condensation, performance of work, imperfection of valve gear, etc., but for the present these are disregarded. [16] The indicator used in practice, to show the action of the steam in the cylinders of steam engines, differs essentially in its construction from that which we have described. The principles of operation are, however, the same in both. We will explain the construction of the Richard’s indicator, the one which is now most generally used, hereafter. [Illustration: _Fig. 32._ _Fig. 33._ _Fig. 34._ _Fig. 35._ _Fig. 36._ _Fig. 37._ _Fig. 38._ Scale ¹⁄₄ in. = 1 inch.] QUESTION 56. _How can we ascertain the pressure of the steam for any point of the stroke from such a diagram?_ _Answer._ By measuring the vertical distance by the expansion curve (fig. 38) from the vacuum or the atmospheric line, as for example 8 _j_, 12 _k_, 16 _l_, 20 _m_. As the indicator spring is extended or compressed one-fortieth of an inch[17] from every pound of pressure per square inch, either above or below the indicator piston, if we construct a scale _S_, _S_, fig. 38, with division of one-fortieth of an inch each, one of them will represent one pound of pressure per square inch if measured vertically from the atmospheric or vacuum line. If we sub-divide the vacuum line with the same number of parts as there are inches in the stroke of the piston (see fig. 39) we can draw vertical lines from these points and thus determine the pressure by comparing the length of such lines with the scale _S_, _S_. Thus the line 8 _j_ measures 100 fortieths of an inch, thus showing that the absolute steam pressure at 8 inches of the stroke was 100 lbs. per square inch; the line 12 _k_ measures 66²⁄₃ fortieths of an inch, thus showing that at 12 inches of the stroke the steam pressure was 66²⁄₃ lbs. At 16, 20 and 24 inches of the stroke the vertical lines measure 50, 40 and 33²⁄₃ fortieths; and therefore there were that number of pounds of steam pressure when the piston was at the point of the stroke named. Similar measurements could be made from other points, such as 2, 6, 10, or any other number of inches of the stroke. Of course, if we measure from the vacuum line we will have the absolute steam pressure, or the pressure _above a vacuum_, as it is sometimes called; if we measure from the atmospheric line we will have the effective pressure, or the _pressure above the atmosphere_. [17] Indicator springs are used of various degrees of tension, in proportion to the steam pressure to be indicated. [Illustration: _Fig. 39._ Scale ¹⁄₄ in. = 1 inch.] QUESTION 57. _How can we determine the average pressure during the whole stroke of steam which works expansively?_