1848.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



likewise that of the eccentric, they must necessarily revolve in 

 equal times, and always at the same distance apart ; tlierefore, 

 when the crank has readied the point d (supposing it to move in 

 the direction of tlie arrow) the eccentric will liave advanced to /, 

 and ed and im represent the positions of the piston and slide re- 

 spectively ; showing-, that when the piston lias descended to e, the 

 steam port a i in the diagram, or a figs. 1 to 4, will be open to the 

 extent a m. Again, — when the crank is at n, and the piston conse- 

 quently at half-stroke, a i will be the position of the eccentric, the 

 port a i being fully open, and the slide occupying tlie extreme posi- 

 tion shown in fig. 3. The direction of the slide's motion is now 

 reversed, and the port is again gradually covered by the slide face 

 until the positions of the crank and eccentric are a c and a o, when 

 the piston will have completed its descent, and the port a i will be 

 completely closed, the slide being again brought into its central 

 position, fig. 2. The opposite steam port a k now begins to open 

 for tlie admission of steam, and the direction of the piston's motion 

 is reversed ; the port continues to open until the crank and eccen- 

 tric reach the points p and /;, when the piston will again be at half- 

 stroke, and the slide in its extreme position, fig. 4. Meanwhile, 

 exhaustion from above the piston has been taking place, to the same 

 extent, through the port a i. Finally, — the piston having com- 

 pleted its ascent, the slide again occupies its original position, fig. 2, 

 and, its course being downward, steam is again admitted into the 

 cylinder, through tlie port a ; the jiiston tlien begins to descend, 

 and, at the same instant, exhaustion ceases from above, and com- 

 mences from below it, through the port h. 



It is sometimes urged against the use of the eccentric, as a means 

 of actuating the slide, that the steam ports are opened and closed 

 too slowly ; but it must be remembered that the piston does not 

 move at a uniform velocity, as the crank does; for example, while 

 the crank describes the arc h rf, the piston descends only from b to 

 e, the versed sine of that arc ; and its velocity is gradually iucreaed 

 as it approaches the middle of its stroke, where it is greatest, 

 being equal to that of the crank. Again, — as the piston approaches 

 the end of its stroke, its velocity is diminished in the same ratio as 

 that in which it had previously increaseil, until the completion ot 

 its stroke, where it remains stationary during the small space of 

 time in which the direction of its motion is reversed. 



Now, it must be olivious that less steam is required to impel the 

 piston at a slow rate than at a rapid one ; and a glance at diagram 1 

 shows that the steam admitted into the cylinder, when tlie slide is 

 actuated by an eccentric, is at all times proportioned to the velocity 

 of the piston, the port being least open when the pistcm is near the 

 end of its stroke, and fully open when it is at half-stroke. 



When an eccentric, instead of being set, as in the preceding case, 

 so that the steam port shall only begin to open when the piston 

 commences its stroke, is so placed that the port shall be open to 

 some extent prior to the commencement of the stroke, the width 

 of that opening is termed 



The Lead. 

 The non-use of lead is disadvantageous, chiefly because at the 

 commencement of every stroke, the steam has to contend « ith the 

 whole force of that which had impelled the piston during its pre- 

 vious stroke. But, besides obviating that disadvantage, the lead 

 is of essential ser\ice in locomotive engines, " where it is found 

 necessary^to let the steam on to the opposite side of the piston 

 before the end of its stroke, in order to liring it up gradually to a 

 stop, and diminish the violent jerk that is caused by its motion 

 being changed so very rapidly as five times in a second. The steam 

 let into the end of a cylinder before the piston arrives at it, acts 

 as a spring cushion to assist in changing its motion ; and if it were 

 not applied, the piston could not be kept tight upon the piston- 

 rod." — Description of Stephenson's Locomotive Engine, " Tredyold." 



Case 2. — When a Slide has Lead without Lap. 



Diagram 2. Let a 1), diagram 2, represent the 



stroke of the piston ; c d the travel of 

 the slide ; and efihe lead; then, sup- 

 posing the piston to be at the top of 

 the cylinder, e a is the position of the 

 crank, and eg that of the eccentric. 

 Following the course of the crank, in 

 the direction of the arrow, we find 

 the port erf fuUy open, not, as in the 

 former ease, when the piston is at 

 half-stroke, but when it has descended 

 to the point h, — the arc a i, described 

 by the crank, being equal to the -drcgd, 

 described by the eccentric. Again, — 

 we find the port re-closed when the 

 piston has descended to »', at which point exhaustion commences 



from above the piston through e d, and steam enters below it through 

 e c, for the return stroke, at the commencement of which the iiort 

 ec is open to the extent el (equal to e/) for the admission of 

 steam, while e d is open to the same extent for exhaustion. 



It is to be remarked, that the amount of lead is necessarily very 

 limited in practice, its tendency being to arrest the progress of the 

 piston before the completion of its stroke. The greatest possible 

 amount of lead equals half the travel of the slide. The eccentric 

 would in that case be set diametrically opposite to its first position, 

 which would have the effect of reversing the direction of the pis- 

 ton's motion. 



In the case of a slide having lead h ithout lap, the distance of a 

 piston from the end of its stroke, when the lead produces its effect 

 is proportional to the lead as the versed sine of an arc is to its 

 sine, supposing the radii of the crank and eccentric to be equal. 

 Demonstration. 

 Diagram 3. Let a b, diagram 3, represent both tlie 



travel of the slide and tlie piston's 

 stroke ; then c a and c b represent the 

 steam ports. And let cd represent the 

 lead; then ca and ce represent the 

 crank and eccentric, the piston being at 

 the top of the cylinder. Now, steam 

 will enter the cylinder, below the piston, 

 when the eccentric is utf, and the crank 

 at g; for the arcs a eg, and ebf are 

 equal. Again, — the arc g b is equal to 

 h e ; therefore, ig is equal to k e, and i b 

 to k h. Now, he IS the sine of the arc h e, and k k (equal to ; 6) is 

 its versed sine : hence 



Rule I. — To find the distance of the piston from the end of its 

 stroke, when the lead produces its effect : — 



Divide the lead by the width of tlie steam port, both in inches, 

 and call the quotient sine; multiply its corresponding versed sine, 

 found in the table, by half the stroke, and the product will be the 

 distance of the piston from the end of its stroke, when steam is 

 admitted for the return stroke, and exhaustion commences. Or, 



Rule II. — To find the lead, the distance of the piston from the end 

 of its stroke being given : — 



Divide the distance in inches by half the stroke in inches, and 

 call the quotient versed sine ; multiply its corresponding sine by 

 the width of steam port, and the product will be the lead. 



Example 1. — The stroke of a piston is 48 inches ; width of steam 

 port 2i| inches ; and lead ^ inch : required tlie distance of the pis- 

 ton from the end of its stroke, when exhaustion commences. 



Here, 'S -;- 2-5 = "2 ^ sine ; and versed sine of sine '2 ^= •0202. 

 Then, -0202 X 24 = -4848 inches. 



Example 2. — The stroke of a piston is 48 inches ; width of steam 



port 2-5 inches ; and distance of piston from the end of its stroke, 



when exhaustion commences, -4848 inches : required the lead. 



Here, -4848 -^ 24 = -0202 = versed sine ; 



and sine of versed sine '0202 =^ "2. 



Then, -2 X 2-5 - -5 — lead. 



When the lead of a slide is equal to the width of steam port 

 multiplied by any number in the first column of the following 

 table, the distance of the piston from the end of its stroke, when 

 steam is admitted on the exhaust-si<le, will be eijual to half the 

 stroke multiidied by the corresponding number of the second 

 column. Or, if the distance of the piston from the end of its 

 stroke, when steam is admitted on the exhaust-side, be equal to 

 half the stroke multiplied by any number in the second column, 

 the width of steam port multiplied by the corresponding number 

 of the first column equals the lead. 



