260 PROCEEDINGS OF THE AMERICAN ACADEMY 



known, it is better to deduce m from its observed altitude, and from 

 this compute the other elevations. Were it not for the uncertain error 

 of refraction, this instrument would give results of extreme precision. 

 Thus an error of 6" in the altitude of a mountain one hundred kilo- 

 metres distant would only correspond to a difference in height of about 

 three metres. The uncertainty of refraction is much greater than this, 

 and far exceeds the instrumental errors, except in a small telescope. 

 Since, however, this cause of error is present when the theodolite is 

 used, we see that altitudes can be obtained by this instrument with all 

 the precision of the best theodolite ; in fact, with all the accuracy of 

 which the method is capable. Apart from its lightness and cheapness, 

 it has this great advantage over a theodolite, — that, since the level is 

 firmly attached to the telescope, there is little liability to error ; while, 

 as the theodolite measures the angle between the telescope and the 

 horizontal limb of the instrument, any injury is liable to throw it out 

 of adjustment. With the instrument as described above, no angles 

 could be measured gi'eater than the diameter of the field of view. 

 This ditiiculty may be remedied by attaching another level, slightly 

 inclined to the first, so that the two fields of view corresponding to a 

 horizontal position of the two levels shall be nearly tangent to each 

 other. A third level serves still further to extend the range of the 

 instrument. Thus, if the field of view is about 2°, angles between 1° 

 and — 1° may be measured by the first level, between 1° and 3° with 

 the second, and between — 1° and — S^ with the third. The instru- 

 ment, in this form, may be called a micrometer-level. One of its 

 greatest advantages is the rapidity with which elevations may be 

 measured. There is no difficulty in measuring thirty or forty moun- 

 tains in this way per hour, without the labor of ascending them ; while 

 by the barometer it rarely happens that more than one can be 

 measured in a day, and with the ordinary level the altitude of a 

 high mountain would be the labor of days or weeks. The rapidity is 

 also much greater than that of a theodolite ; since no accurate mount- 

 ing is needed, and a micrometer-scale can be read at least as quickly 

 as the telescope can be set, so that the entire time of reading the circle 

 by the vernier is saved. 



One of the principal advantages of both the instruments here pro- 

 posed is, that either may be made out of a telescope such as any 

 explorer would be likely to carry. By simply adding a mirror in 

 front, a photographed scale, and three levels,- distances and elevations 

 may be measured with all the accuracy ordinarily required. This 

 method may be applied with especial advantage on a mountain-top ; 



