68 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



III. DETERMINATION OF THE ANGULAR EQUIVALENT OF 

 ONE DIVISION OF A SPIRIT LEVEL. 



The methods most in use in this country for the deter- 

 mination of the value of one division of a level require 

 that the level should be attached either to a level-trier or 

 to a telescope provided with a good micrometer. In field 

 astronomy it frequently happens that neither of these aux- 

 iliaries is available and the following method, which in 

 respect of precision is not inferior to either of the others, 

 may be employed with advantage since it requires no aux- 

 iliary apparatus other than a theodolite or engineer's tran- 

 sit. The original suggestion of this method is supposed 

 to be due to Braun. 1 



Let the spirit level be firmly attached to a theodolite 

 which is thrown out of a level so that its vertical axis makes 

 an angle of from 1 to 3 with the true vertical. It is prac- 

 tically convenient to so attach the level that the radius of 

 curvature drawn through the middle point of its scale shall 

 be approximately parallel to the vertical axis of the theod- 

 olite, i. e. the level shall be in adjustment. As the theod- 

 olite is turned about its vertical axis the level bubble will 

 run from one end of its tube to the other and back again 

 during a complete revolution of the instrument, and two 

 positions, two readings of the azimuth circle, may be found 

 in which the bubble will stand near the middle of its scale. 

 A small turning of the instrument either way from one of 

 these positions will produce a corresponding small motion 

 of the bubble in its tube, and this turning of the theodolite 

 and resulting motion of the bubble may be made to furnish 

 not only the value of a division of the level, but also a test 

 of the uniformity of its curvature. 



To determine the relation between the readings of the 



l Astronomische Nachrichten, No. 2490. 



