values of 100 cos2a and 1/2(100) sin 2a are alreadycomputed at 2-minute intervals for angles up to 30°. Youneed to multiply the values in the table by the stadiareading, then add the value of the instrument constantgiven at the bottom of the page.To find the values from the stadia table, for theexample that we have been discussing, read under 25°and opposite 14’. Under Hor. Dist. you find that100 COS^{2 }25°14’ = 81.83.Under Diff. Elev. you see that1/2 (100) sin 2 (25014’) = 38.56.The values of the term containing the instrumentconstant are given at the bottom of the page.ForYou findThereforeUsing these values in the formulas, you haveandAPPROXIMATE FORMS OF STADIAFORMULAS.— Because of the errors common instadia surveying, it has been found that approximatestadia formulas are precise enough for most stadia workIf you will refer again to figures 8-5 and 8-6, you willnotice that it is customary to hold the stadia rod plumbrather than inclined at right angles to the line of sight.Failure to hold the rod plumb introduces an error causingthe observed readings to be longer than the truereadings. Another error inherent in stadia surveying iscaused by the unequal refraction of light rays in thelayers of air close to the earth’s surface. The refractionerror is smallest when the day is cloudy or during theearly morning or late afternoon hours on a sunny day.Unequal refraction, also, causes the observed readingsto be longer than the true readings.Figure 8-7.-Stadia arc (multiplier type).Figure 8-8.-Stadia arc (horizontal scale subtraction type).To compensate for these errors, topographers oftenregard the instrument constant as zero in stadiasurveying of ordinary precision, even if the instrumenthas an externally focusing telescope. In this way, the lastterms in the stadia formulas for inclined sights vanish;that is, become zero. Then the approximateexpressions for horizontal and vertical distance areBEAMAN STADIA ARC.— The Beaman stadiaarc is a specially graduated arc on the vertical scale ofthe transit (fig. 8-7) or on the plane-table alidade (fig.8-8). The Beaman arc on the transit is also known as thestadia circle. These arcs are used to determine distancesand differences in elevation by stadia without usingvertical angles and without using tables or diagrams. Astadia arc has no vernier, but readings are indicated byindex marks.8-7