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LXXXIV. The Accuracy of the Internally Focussing Telescope 

 in Taclieometry. By T. Smith, F.Inst. P.* 



SINCE its first introduction by Zeiss the internally 

 focussing telescope has come into very general use 

 in surveying instruments. Its adoption appeals to manu- 

 facturers since it makes for compactness in other parts 

 of the instrument to which it is fitted, and to surveyors 

 on account of the convenience in an instrument inevitably 

 exposed to all kinds of weather of having all delicate parts 

 permanently sealed up. At first sight it would appear 

 to be unsnited to tacheometrical methods of survey } since 

 the value of a distance determined by the reading on a 

 staff between fixed stadia lines does not differ by a constant 

 length from the actual distance. It is by now well known 

 :that with a suitable construction of the telescope the errors 

 involved in its use are not serious over a reasonable range 

 of distances, but the theoretical discussions of these errors 

 hitherto published appear needlessly complex, and the 

 results to which they lead are less general and conclusive 

 than is desirable. Largely as a consequence of the un- 

 satisfactory treatment of the problem, the best procedure 

 in designing and calibrating such telescopes has not been 

 .apparent. It is hoped that this discussion avoids these 

 faults. 



The staff reading given by the instrument, it must be 

 Tealized, is essentially a constant divided by the magni- 

 fication for the image formed by the telescope in the plane 

 of the stadia lines. The distance, apart from an additive 

 -constant, is assumed for practical purposes to be a constant 

 multiple of this reading. This consideration forms the key 

 to the following investigation. 



Let the staff' S be a distance d in front of the first 

 principal focus F of the objective, and the stadia lines S' 

 -a distance x in front of the second principal focus F' of 

 -the focussing lens. Denote the powers of these two lenses 

 by k and k respectively, and the power of the combination 

 for the particular configuration in which the image of S is 

 coplanar with S ; by K. Then since, apart from a constant, 

 x is the separation of the two component lenses, 



K = A-xfCfc', (1) 



where the constant A is the value assumed by K when 



_F' coincides with S'. Now suppose that the magnification 



* Communicated by the Author. 



