1837-] Captain Kater's Altitude and Azimuth Instrument. 139 



error of the hour angle in seconds of space. 



In surveying extended tracts of country, the circle may also be used 

 with advantage, for, small as it is, from the fineness of its wires and 

 steadiness, it is capable of as much exactness as those lumbering in- 

 struments the theodolites, as generally constructed in England for land 

 surveying, beyond which purpose they are fit for nothing. In measur- 

 ing six horizontal angles round a station, each angle being measured 

 on a different part of the circle, after moving the instrument, the sum 

 was but little less than 360° viz. = 359° i'0"; whence it appears the 

 instrument will measure an horizontal angle with only a maximum er- 

 ror of 10", a degree of exactness to which no theodolite can generally 

 approach. 



From the readiness with which it gives accurate results for the lati- 

 tude, the circle when used in surveying would make very apparent the 

 error caused by neglecting the difference of latitude between the foot 

 of the perpendicular and the parallel, or by taking the distance from 

 the perpendicular as the difference of latitude, as is sometimes done in 

 rough work. The amount of this error is shewn by the subjoined table 

 computed from the formula. 



"i 



error — \ tt • tang. \. sin 1" 

 when it" is the perpendicular in seconds of the equator, and V the lati- 

 tude found by turning the distance from the perpendicular into seconds 

 by Lambton's table. 



Table of the error always subtractive from X. 



X 



PERPENDICULAR. 





30' 



1° 0' 



1° 30' 



2° 0' 



2° 30" 



30° 0' 



5° 



1" 



3" 



8" 



11" 



17" 



25" 



10 



L4 



5 



12 



22 



35 



50 



15 



2 



8 



19 



34 



53 



76 



20 



3 



11 



26 



46 



71 



103 



25 



4 



15 



33 



59 



91 



132 



30 



5 



18 



41 



72 



113 



163 



Now, as the error likely to be committed in using an indiffernt in- 

 strument is not likely to be more than thirty feet in sixty miles, the 

 error, as shewn in the table, is too great to be neglected. This error 

 may be more conveniently applied by computing a table in which as 



