430 LECTURE XLV. 



The quadrant in most common use, especially for nautical observations, 

 was first proposed by Newton,* but improved, or perhaps reinvented, by 

 Hadley.t Its operation depends on the effect of two mirrors which bring 

 both the objects, of which the angular distance is to be measured, at once 

 into the field of view ; and the inclination of the speculums by which this 

 is performed serves to determine the angle. The ray proceeding from one 

 of the objects is made to coincide, after two reflections, with the ray coming 

 immediately from the other, and since the inclination of the reflecting sur- 

 faces is then half the angular distance of the objects, this inclination is read 

 off on a scale in which every actual degree represents two degrees of 

 angular distance, and is marked accordingly. There is also a second fixed 

 speculum, placed at right angles to the moveable one, when in its remotest 

 situation, which then produces a deviation of two right angles in the ap- 

 parent place of one of the objects, and which enables us, by moving the 

 index, to measure any angle between 180 and 90. This operation is 

 called the back observation ; it is however seldom employed, on account of 

 the difficulty of adjusting the speculum for it with accuracy. The reflect- 

 ing instrument originally invented by Hooke was arranged in a manner 

 somewhat different. (Plate XXXV. Fig. 511.) 



From the meridian altitude of any point, it is easy, when the elevation of 

 the pole is known, to deduce its declination ; and its right ascension may 

 be found from the time of its passage over the meridian after that of the 

 equinoctial point, allowing 15 degrees for each sidereal hour. (Plate 

 XXXV. Fig. 512.) 



In all astronomical observations it is necessary to make proper cor- 

 rections, according to the rules of optics, for the effects of atmospherical 

 refraction ; and also, in observations on the moon more especially, for those 

 of parallax, or the difference of the apparent place of the luminary with 

 respect to the earth's centre, and to the place of the spectator, which is 

 equal to the angle subtended at the centre of the luminary by the semidia- 

 meter of the earth passing through the place of observation ; since all cal- 

 culations of the geocentric places of the heavenly bodies are referred to the 

 earth's centre. This angle, which is to be added to the apparent altitude, 

 amounts sometimes, in the case of the moon, when near the horizon, to 

 more than a degree ; the refraction, which is in a contrary direction, and is 

 to be subtracted from the altitude, being at the horizon about 33 minutes. 

 (Plate XXXV. Fig. 513.) 



The most important applications of practical astronomy are in the de- 

 termination of the latitudes and longitudes of places on the earth's surface. 

 The latitude, which is the angular distance of the place from the equator, 

 or the angle formed by the plane of its horizon with the earth's axis, is 

 easily ascertained by finding the meridian altitude of a body, of which the 

 declination is known ; since, by deducting or adding the declination, we 

 have at once the elevation of the equinoctial, or of the plane of the equator 

 above the horizon, and subtracting this from a right angle, we find the 

 elevation of the pole, or the latitude. (Plate XXXV. Fig. 512.) 



It is also common to determine the latitude of a place by means of two 

 * Ph. Tr. 1742, p. 155. f See Lect. XXXVI. 



