OF ARTS AND SCIENCES. 257 



night, determine their hititude and longitude, and, during the day, 

 locate all prominent visible objects. 



To measure small distances, the method of the stadia and telemeter 

 gives excellent results, but is open to the objection that an assistant is 

 needed, who must carry a graduated pole to each point whose distance 

 is to be determined. This method also is only applicable to short 

 distances ; as beyond five hundred, or at most a thousand metres, the 

 pole appears so small, that its apparent length cannot be determined 

 with accuracy. 



These difficulties are, in a great measure, avoided in the following 

 instrument. A good traveller's telescope, or spy -glass, is mounted 

 firmly on a tripod, and a spider-line micrometer or scale of equal 

 parts is inserted in its eye-piece. In front of the object-glass is 

 fastened a piece of plane-glass, which may be set at any desired angle, 

 and clamped firmly. The angle may be roughly measured by a small 

 circle divided into degrees. The whole is free to turn around the 

 axis of the telescope. To measure the distance of any object, D, 

 Fig. ], the angular magnitude of the divisions 

 of the scale in the eye-piece, is first determined 



by the usual methods. The telescope is ^ * I> * 



then mounted at A, and directed towards D, d , 

 taking care to select for it some sharply 

 defined object, as a rocky crag, the trunk of 

 a tree, or the edge of a snow-bank. Select a 

 second object, C, nearly at right angles to D, ^ ' 

 and turn the glass in front of the telescope Fig. 1. 



until the reflection of C in its front surface 



shall be in the field at the same time as the image of D transmitted 

 through the glass. Measure accurately the interval between the two 

 images with the micrometer. Next measure off a distance AB from 

 A towards Cof one or two hundred metres, and place the telescope at 

 B. Again measuring the interval between the two images, takino- 

 care not to disturb the mirror, a result will be obtained which will 

 differ from the previous measurement by the angle ADB. From 



this triangle we deduce DB = AB - — ^ = AB sin A — r— , in which 

 ° sin D as ' 



d is the difference in the scale-readings, and s the magnitude of each 

 division in seconds. A should be taken nearly 90° ; in which case 

 sin A will very nearly equal unity. Its value may be found with suf- 

 ficient precision with the divided circle attached to the mirror, or by a 

 plane-table. The greatest accuracy will be attained when AB has 



VOL. XI. (N. 8. III.) 17 



