ALIXKMKXT CriAKTS I X I'ORKST MEXSUKATIOX T83 



E, the second initial axis of this system, measures vakies of c, it is 

 evident that D. the final axis, will measure the values of .r + v + -. 

 and therefore of v. In this chart, if A and C are graduated with the 

 same unit, B will be equidistant from them and graduated with a scale 

 one-half as great. As values of B are not recorded, the graduation of 

 this axis may be omitted. E, however, must be graduated with the 

 same reduced scale (one-half that of A and C) if D is to be equidistant 

 from it and from B. Finally, the scale with which D is graduated 

 must be one-half that of B and E or one-fourth that of A and C. 



To use such a chart a straight-edge is laid across the values of z and 

 V on A and C. and its intersection with B caught and held with a sharp- 

 pointed pencil or a needle point. The straight-edge is then shifted to 

 connect this point with the given value of z on E, and the resulting 

 value of V read on D. The broken lines of figure 7 indicate the solution 

 3+4 + 5=12. 



It is often possible to simplify the appearance of such a chart by com- 

 bining two axes into one with a double set of graduations. Examples 

 of this will appear in the charts which follow. 



SELECTION OF SCALES AND ARRANGEMENT OF AXES 



In applying the simple principles which have been described, good 

 judgment is required in choosing proper scales for graduating the axes. 

 ( )n the one hand the units must be large enough to permit readings to 

 the required degree of accuracy, and on the other the whole chart must 

 be kept within reasonable limits of size. Oftentimes both objects can- 

 not be obtained on a single graph, and two charts, one for low and one 

 for high values, must be employed. The two can usually be combined 

 on a single set of axes by using a double set of graduations. The same 

 expedient is often desirable on a z chart to avoid too acute intersections 

 between the straight-edge and the diagonal axis in the case of small 

 values. In choosing the positions of the axes the chief considerations 

 are the avoidance of acute intersections and the securing of a compact 

 chart of moderate size. All of these points will become clear through 

 a consideration of the graphs which are described in subsequent pages. 



MODIFICATION OF SCALES 



In certain cases it is impossible to prepare by the methods already 

 described a chart which does not have one or more of its scales badly 

 congested in one part and unnecessarily expanded in another. Such a 



