Proceedings of the Polytechnic Association. 1081 



tliest from the end of the diagram, p and ^==respectively the 

 same quantities for the other point, and a;=the clearance, then 



pdr—p'd 



(x -f d) p={x H d) p and thence we have the formula x= 



P—P 

 p and d may be measured in any convenient scale, and x will be in the 

 same scale as d. Or we may determine the clearance geometrically 

 by the following construction (see Fig. 2). Assume two points a 

 and B in the compression curve, and connect them by a right line a b, 

 continuing this line until it cuts the line of no pressure, f e at e. 

 Draw A D and b c perpendicular to f e, and make f d = c e. Then 

 F is the end of the theoretical diagram including clearance, and the 

 distance of f from the boundary of the indicator diagram is the clear- 

 ance in the scale of the length of the diagram, which represents the 

 stroke of the piston. 



Having determined the clearance, we proceed to lay out the theo- 

 retical diagram as follows : "We first draw a line representing the 

 boiler pressure, which is given in the scale of the instrument, and 

 also a line of no pressure or perfect vacuum, at 14.7 pounds from the 

 atmospheric line, unless the true barometric reading is given. "We 

 then divide the length of the diagram, including clearance, into a 

 number of equal parts, generally ten, though any number will answer. 

 We next measure the pressure at the point of exhaust, which is usu- 

 ally a little before the end of the stroke, and find the terminal press- 

 ure therefrom either by the inverse proportion of the distance from 

 the commencement -of the diagram to the whole length, or by the 

 method shown in Fig. 3, in which a b is the length of the diagram 

 including clearance, and the line of no pressure, and d is the point of 

 exhaust. Draw d e parallel to a b, and join a e cutting d c at f. 

 Then draw f g parallel to a b, and b g will represent the true termi- 

 nal pressure, or in other words, the tension at which a quantity of 

 steam equal to the whole capacity of the cylinder and clearance is dis- 

 charged at the termination of the stroke. 



Having thus found the terminal pressure, the pressure at any other 

 point of the stroke is easily found by the usual formula, or what is 

 known as Mariotte's law, in which the pressure increases inversely as 

 the distance from the commencement of the stroke. Where there are 

 ten divisions of the diagram, the several ordinates of the expansion 

 curve may be obtained by multiplying the terminal pressure by the 

 following series of numbers: 1., 1.11, 1.25, 1.429, 1.667, 2., 2.5, 



