velocity." 



On reference to the article alluded to, it will at once be perceived that these remarks are 

 based entirely on M. Pambour's own misconception of what Tredgold has really given. The 

 formula in question has no reference whatever to the velocity of the piston. It will be 

 observed, that instead of the velocity of the piston, it is distinctly given as the velocity of the 

 steam through the steam pipe, and that the sole object of Tredgold's inquiry is no velocity at 

 all, but merely the determination of the requisite aperture of the steam pipe ! This sufficiently 

 accounts for M. Pambour having puzzled himself with the case of the Liverpool Railway 

 locomotive engine, and leaves us with the full assurance that Tredgold was too well acquainted 

 with the nature of his subject to allow himself to wander so immeasurably from the truth as 

 M. Pambour had supposed. 



We have not made the preceding remarks with any view to the disparagement of what the 

 Chev. de Pambour has done towards our knowledge of the steam engine, which we by no 

 means hold to be unimportant: he is evidently well versed in the practical nature of its 

 action ; he has, doubtless, furnished the best set of experiments on locomotive engines, and 

 his general remarks embody much sound and valuable information on that subject. We 

 cannot, however, admit that he has made any important advance in the mathematical 

 theory of the steam engine, much less that he has brought it to absolute perfection ; and so 

 long as the theory remains incomplete, we must continue to make certain estimations by 

 assumed and approximate rules. It is fortunate, however, that the theory of transmission 

 from the boiler to the cylinder ' and other points, which Tredgold left untouched, and which 

 are still open for future investigation, are matters that may be practically dispensed with. 



V. PADDLE WHEELS. 



It was originally our intention to have. entered rather fully into the theory of the action of 

 paddle wheels ; but this has been rendered almost wholly unnecessary by the valuable con- 

 tributions of Mr. Barlow and Mr. Mornay, who have each discussed the subject with great 

 ability and at considerable length. Mr. Barlow's paper is interspersed with numerous ex- 

 perimental results arranged in the convenient form of tables, and he has successfully applied 

 these results to the solution of various practical questions of great importance. Mr. Mornay 

 has classified the various kinds of wheel, and treated the subject of their capabilities and 

 relative merits with an attention to mathematical precision much to be desired, but which we 

 think, in some cases, unfortunately, to be beyond the practical nature of the inquiry, since 

 the action of the floats must always be affected, in some degree, by the disturbance of the 

 fluid through which they have to pass, more particularly when the velocity of the vessel is 



1 It would be highly desirable to have a series of well-conducted experiments on this point. 



