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 instruments the theodolites, as generally constructed in England for land surveying, beyond which purpose they are fit for nothing. In measuring 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° 1′0″; whence it appears the instrument will measure an horizontal angle with only a maximum error of 10″, a degree of exactness to which no theodolite can generally approach.
From the readiness with which it gives accurate results for the latitude, 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.
when π″ is the perpendicular in seconds of the equator, and λ′ the latitude found by turning the distance from the perpendicular into seconds by Lambton's table.
Table of the error always subtractive from λ.
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λ PERPENDICULAR
30′ 1° 0′ 1° 30′ 2° 0′ 2° 30″ 30° 0′
5° 1″ 3″ 11″ 17″ 25″
10 1.4 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 instrument 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
