OF ARTS AND SCIENCES. 259 



simply of the telescope, described above, turned around its axis 90", 

 and a delicate level screwed firndy to its tube. To make sure that the 

 telescope is turned by precisely the right amount, it is well to have a 

 second level at riu;ht angles to this to render the threads of the mi- 

 crometer exactly horizontal. The size of the divisions of the level and 

 of the micrometer must be previously determined; their relative value 

 being most easily found by directing the telescope towards any distant 

 object, and slightly inclining it, so that the bubble shall occupy various 

 positions in the tube. The corresponding positions of the object are 

 read by the micrometer, and a curve constructed with ordinates ecpial to 

 these readings, and abscissas to the position of the middle of the l)ubble 

 of the level. The reading of the micrometer corresponding to a perfectly 

 level line must next be determined. This may be found by setting the 

 telescope up at two not very distant points, and reading the height of 

 each from the other. The mean will give the direction of a horizontal 

 line ; since the elevation in one case equals the depression in the other. 

 The direction is, however, best found by observing the height of some 

 known objects ; since this eliminates various errors, as will be described 

 below. The height of any object is more readily determined by direct- 

 ing the telescope towards it, and bringing the bubble nearly to the 

 centre of the tube. Then read the position of the object by the mi- 

 crometer ; and, finally, read the exact position of the two ends of the 

 bubble, taking care not to touch the telescope. These readings may 

 then be reduced to seconds of altitude, as follows : Call A the required 

 altitude in seconds, m the reading of the micrometer, m} its reading 

 when the telescope is directed towards an object at the same height as 

 its own, and b the mean of the two ends of the bubble of the level. 

 Again, let s equal the magnitude of each division of the level in 

 seconds, and I the corresponding magnitude of the level divisions. 

 Then A =. (m — ?m^) s -{- hi. The elevation in metres or feet is then 

 found by multiplying the tangent of this angle by the horizontal 

 distance of the object, and correcting for the curvature of the earth and 

 for refraction. The fii-st of these corrections may be made with great 

 precision by the formulas or table given in the Coast-Survey Ileport for 

 1871, pp. 160 and 169. The second correction is, however, very 

 irregular, and may, therefore, generally be regarded as nearly propor- 

 tional to the square of the distance. Since the correction for 

 curvature is also nearly proportional to the square of the distance, we 

 may write the elevation A' = Z> tang A -\- m Z)-, in which D is the 

 horizontal distance, and m a quantity dependent on the condition of 

 the air. If, therefore, the height of any distant object visible is 



