90 



within 500"; that means, that the inclination of the stadia shall not be more than 

 0.023' in a 10' stadia, or 0.034' in a stadia of 15' length. 



Determination of the two constant coefficients c and k. Although the stadia wires 

 are usually arranged so that the reading of one foot signifies a distance of 100 feet, 

 I will explain here, how to determine the value of it for any case. Suppose the 

 engineer goes to work without knowing his constant, and not having adjustable 

 stadia wires. The operation then is as follows : 



Measure off on a level ground a straight line of about 1000' length ; mark every 

 100', place the instrument above the starting point, and let the rodman place his 

 rod on each of the points measured off; note the reading of all three wires separ- 

 ately, repeat this operation four times ; the telescope must be as level as the ground 

 allows ; measure the exact height of the instrument, i. e., the height of the telescope 

 axis above the ground. Then find the difference between upper (o) and middle 

 (m) wire ; between middle (w) and lower (M) wire, and between upper (o) and 

 lower (M) wire, from the four different values for each difference, determine the 

 average value ; then solve the equation for the horizontal distance (1) D = k.a -f- c., 

 with the different average values, and you find the value of k and c. In case the 

 stadia wires should not be equi-distant from the center wire, there will be three 

 different constants, one for the use of the upper and middle, one for the use of the 

 middle and lower, and one for the upper and lower wire. 



If the stadia wires are adjustable, the engineer has it in his power to adjust them 

 so that the constant k = 100, or k = 200, which he accomplishes by actual trial along 

 a carefully measured straight and level line. 



The constant c, which is usually one and a half times the focal length of the object- 

 glass, can be found closely enough for this purpose by focussing the telescope for a sight 

 of average distance, and then measuring from the outside of the object-glass t<> the 

 capstan-head si'ivws of the cross-hairs. This constant must be added to every stadia 

 sight; it may be neglected for longer distances. 



Stadia Measurements. 



Written for this catalogue and manual by H. C. PEARSONS, C. E., Ferrysburg, Mich. 



In view of the great and growing interest in the subject of ''Stadia Measurements," 

 the following solution of the problem is offered, as applied to inclined measurements. 



This solution is made from a different geometrical consideration than that usually 

 employed, and it effectually does away with the necessity for any subsequent cor- 

 rections, as with most schemes in use for inclined distances. 



In the following discussion, let 



R =the reading of the stadia rod; 



D = the horizontal distance from plumb line of transit to stadia rod, which must 



be vertical. 



m = the angle of elevation or depression to the smaller reading of the stadia rod. 

 n = the same angle to the larger reading. 



Through the point c, at the distance of unity from the centre of instrument, 

 draw the vertical c b. Then the rod A B, being also vertical, the triangles a o b 

 and AoB are similar, as are also the triangles cob and CoB. But the read- 



