AMPLITUDE

, in gunnery, the range of the projectile, or the right line upon the ground subtending the curvilinear path in which it moves.

Amplitude, in astronomy

, is an arch of the horizon, intercepted between the true east or west point, and the centre of the sun or a star at its rising or setting: so that the amplitude is of two kinds; ortive or eastern, and occiduous or western. Each of these amplitudes is also either northern or southern, according as the point of rising or setting is in the northern or southern part of the horizon: and the complement of the amplitude, or the arch of distance of the point of rising or setting, from the north or south point of the horizon, is the azimuth.

The amplitude is of use in navigation, to find the variation of the compass or magnetic needle. And the rule to find it is this: As the cosine of the latitude is to radius, so is the sine of the sun's or star's declination, to the sine of the amplitude. So in the latitude of London, viz, 51° 31′, when the sun's declination is 23° 28′; then

cos. 51° 31′ the lat.	-9.7939907
sin. 23 28 the decl.	+9.6001181
sin. 39 47 the ampl.	9.8061274

That is, the sun then rises or sets 39° 47′ from the east or west point, to the north or south according as the declination is north or south.

Magnetical Amplitude, is an arch of the horizon, contained between the sun or star, at the rising or setting, and the magnetical east or west point of the horizon, pointed out by the magnetical compass, or the amplitude or azimuth compass. And the difference between this magnetical amplitude, so observed, and the true amplitude, as computed in the last article, is the variation of the compass.

So if, for instance, the magnetical amplitude be observed, by the compass, to be 61° 47′, at the time when

it is computed to be	39	47,
then the difference	22	0 is the variation west.