Twentieth century hand-book for steam engineers and electricians, with questions and answers .. . sents the workdone by the expansion of the steam after cut offoccurs. This area and the amount of work it repre-sents may be computed by means of the known rela-tions of hyperbolic surfaces with their base lines; asfor instance, if the base lines A B, A C, A D, etc.,extend in geometrical ratio, as r, 2, 4, 8, 16, etc., thesuccessive areas, B H L C, B H K D, B H G E, etc.,increase in arithmetical ratio, as 1, 2, 3, 4, etc. DIAGRAM ANALYSIS 249 On the principles of common logarithms, whichrepresent
Twentieth century hand-book for steam engineers and electricians, with questions and answers .. . sents the workdone by the expansion of the steam after cut offoccurs. This area and the amount of work it repre-sents may be computed by means of the known rela-tions of hyperbolic surfaces with their base lines; asfor instance, if the base lines A B, A C, A D, etc.,extend in geometrical ratio, as r, 2, 4, 8, 16, etc., thesuccessive areas, B H L C, B H K D, B H G E, etc.,increase in arithmetical ratio, as 1, 2, 3, 4, etc. DIAGRAM ANALYSIS 249 On the principles of common logarithms, whichrepresent in arithmetical ratio natural numbers ingeometrical ratio, tables of hyperbolic logarithms havebeen computed for the purpose of facilitating the cal-culation of areas of work due to different degrees ofexpansion. Such a table is given elsewhere in thisbook, and in Chapter IX is described the method ofcalculating the M. E. P. by this means. A theoretical curve may be constructed conjointlywith the actual expansion curve of a diagram by firstlocating the clearance and vacuum lines and then pur-. figure 87. suing the method illustrated by Fig. 87. A curve soproduced is called an isothermal curve, meaning acurve of the same temperature. Referring to Fig. 87, suppose, first, that it is desiredto ascertain how near the expansion curve of the dia-gram coincides with the isothermal curve, at or nearthe point of cut off. Select point R near whererelease begins, but still well within the expansioncurve. From this point draw the vertical line, R T,parallel with the clearance line, V S. Then draw thehorizontal line, S T, parallel with the atmospb^c line, 250 ENGINEERING and at such a height above it as will equal the boilerpressure as measured by the scale adapted to the dia-gram; such measurement to be made from the atmos-pheric line to correspond with the gauge T draw the diagonal T V, and from R draw thehorizontal line R D parallel with the atmospheric D, where t
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