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values of 100  cos2a and 1/2(100) sin 2a are already computed at 2-minute intervals for angles up to 30°. You need to multiply the values in the table by the stadia reading, then add the value of the instrument constant given at the bottom of the page. To find the values from the stadia table, for the example that we have been discussing, read under 25° and opposite  14’. Under Hor. Dist. you find that 100 COS2 25°14’  = 81.83. Under Diff. Elev. you see that 1/2 (100) sin 2  (25014’)  = 38.56. The  values  of  the  term  containing  the  instrument constant are given at the bottom of the page. For You find Therefore Using these values in the formulas, you have and APPROXIMATE   FORMS   OF   STADIA FORMULAS.—   Because  of  the  errors  common  in stadia  surveying,  it  has  been  found  that  approximate stadia formulas are precise enough for most stadia work If you will refer again to figures 8-5 and 8-6, you will notice that it is customary to hold the stadia rod plumb rather than inclined at right angles to the line of sight. Failure to hold the rod plumb introduces an error causing the  observed  readings  to  be  longer  than  the  true readings. Another error inherent in stadia surveying is caused by the unequal refraction of light rays in the layers of air close to the earth’s surface. The refraction error is smallest when the day is cloudy or during the early morning or late afternoon hours on a sunny day. Unequal refraction, also, causes the observed readings to 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 often regard  the  instrument  constant  as  zero  in  stadia surveying of ordinary precision, even if the instrument has an externally focusing telescope. In this way, the last terms in the stadia formulas for inclined sights vanish; that  is,  become  zero.  Then  the  approximate expressions for horizontal and vertical distance are BEAMAN STADIA ARC.— The Beaman stadia arc is a specially graduated arc on the vertical scale of the transit (fig. 8-7) or on the plane-table alidade (fig. 8-8). The Beaman arc on the transit is also known as the stadia circle. These  arcs  are  used  to  determine  distances and differences in elevation by stadia without using vertical angles and without using tables or diagrams. A stadia arc has no vernier, but readings are indicated by index  marks. 8-7

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