252 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[AuGtST, 



for the same in relation to (c') a: = — (l-{-2 c). And we have 



.-_,.„,,.^„.- <l«^'-lc-c') + d^(a^-lc-c'y-a^P 



rf(l 



— lc — c')+dy./\^(\ — lc — c')—r-j. Whena = I 

 «=-(/ + 2c) y=c' = 



(f(l + c/ + c') + rfi/ f (l + c/ + a=— (/ + 2e)2J 



Having now found the values of (a' b and c'), we must next find the 

 effect gained by the expansion of the steam from (a' to 6), and the 

 effect lost by the compression of the steam from (6 to c')- But ex- 

 pansion may take place in two ways, the operations of which are quite 

 distinct, first, the cylinder may remain of the same volume and the 

 steam be increased in pressure before entering them ; or, the cylinders 

 may be enlarged and the pressure of the steam be constant, which is 

 the plan virtually adopted in locomotives; for those of them that do 

 not work by expansion when properly constructed, are so made that 

 their cylinders are not capable of consuming a greater volume of steam 

 than the boiler can furnish of the greatest safe pressure. 



The eduction passage being shut by the time that the piston arrives 

 at the end of (6), saves, or at least prevents from flying to the atmo- 

 sphere a quantity of steam of a pressure {t), that fills {id— b) of the 



cylinders, which at a pressure (;;) would fill ^Mz^ of the cylinders 



hence when the steam is cut off' at (a'), there is only admitted so much 



fresh steam as fills {a' — ^'- — ^— ) and since the quantity of fresh 



steam admitted must (whatever the expansion is) be constant, we have 



. K-^') -2. X 1. .-. -^:;f^, (.) being the 



area of the piston. 



Again in figure let (x) be any portion of the stroke greater than (a), 

 and less than (4), and letj»' be the pressure into which the steam has 



ap 



expanded at the end of (j-) then x \ a' \ : p ; p', .'. p' = 

 effective working pressure =: — — /. 



•' differential of work performed = d efficiency = s { - — t) d x, 

 .'. efficiency in part (6) of the stroke = s a/) (log - + 1) — 8/6. 



Agaiir; for the effect of compression caused by the shutting of the 

 eduction passage let (x) (measuring from DCj be anv portion of the 

 stroke between (6 and c), and (;/; the piessuie, to which the confined 

 steam has been compressed, then x : 'Id — b : : t : p' .'. p' — 



(2d — b)t (id — b)! 

 , . • . effective workmg pressure = ^^ 1 . • . d effi- 



/{2d — b)l \ , 

 ciency = I 1 \ » d x, 



il(2d-b) flog. ^^^^_lj +sC2d-c)(p + l.) 



By deducting tlie effect of compression from the efficiency of the 

 part (b) of the stroke, we have whole work performed = 



»a'p(\og.~ + l\-~stb-st{2d-b) {log. ~^-^^_l\ 



— 8 (2 d— c) (p + 0- Pi't 2 rf= 1, < = 1 and (p) is then expressed 

 in multiples of (/). . • . whole work performed = 



s a' p( log. ,+ 1 — s b — s(l — 6) ( log. — i ■ J 



— Ml-c)(jB+l). 



whole effect of compression = 



But gnr 



a' p — 1 + 6 



Whole work performed =; 



a'^+i— 1 



multiplied into 



'ya' p\og. -—Q-b)\og.]^—-J^a' p — 2b—p+pc + c.^ 



An expression for the work performed by a unit of volume of steam, 

 formed of known quantities, or rather of quantities which become 

 known when (/) the lead, and (c) the cover of the valve are given. 



Let the safety valve be so loaded that (p) is equal to (a), and let 

 the lead (/) of the slide valve be nothing, and the cover (c) be nothing. 

 Then a'^ 1, 6i= 1, c' = 0, .-.whole work performed =rp — 1=^4, 

 which is exactly what another mode of proceeding gives for when the 

 valve has no cover and no lead, the work performed is evidently = 

 2d (p — I) s. But 2rf= ], t = 1, and when the valve gives no expan- 

 sion s ^ 1, therefore work performed ^p — 1 = 4. 



Again, let the lead (/) be equal to ^ of the breadth of the port, and 

 the cover (c) equal to i of the breadth of the port. And then 



a' = 0-88S h z= 0-9545 c' = 0-992 . • . whole work 



performed = 4-2378. 

 Again, let / = ^ breadth of port, c =r i breadth of port, and then 

 a' — 0-G5G b = 0-873 c' = 0-99 . - . whole work 



performed = 4-8960. 

 Again, let /^^ breadth of port, c = I breadth of port, and then 

 a' = 0-2884 6 = 0-7 c' — 0-975 . • . whole work 



performed = 7-). 

 Again, I = -^ breadth of port, c = 5 breadth of port, and then 

 a' = 0-43 6 = 0-825 c' = 0-999 . • . whole work 



performed = 4-97. 

 Hence the following conclusions: — In a locomotive in which the 

 stroke of the cylinder is 18 inches, and breadth of port H inches, if 

 the work it performs with a ton of coke when the valve has no cover 

 be called 1 ; then by giving the valve i of an inch of lead, and i of an 

 inch of cover, the steam will be cutoflTat 15-98 inches from commence- 

 ment of stroke, and the work performed by a ton of coke will be 1-0591. 

 Again, by giving the valve i of an inch of lead, and J of an inch of 

 cover, the steam will be cut off' at 11-8 inches from commencement of 

 stroke, and the work performed by a ton of coke will be 1-2241. 



Again, by giving the valve I of an inch of lead and U inches of 

 cover, the steam will be cut off' at 5-2 inches from commencement of 

 stroke, and the work perf;irn;ed bv a ton of coke will be 1-7.). 



Again, by giving the valve Yrni of t'le breadth of the port of lead, 

 and 14 inches of cover, the steam will be cut off" at 71 inches from 

 commencement of stroke, and the work performed by a ton of coke 

 will be 1-242. 



In the two last examples the cover of the valve is the same, but in 

 the latter the lead is much less than in the former, which has diminished 

 the efficiency of a ton of coke from 1-75 to 1-242, or nearly in the ratio 

 of 3 to 2 ; and if the lead was still a little less the advantage gained 

 by the cover would be altogether neutralized. Hence it appears that 

 the lead is an important feature in the construction of the slide valve, 

 and might be a good subject of enquiry as to what relation it ought to 

 bear to the cover so as not to interfere with the operation of expansion. 

 I am. Sir, your obedient servant, 



J. G. Lawrie. 

 Carlsdyke Foundry, Greenock, 

 Jam: 27, lb41. 



N.B. — Should you consider this letter worthy of insertion in your 

 Journal, I shall probably request insertion of another in continuation of 

 the same subject, in which the lead will come under consideration. 



J. G L. 



REMARKS ON MR. DREDGE'S SUSPENSION BRIDGE. 

 Sir- — Feeling some interest in the subject of suspension bridges, I 

 wasgratifii'd to find in a recent number of vuur instructive publication, 

 a description of Mr. Dredge's newly invented suspension bridge, re- 

 jiresented as off'ering such superior advantages, in all the essential 

 particulars of strength, durabilitv, and economy of construction. At 

 the same time, however, 1 was somewhat disappointed when, having 

 perused the article in question, I found that noattHMi|it had been made 

 to demonstrate the possession of such dosiral)le ipi.dities, by a reference 

 to those well known principles and laws which govern the forces to 

 which a suspension bridge is subject, and not having subsequently seen 

 in the Journal or other publications, any such investigation of the sub- 

 ject, I am induced to forward to you the few rem irks which follow, in 



