Figure 8-4.-(A) Angle of elevation and (B) angle of depression.The instrument constant is the same for all readings.Suppose that you are using an externally focusinginstrument with an instrument constant of 1.0. If thestadia interval is 1 foot, then the horizontal distance isas follows:h = (100)(1) + 1 = 101 feet.If the stadia interval is 2 feet, the horizontal distance isas follows:h = (100) (2) + 1 = 201 feet.Now suppose that you are using an internallyfocusing instrument. In this case, the instrumentconstant is zero and can be disregarded. This is theadvantage of an internally focusing telescope. So, if thestadia interval is 1 foot, the horizontal distance is simplythe stadia distance which is 100 feet. For a stadia readingof 2 feet, the horizontal distance is 200 feet.Horizontal distance usually is stated to the nearestfoot. Occasionally on short distances (under 300 feet),it maybe specified that tenths of a foot be used.Stadia Formulas for Inclined Sights.— -Most oftenthe sights needed in stadia work are not horizontal. Itmay be necessary to incline the telescope upward ordownward at a vertical angle. This vertical angle (a)may be either an angle of elevation or an angle ofdepression, as shown in figure 8-4. If the line of sight iselevated above the horizontal, you speak of it as an angleof elevation. If the line of sight is depressed below thehorizontal, the vertical angle is an angle of depression.In either case, you find the horizontal and verticaldistances by using the following formulas:These two expressions are called the stadiaformulas for inclined sights in whichh^{=}v^{=}h =a =f + c =horizontal distancevertical distancestadia distancevertical angleinstrument constantRefer to figure 8-5 for clarification of the terms inthe stadia formulas for inclined sights.Figure 8-5.-Stadia Interval—inclined sight.8-5