371 



THE CIVIL I:NT;INEER and ARCHITECT'S JOURNAL. 



[November, 



is previously very little reduced by expansion. Mr. M. ought to have 

 told us what degree of expansion he alludes to, as that altogether de- 

 cides the extent of diminution of pressure by expansion, and when he 

 considers that at this part of the stroke the motion of the piston is 

 very slow, and the motion of the valve very quick, he will be able to 

 see that the contemplated effect of this part of the stroke is consider- 

 able. Mr. M. next states that the elfect of the coin|)ression of the 

 educted steam is so small that it miglit be di^regarded. I am sorry to 

 see Mr. M. make sucli a remark, after having read the last paragraph 

 of my paper, as the effect of this compression is altogether dependent 

 on the extent of the cover ami the lead. 



Mr. M. in his concluding paragraplis has got into a sad maze, he 

 supposes that I put the initial pressure of the steam in atinosiiheres 

 equal to the area ot the piston, and founding upon this most wonderful 

 C(|uation some beautiful deductions, he states that "these results show 

 the manifest absurdity of the supposition." If Mr. M. would substi- 

 tute for the letter (s) the figure (."i), he would immediately be relieved 

 from a multitude of his diHicullies, and you are able to say whether 

 the letter or the figure is in my ]>aper. With tlie assistance of these 

 remarks, perhaps Mr. M. will find out that the paper which he states 

 requires " revision "and correction'' virtually less requires either than 

 his own letter. 



And I am, your obedient servant, 



J. G. Lawrie. 



Carlsdyke Foundry, Greenock, 

 OcioberG, 1811. 



SiR^— I regret exceedingly that any expressions contained in my 

 letter concerning Mr. Lawrie's communication on the Economy of Fuel 

 in Locomotives consequent to Expansion as produced by the cover of the 

 Slide-valve, and which you favoured witli insertion in your Journal for 

 this month, should have given that gentleman offence, as I perceive by 

 his letter, which you were kind enough to send me fur perusal, to have 

 been the case. I therefore take the earliest opnortunity of assuring 

 him, through the medium of your columns, that such was perfectly 

 unintentional, and also of acknowledging two errors into which I had 

 fallen, though not altogether by my own fault, as I think I shall now 

 show. lu the first place 1 objected unjustly to his equation 



in which he merely stated (s) to be the area of the piston, having in- 

 advertently omitted to mention at the same time that the area of 

 piston required to use the same quaiiity of steam without ex[)ansion 

 was considered as unity, so that (s) is not the absolute, but the relative 

 area of the piston, or the ratio of its area when the steam is cut off 

 after the piston has travelled a distance (a') to what it would be if the 

 steam were not cut off at all ; and I think Mr. Lawrie will allow that 

 any other reader v\ou!d be liable to be led into the same mistake as 

 myself through this oversight on his jjart. 



The second error which I have to acknowledge is the having attri- 

 buted to Mr. Lawrie the absurd hypothesis that the safety valve be so 

 loaded that (p) is equal to (s) (whicli he would have seen to be so 

 printed in the Journal, if lie had taken the trouble to refer to it before 

 writing his letter), whereas I ought to have supposed it to be a mis- 

 print, as in fact it is, and I now see clearly that the (s) was intended 

 by Mr. Lawrie fur a (5). 



I shall now endeavour to convince Mr. Lawrie that the rest of my 

 remarks were not thrown out without due consideration. 



First then, although a school boy might have been able to find out 

 that the two expressions alluded to in the first part uf my former com- 

 munication iveve identical, if the problem had been proposed to him, 

 yet 1 should very much doubt whether he would see it at a glance, 

 without having any previous suspicion of the fact ; but, having dis- 

 covered it in tlie course (>f my investigation (for which discovery, 

 however, 1 beg to be understood to claim no particular merit), 1 thought 

 it would lie useful to communicate it to your readers, since it saves 

 the trouble of calculating the same (|uantity twice over by two dif- 

 ferent methods. 



1 have now to return to the equation already quoted above, in the 

 second member of w hich the factor ( I) expresses the area of the pis- 

 ton wlien there is no expansion, and (s) its area when the steam is cut 

 off at (a'), the same quantity of steain being admitted during the 

 stroke in both c.ises ; and with this explanation 1 acknowledge the 

 correctness of the above equation, except inasmuch as tln^ waste space 

 at the end of the cylinder, which has to be filled with steam as well as 

 the length fa') (.f the cylinder, li.is been omitted in the account (and 

 this Mr. Lawrie must excuse me from admitting to be rtduced lo almost 

 nothing), and also inasmuch as the pressures (p) and (/) are used in- 

 stead of the corre.sponding densities of the steam. The Count de 



Pambour, in his Treatise on Locomotite Engines, and Theory of the 

 Steam Engine, assumes this waste space to be equal to J^ of the con- 

 tents of the cylinder within the limits of the stroke of the piston, and 

 I believe this estimate to be, in all cases, rather below than above the 

 truth. Besides, where is the necessity or advantage of neglecting 

 that quantity, when there is no difficulty in taking account of it, at 

 least by approximation? Its actual value may be employed, when 

 known, otherwise by using an approximation such as ^, a more correct 

 result would be obtained than by omitting it altogether. The above 

 equation, corrected for the waste space, and with the substitution of 

 the densities (5) and (5') for the pressures (p) and (t) respectively, 

 becomes 



[g. (^d-b)^ 



whence 



5 — y , 5 — 5' 



2dh+w (5—5') 



a' i — ('>d — b)V -\'Wyi—h'y 



where {w) expresses the length of a portion of the cylinder equal to 

 the waste space at either end of it. 



In order to show that the corrections which I have introduced, al- 

 though not greatly affecting the result, ainount notwithstanding to 

 sometliing appreciable, I shall presently apply tliem to one of the ex- 

 amples at the end of Mr. Lawrie's former communication; but it will 

 be necessary first to make a further correction in the latter, which I 

 shall do as soon as I have replied to the remaining paragraphs of his 

 present letter. 



With regard to my understanding the mode of analysis it is neces- 

 sary to follow in estimating the work performed by an engine working 

 expansively, I am sorry tlie want of perspicuity in my former letter 

 was such as to create a doubt in Mr. Lawrie's mind, and I trust I shall 

 now succeed in dispelling it; indeed the doubt has arisen from his 

 assigning a more extended signification to an expression, which I used 

 in common with himself, than the said expression had any right to 

 bear, or was originally intended to bear by either of us. When I said 

 that he found the effective working pressure during the expansion to be 



"a' p 

 equal to /, I did not mean the mean effective rrorking pressure, 



nor could I mean that that quantity, which so evidently varies with 

 the value given to (x), could be supposed constant during tlie whole 

 of the expansion, but precisely what Mr. Lawrie himself meant, viz., 

 that it was the general expression of the effective trorking pressure 

 during expansion, the particular value of which at any given instant 

 would be found by substituting for (x) its value for the position of the 

 piston at the given instant. 'This is, however, merely a misconception 

 on the part of Mr. Lawrie, who no doubt thought my objection rested 

 on the supposed difference which I liave just explained away, whereas 

 the real point at issue is whether the constant term (/) in the above 

 expression f.uthfuUy represents the negative part of the effect, or the 

 resistance of the waste steam on the back of the piston, or not. Now 

 (/), as I stated in my former communication, is used by Mr. Lawrie to 

 express the lowest pressure of the waste steam in the cylinder, which 

 probab'y scarcely exceeds the pressure of the atmosphere, and he has 

 likewise used it for the mean resistance of the waste steam, that is, 

 the resistance due to the blast pipe added to the pressure of the at- 

 mosphere, during the whole of the portion (6) of the stroke. Now, 

 according to the Count de Pamboui's experiments, with the mean 

 evaporation of locomotive boilers, and the size of orifice of the blast 

 pipe commonly adopted, the mean resistance due to the blast pipe, 

 when the velocity of the engine is 20 miles an hour, is 3-i ft. per 

 square inch of the piston. In the description of Robert Stephenson's 

 |j.itent locomotive engine in the new edition of Tredguld on the .Steam 

 Engine, jiage 451, it is stated that that resistance is " G lb. per square 

 inili when running at the usual rate of 2;') or 28 miles an hour," au'd 

 that at greater velocities it "has been found to increase to double that 

 amount, and even more." I think I am therefore fully borne out in 

 the opinion that Mr. Lawrie's calculation makes the effective working 

 pressure (I should have added, on the average) 3 or 1 lb. per square 

 inch too much, if not more. 



Willi respect to the diminution of temperature consequent on ex- 

 pansion, Mr. Lawrie must snrely be aware of the possibility of re- 

 ducing the temperature of elastic fluids, by sudden dilatation, many 

 degrees below that of the surrounding bodies ; but, since he wishes 

 me to tell him how much the temperature will be reduced in the hot 

 climate of a locomotive's smoke-box, 1 answer that, when the time 

 given for expansion is excessively short, as it is in locomotives, this 

 reduction is not sensibly affected by the climate, but depends on the 

 primitive pressure and degree of expansion of the steam, and that in 



