274 



THE CIVIL ENGINELR AND ARCHITECT'S JOURNAL. 



[Sept. 



1st. How the velocity must be changed if I, II, and III remain un- 

 changed. 



2d. How the load must be changed if I. II. and IV. remain un- 

 changed. 



I I do not mean to say that the lead of the slide might not be made 

 to produce changes in both effecis at once, but the subject will be ex- 

 hibited most cle.irly by the plan suggested of considering each change 

 separately. 



On the alteration of the velocity produced hy a had of the slide. 



1. To examine the alteration in the velocity produced by a lead of 

 tlie slide, the rapidity of evaporation being the same, and the load of 

 resistance remaining unchanged. Suppose the evaporation such that 

 it would produce per minute m cylinders-full of steam of the pressure 

 «: then it would produce 2 to cylinders-full of the pressure ip,cim 

 cylinders-full of the density i p, and, for the same reason, 



^-(1 + loga-logA) m cylinders-full of pressure XTI+loga-log/i);.. 



If however the steam be cut off when it has filled the cylinder to a 

 height h instead of a, the number of times the cylinder is filled per 

 minute will be increased in the proportion a:h. Hence finally the 

 number of cylinders- full of steam, and therefore the number of strokes 

 per minute are defined in reference to (B) by the expression 



^- (1 + loga — logi)?n 



or the velocity will be increased in the ratio 



1: 1 + log a — log A _(^'L. 



Hence the smaller the value of h, the greater the velocity, subject 



only to this limit that the value of h must never be such as would sup- 



pos'e a higher pressure in the cylinder than that in the boiler. We 



obtain therefore the following practical rules. 



The highest velocity for a given load and given evaporation is obtained 

 hy cutting off the steam at such a point that the steam in the cylinder 

 shall, during admission, have the same pressure as tie steam in the 

 boiler. 



The velocity mill be increased by increasing the hoiler-pressure and 

 the lead of the slide conjointly. 



The rules which are here demonstrated are of the highest im- 

 portance, and I confess that it is with no little satisfaction that I arrive 

 at results which I did not foresee till the very moment of interpreting 

 the analytical formula which I have here exhibited. These rules, 

 even when viewed apart from the analysis which has led to them, 

 bear the highest marks of probability; and they have this advantage 

 that they are not merely theoretically true, but correspond to the actual 

 working condition of steam engines, and require no practical modifi- 

 cations arising from friction of machinery and other unknown resist- 

 ances. 



Before quitting the subject it will be well to see what is the value 

 of the lead of the slide which gives the cylinder-pressure equal to the 

 boiler-pressure, and therefore, as we have shown, produces the greatest 

 velocity. 



Let the effective pressure in the boiler be P lb. to the square inch, 

 and, as before, let the load offer a resistance of ;i lb. on each square inch 

 of the piston. Then we have from equation (B) for the maximum 

 value of A 



From this equation we can easily find what relation to the load and 

 the boiler-pressure the lead the slide should have for a maximum ve- 

 locity. For instance let us suppose the resistance to the piston 48 lb. 

 per inch, and the boiler-pressure 50 lb. per inch. In this case it will 

 be found on trial that the equation is nearly satisfied by putting A = 

 i o, for we have 



|=|(l-flog^t) 



= 1(1 + .2876) =.9G nearly. 



This would give the relation of ;? to P equal to 48 : 50, or conversely 

 if the effective boiler-pressure were 50 lb. per inch and the resistance 

 48 lb., the maximum velocity for a given evaporation (and therefore 

 for a given amount of fuel) would be obtained by cutting off the steam 

 at I ths the stroke. 



" Suppose, in effect, that a load of 50 tons gross, tender Included, 

 be drawn up a plane inclined -;i^, by an engine with 2 cylinders 11 

 inches in diameter, stroke of the piston 10 inches, wheels 6 feet, fric- 

 tion 103 lb., total pressure of the steam in the boiler 05 lb., or effective 

 pressure 50 lb. per square inch." 



" We have already found above that the total resistance opposed 



by that load to the motion of the piston, in the case of this engine, is 

 48 lb. per square inch." 



I have taken this extract from M. de Pambout's account of his ad- 

 mirably conducted experiments, to show that the case I have sup- 

 posed accords with practice. It appears that in this case, with an 

 evaporation of one cubic foot of water per minute, the engine would 

 move the train at the rate of 20-7 miles per hour, there being no lead 

 of the slide. The lead being |th, we find from (C) that the velocity 

 (for the same evaporation) would be increased in the ratio 



1 : 1 + log I, or 1 : 1-2876 

 or the velocity would be increased from 20-7 to 20'G1 miles an hour — 

 no trifling advantage certainly. It is necessaiy, however, to refer the 

 reader to another extract from M. de Pambour's work, because the 

 considerations which it offer apply to the investigation here made, and 

 are essential to its accuracy. 



" It is necessary here to remark, that as this lead offers a resistance 

 precisely equal to the pressure of the steam in the boiler, and as we 

 have seen that at the moment of starting of every engine, the power 

 must necessarily exert an effort greater tlian the resistance, it would 

 be impossible for the engine to set itself in motion with the load. If 

 then we would make the engine work with this load, it is understood 

 that the aid of another engine would be requisite to start it ; or else 

 the engine-man must for a tew minutes close the safety-valve, to create 

 in the boiler a sufficient excess of pressure, till the uniform motion be 

 attained. Then the momentary excess of pressure may be withdrawn 

 and the engine will continue its motion without any external aid. 



"However, as on railways there continually occur little inequalities 

 or accidental imperfections in the road, and as the engine ought to be 

 capable of overcoming them, it is not to be expected that it can be 

 made to perform an entire trip, working precisely at its maximum of 

 useful effect, or with its maximum load. The preceding determina- 

 tion therefore is to be considered only as showing what the engine 

 may perform on arriving with a velocity already acquired, at an in- 

 clined plane situated at a certain point of the line, or as indicating the 

 point towards which our aim should tend as much as possible, in order 

 to accomplish ])roducing the maximum of useful effect, but without 

 reckoning on obtaining it completely in practice. 



"We here neglect the little necessary difference between the pres- 

 sures in the cylinder and in the boiler, from the flowing of the steam 

 from the one vessel to the other. It plainly tends somewhat to reduce 

 the load of the engine, increasing in a corresponding manner the 

 velocity of maximum useful effect. 



I ought, perhaps, to add that by improvements which have been (I 

 believe) invented since M. de Pambour wrote, the expansion gearing 

 is placed under the control of the engine-driver, so that be can regu- 

 late the lead of the slide while the engine is in motion. The slide 

 need not, therefore, have any lead till the engine has attained its full 

 velocity. 



On the alteration in the load produced by a lead of the slide. 

 2. I come now to consider what alteration must be made in the load 

 or resistance for a lead of the slide, supposing the evaporation and 

 the velocity to remain unchanged. It will be clear that as far as con- 

 cerns locomotive engines this second enquiry principally affects lug- 

 gage trains, while the former enquiry as to the means of increasing 

 velocity most affects passenger trains. 



Suppose, as before, that when there is no lead of slide the boiler 

 supplies TO cylinders full of steam of the pressure p. If now we sup- 

 pose the velocity unchanged, there will still be the same number of 

 strokes per minute, and the quantity of steam supplied for each stroke 

 will also be the same as before, only it will fill the cylinder to a height 

 h instead of a, its pressure will therefore be increased in the propor- 

 tion a '. h. Now by the principles already laid down the work done 



by steam of this pressure - p used expansively is 



-p. h (1 + log^a- log^A) or ap (1 + log^ a - log A) 



When, however, the steam was used without expansion the total 

 work done in each stroke was a /). We have, therefore to multiply 

 by the quantity within the bracket to get the increased effect for ex- 

 pansion. It is clear also that the increased load or resistance, since it 

 acts through a distance a, is found by dividing by a, that is, the in- 

 creased load, which we will callj:/',is expressed by the equation 



p'—p (1 + loga - log a) 

 or the load for a given amount of fuel and a given velocity is increased 

 by the lead of the slide, in the proportion 



1 : 1 + log a - log A (D.) 



The greater then will be the load which can be moved, as the value 



