The instrument should have a vertical limb of superior con- 

 struction and its index error should be either allowed for, or regulat- 

 ed constantly with a Control Bubble. For stadia work the control 

 bubble (see p. 94) is nearly indispensible. 



The Accuracy of Stadia Surveys depends upon the fineness 

 of the wires, the power, illumination and character of the field in 

 the telescope, the length of sight,* atmospheric conditions, the value 

 and stability of the wire interval, the nearness of the sight to the 

 surface of the earth, the personal equation, the kind of graduations 

 on the rod and the number of observations or the extent of the 

 survey. 



The size of the web runs from .0001 to .0003 in. The 

 latter is considered coarse if under high magnification, but some 

 prefer them so, to distinguish them from the finer central cross 

 wires (see also p. 144). 



Theory 



The principle upon which the stadiametric distance is deter- 

 mined is the simple geometric proposition that the homologous 

 sides of similar triangles are proportional. In Fig. 60 let the two 

 dots at the diaphragm, F, represent the stadia wires. The focal 

 length of the objective being F, let the interval between the wires 

 be one one-hundredth of that amount and let it be represented by 



F -r- 100 *a ab = /. 



Every lens has two focal planes. In this case let the anterior 

 focal plane be designated by Fi so that OFi FO. In any tele- 

 scope the lines of vision are not projected from the eye but rather 

 there is received an impression of the field of view. Then let it be 

 assumed that a rod being placed a certain distance from the instru- 

 ment, a ray of light proceeding from the point A, will pass through 

 Fi, on to , then by refraction through the objective, finally pass 

 the upper stadia w r ire and out through the eyepiece .omewhat as in- 

 dicated. The same course of reasoning is true for the point B and 

 it is obvious that the further the rod from the instrument the greater 

 will be the interval and that this interval, /, will always be propor- 

 tional to the distance of the rod from Fi. Then, 



ab : OFi : : I : D or 



/ : / : : / : D 



by which it appears that the origin of the distance, J), is at Fi and 

 not at the center of the instrument, and further that 



D = I (/-r- fl 



/ -f- i is a constant factor for each instrument, usually known 

 as K, corresponding to 100 more or less closely. Our method of 



* L. H. Goodwin in h. & M. Jour., Nov. 24, 1914, p. 957 sets 700 ft. as the 

 limit by which tht probable error < 1:800. 



104 



