THE STEAM-ENGINE. 



439 <! 



proportion of 3 to 2, and the pressure at B being one ton, it would be two 

 thirds of a ton at. P'. In like manner when the piston would arrive at C, the 

 space occupied by the steam being double that which it occupied when the 

 piston was at B, the pressure of the steam would be half its pressure at B, 

 and therefore at the termination of the stroke, the pressure on the piston would 

 be half a ton. 



If the space from B to C, through which the steam is here supposed to act 

 expansively, be divided into ten equal parts, the pressure on the piston at the 

 moment of passing each of those divisions would be calculated upon the same 

 principle as in the cases now mentioned. After moving through the first di- 

 vision, the volume of the steam would be increased in the proportion of 10 to 

 11, and therefore its pressure would be diminished in the proportion of 11 to 

 10. The pressure, therefore, driving the piston at the end of the first of 

 these ten divisions would be -j-fths of a ton. In like manner, its pressure at 

 the second of the divisions would be -}-Jths of a ton, and the third yjths of a 

 ton ; and so on, as indicated in the figure. 



Now if the pressure of the steam through each of these divisions were to 

 continue uniform, and, instead of gradually diminishing, to suffer a sudden 

 change in passing from one division to another, then the mechanical effect 

 produced from B to C would be obtained by taking a mean or average of the 

 several pressures throughout each of the ten divisions. In the present case 

 it has been supposed that the force on the piston at B was 2,240 pounds. To 

 obtain the pressure in pounds corresponding to each of the successive divis- 

 ions, it will therefore only be necessary to multiply 2,240 by 10, and to divide 

 it successively by 11, 12, 13, &c. The pressures, therefore, in pounds, at 

 each of the ten divisions, will be as follows : 



1st 2,036-3 



2d 



3d 



4th 



5th 



6th 



7th 



8th 



.866-6 

 ,723-1 

 ,600-0 

 ,45)3-3 

 ,400-0 

 ,317-6 

 ,244-4 



9th ,179-0 



10th 1,120-0 



If the mean of these be taken by adding them together and dividing by 10, 

 it will be found to be 1,498 pounds. It appears, therefore, that the pressures 

 through each of the ton divisions being supposed to be uniform (which, how- 

 ever, strictly, they are not), the mechanical effect of the steam from B to C 

 would be the same as if it acted uniformly throughout that space upon the pis- 

 tori with a force of about 1,500 pounds, being rather less than three fourths 

 of its whole effect from A to B. 



But it is evident that this principle will be equally applicable if the second 

 cylinder had any other proportion to the first. Thus it might be twice the 

 length of the first ; and in that case, a further mechanical effect would be ob- 

 tained from the expansion of the steam. 



The more accurate method of calculating the effect of the expansion from B 

 to C, would involve more advanced mathematical principles than could proper- 

 ly be introduced here ; but the result of such a computation would be that the 

 actual average effect of the steam from B to C would be equal to a uniform 

 pressure through that space, amounting to one thousand five hundred and forty 

 five pounds, being greater than the result of the above computation, the differ- 



