STEAM ENGINES 189 



spring is available, the M. E. P. may be obtained by measuring 

 the ordinates in pounds instead of in inches; the sum of the 

 lengths of the ordinates as so measured divided by their number 

 gives the M. E. P. of the diagram. For example, let the scale 

 of the spring be 40; then each -fo in. in the length of an ordinate 

 represents a pressure of 1 Ib. per sq. in., and by measuring the 

 length of an ordinate with a scale graduated in fortieths of an 

 inch, the number of pounds of pressure represented by that 

 ordinate is found. 



A convenient method of finding the sum of the lengths of 

 the ordinates of a diagram, and one that is especially to be 

 recommended when a decimal scale is not available, is the 

 following: Take a strip of paper having a straight edge a little 

 longer than the sum of the lengths of the ordinates. Lay this 

 strip along the first ordinate. From the point on the strip 

 representing one end of the first ordinate lay off the length of 

 the next ordinate. In the same way lay off on the strip the 

 length of each of the ordinates in succession. The length of 

 the strip included between the extreme, or first and last, points 

 so marked will be equal to the sum of the lengths of the ordi- 

 nates, and this length divided by the number of ordinates will 

 give the length of the mean ordinate. 



Locating the Ordinates. The length of the diagram will 

 seldom be divisible into equal parts that can readily be laid 

 off by a scale, and to divide the length into equal parts by a 

 cut-and-try process will be found very tedious. These diffi- 

 culties may, however, be overcome by an application of a 

 simple geometrical principle, in the manner illustrated in Fig. 4. 

 The tangent lines at the ends of the diagram are drawn perpen- 

 dicular to the atmospheric line AZ. Suppose, now, that it is 

 desired to have fourteen ordinates. Draw any other line from 

 A, as AB, at a small angle to AZ, and then lay off any con- 

 venient distance AC fourteen times successively, along AB. 

 Connect the last point B with Z, and from the other points 

 D, E, etc. draw lines parallel to BZ until they intersect AZ. 

 These points of intersection will divide the line AZ into four- 

 teen equal spaces. The middle points of these spaces can 

 then be located by direct measurement and the ordinates may 

 be erected at these middle points. 

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