AMPLITUDE, in astronomy, an arch of the horizon intercepted between the east or west point thereofond the centre of the sun, star, or planet, at its rising and setting, and so is either north or south.
If the amplitude be taken from the rising sun, or star, it is called its risin,g or ortive amplitude ; if, when it sets, its setting or occasive amplitude. The sun's amplitude, either rising or setting, is found by the g, lobes, by bringing the sun's place to the horizon, either on the east or west side, and the degrees from the, east point, either north or south, are the amplitude required. To find the ampli tude trigonometrically, say, as the cosine of the latitude : radius:: sine of the pre sent declination : sine of the amplitude. This problem is useful in navigation, to find the variation of the compass. Thus in latitude 51° 31', when the sun's dee& nationis 23° 28', then we say, As 60. S. 51° 31', : 10. &c. :: S. 28° 28'
: S. Amp. or, a.s 9.793990 : 10. &c: 9.600118 : 9.806127 = sine of 39°47' = the amplitude sought : tlrat is, the sun then rises or sets 39° 47' from the eitst or west point to the north or south, as the declination is either north or south.
Ametrrune, map:erica!, the different rising or setting of the sun, from the east or west points of the compass. It is found by observing the sun, at his rising and setting, by an amplitude compass. The difference between the magnetics.' amp& tude and the true amplitude is the raria tion of the. compass. If the magnetical amplitude be found to be . . . 61' 55' at the time it is computed as above to he . . . 39° 47' then the difference 22° 8' is the variation westward.