meridian, in which case the variation observed was allowed upon the beatings. But in all other cases it was necessary to find, first what was the true variation, and second what it would be with the ship's head in the given direction.
Example. Suppose that with the ship's head W.S.W., the variation was observed to be 29° 12′ west in the English Channel, where the dip is 72° north; and I wished to know what variation is to be allowed upon a set of bearings taken when the head was N.E. ½ E.
1st. To find the true variation.
Dip 72 × ,053 = error for eight points 3°,816 = (3° 49′ =) 229′. Course 6 points, distance 229′ = departure 212′, or 3° 32′ correction. Being in north dip, the north end of the needle was drawn forward, that is westward in this case, and the west variation observed was too great; therefore 29° 12′ observed, −8° 32′ correction = 25° 40′ the true west variation.
2nd. To find from thence what is to be allowed with the head at N.E. ½ E.
Course 4½ points, distance 229′ = departure 177′, or 2° 57′ correction. With the head N.E. ½ E., the north end of the needle at the binnacle would be drawn eastward, and the west variation be less than the true; therefore, true variation 25° 40′ − 2° 57′ = 22° 43′ to be allowed, deduced from 29° 12′ observed.
This operation will at first seem complex and tedious to the seaman; but when a common multiplier is once obtained and the principle of its use understood, it will be found not more troublesome than working a meridian altitude for the latitude; and the accuracy required is generally much less.
Some persons will be disposed to doubt whether the differences found in the azimuths and amplitudes on changing the direction of the ship's head, really took place in the bearings themselves; a few instances are therefore subjoined, in which bearings were taken the instant before tacking from the shore, and so soon as the ship was round and compass steady, the same objects were again set. Differences took place without exception, and always the same way; but some of the objects being too near for the bearing not to be affected by a small change in the ship's place, those only are selected whose distance was more considerable. The first examples