The stadia arc shown in figure 8-7 is the multiplierstadia arc (the vertical index is at zero); that is, theobserved stadia interval is multiplied by the Hor stadiaarc reading to get the horizontal distance; or the stadiainterval is multiplied by the Vert stadia arc reading toobtain the vertical distance from the center of theinstrument to the point sighted on the rod This verticaldistance, combined with the HI and the rod reading, willgive the difference in elevation between the instrumentstation and the point where the rod is heldThe stadia arc, as shown is figure 8-8, is called thehorizontal scale subtraction stadia arc (the verticalindex is at 50). The use of the Beaman stadia arc toobtain a horizontal distance and difference in elevationis explained in the following sections.Horizontal Distance (Subtraction Scale).— TheH scale gives you a percentage that you can apply to aninclined stadia shot with the alidade to get thecorresponding horizontal distance from the slopedistance. Suppose that with the telescope inclined (thatis, at a vertical angle other than 0°), you read an intervalof 2.45 feet on the stadia rod. The slope distance, thenWhat is the corresponding horizontal distance? You readthe graduation indicated by the Beaman arc indicator onthe H scale, and find that the reading is 5. This meansthat the horizontal distance is 5 percent less than theslope distance, or245 feet – (0.05 x 245 feet), or245 – 12.25 = 232.8 feet.Difference in Elevation (Vertical Index at50).— The V scale on the Beaman arc is used todetermine the difference in elevation between theelevation of the line of sight through the telescope (thatis, the HI) and the elevation of the point you sighted onthe level rod Note that when the telescope is horizontal,the V scale on the Beaman arc reads 50. Thisarrangement makes the use of minus values unnecessarywhen you are sighting with the telescope at a negativevertical angle.To read the V scale, you take the difference between50 and whatever you read on the scale and apply thisdifference as follows to determine the difference inelevation.Suppose that when you made the shot previouslydescribed (where you read 5 on the H scale), the readingon the V scale was 71. In practice, it is the custom toshoot the rod at a point that will give you an even readingon the V scale.Because the reading was 71, the value you will useis71 –50, or 21%.This means that the difference in elevation between theHI and the point you sighted on the rod is 21 percent ofthe slope distance. The slope distance, in this case, was245.0 feet; therefore, the difference in elevation is245.0 x 0.21 = 51.45 feet. Now that you know how to read stadia and computehorizontal and vertical distances using stadia, we willnow discuss typical field procedures.Field ProceduresFigure 8-9 shows two situations that areencountered in transit-stadia work First, let us discussthe common situation in which you desire to determinethe difference in elevation between an instrument stationof known elevation and a ground point of unknownelevation. This situation is shown in figure 8-9, view A.In this view, the elevation of the instrument station P isknown and it is desired to determine the difference inelevation between P and the rod station P_{1}. Thehorizontal center-line height of the instrument (h.i.)above point P is equal to PA. As you can see, this h.i. isdifferent than the HI that you are accustomed to workingwith indirect leveling. The rod reading is P_{1}B.From your studies, you know that the difference inelevation (DE) between P and P_{1 }can be expressed asfollows:Therefore, the ground elevation at P_{1 }can be expressedas follows:Now let us sight on the rod such that P_{1}B = PA = h.i. Inthis case, the situation occurs in which a similar triangle(PC_{1}P_{1}) is formed at the instrument station P. Fromobservation of these similar triangles, you can see thatthe DE= P_{1}C_{1 }= BC. Therefore, the ground elevation atP_{1 }can be simply expressed as follows:This is an important concept to understand whenshooting stadia from a station of known elevation As8-8