On Stadia Measurement. 



Written especially for this Catalogue by GBO. J. SPECHT, C. E., San Francisco, Cal. 



A transit or theodolite, which is provided with the so-called stadia wires and a 

 vertical circle, furnishes the means to obtain simultaneously the distance and the 

 height of a point sighted at without direct measurement, and with the only use of 

 a self-reading rod, held at the point of which the horizontal and vertical position 

 is to be determined in reference to the instrument-point. 



Besides the ordinary horizontal arid vertical cross hairs of the diaphragm of the 

 telescope, two extra horizontal hairs are placed parallel with the center one, and 

 equally distant on each side of it, which, if the telescope is sighted at a leveling 

 rod. will inclose a part of this rod or stadia-rod, proportional to the distance from 

 the instrument to the rod. By this arrangement we have obtained an angle oi 

 sight, which remains always constant. 



* Supposing the eye to be in the point O (Fig. 1) , 

 the lines O e and O k represent the lines of sight 

 from the eye through the stadia-wires to the rod, 

 which stands consecutively at k e, i d, h c, g b and 

 / a. According to a simple geometrical theorem 

 we have the following proportion : 



Oa:Ob:O c:O d:Oe=af:b g:ch:di: ek, 



which means that the reading of the rod placed 



on the different points a, 6, c, d and e is propor- 



<* tional to the distances O a, O &, O c, O d and O e. 



The system of lenses which constitute the telescope do not allow the use of this 

 proportion directly in stadia measurements, because distances must be counted 

 from a point in front of the object glass at a distance equal to the focal length of 

 that lens. 



a a 



Figure 2 shows a section of a telescope provided with stadia wires. 

 In order to determine the distance of the rod from the instrument it will be neces- 

 sary to use the following equations. From the "law of lenses " we have the relation 



in which /, and /, are "conjugate foci " and /is the focal length of the object glass. 

 From the diagram it is evident that C : A B = D : a b. If we let p = the dis- 

 tance of the stadia wires from each other, /,= distance C and a = the space on the 

 rod AB, and D the distance from the center of the instrument to the rod, then the 

 second equation becomes / 2 : a = /. : p. Eliminating/! from these equations we find : 



or we may write, since is constant, 



