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λ DIFFERENCE OF LONGITUDE.
30′ 1° 1′ 1° 30′ 2° 0′ 2° 30′ 3° 0′
5° 1″ 3″ 6″ 11″ 17″ 24″
10 1 5 12 21 34 48
15 2 8 18 31 49 70
20 2 10 23 40 63 91
25 3 12 27 48 75 108
30 3 14 31 54 85 122
By using a table of this kind, the error may be corrected without any additional trouble, or wasting time in the niceties of the computation by the formula; if it is ever necessary to undertake a survey of any extent with the small circle, or to use inferior instruments, when others cannot be procured.
In sketching in a hilly country, like those which are common among the mountainous tracts of India, when it is difficult, and sometimes impossible, to ascend to the summit of hills, from the impenetrable jungle which generally clothes the sides, the circle becomes a very useful instrument, from the facility with which azimuths of the sun or moon may be taken with it; by which means an azimuthal triangulation may be carried on, with as much readiness as with a circumferentor, but with infinitely greater exactness.
In using the circle in this way the subjoined diagram will explain the method of operation.
Let A (Pl. 4 fig. 4) be the plan of a camp, from whence the hill stations D and C can be seen. Let B be a little hill from where D and C can also be seen. Let the distance A B be assumed as a base, and the distance guessed by the perambulator. Let the latitude be exactly ascertained at A, and also the angles B A C and B A D be measured from A, and also the angle between B and the sun's centre. Let the angles A B D and A B C be observed from B, then with the base A B the distance D C may be computed. From E, another camp beyond the range of hills D C, let the angle D £ C be measured, and also the angle between the sun and one of the stations D or C. Then, if M express the meridian, the angle M £ C being known, the angle M C E is also known, from the azimuth at E, and also the angle M C D from the azimuth at A, and, the distance D C being given, the triangle D E C may be computed. Again if F is another camp, separated from F by another range of hills, but from D and C can be seen, D E and C E can be computed in the some manner, and from E and F more points as G &c.
