II. To take the Moon's Altitude at Sea.

62. Prepare the sextant as in last Article:-if the time of observa-
tion be at night, let the green shade, or one of the lightest red screens,
intervene betwixt the two reflectors (by day this becomes unnecessary):
-then proceed as directed for the sun; observing that it is the round
or well-defined limb of the moon, whether it be the lower or the upper,
that is to be brought in contact with that point of the horizon on which
a plumb-line would fall if dropped from the moon's centre. Now, the
angle indicated by the vernier, read-off by means of the microscope,
will be the observed altitude of the moon's lower or upper limb, ac-
cording as it may be enlightened.

III. To take the Altitude of a Star at Sea.

63. Set the index of the quadrant or sextant to zero on the limb.—
Hold the instrument in a direct vertical position: look through the
sight-vane of the quadrant, or the socket of the sextant, as the case
may be, and direct the sight to the star through the transparent part of
the horizon-glass; then, by a slight motion of the instrument to the
left hand, the reflected image of the star will be seen in the silvered
part of that glass. Move the index forward, by hand, and the star will
appear to descend: continue the motion of the index, in a gentle man-
ner, and follow the reflected image of the star with the eye, directing
the sight lower and lower till the star seems to touch the horizon,
Screw a telescope, with a good field of view and properly adapted to the
purpose, into the socket; clamp the index sufficiently tight for observa-
tion; and make the contact of the star and the horizon perfect by
means of the tangent-screw. Give the instrument an immediate vibra-
tory motion, of which the eye is to be the centre, so as to be satisfied
that the reflected image of the star touches the horizon exactly in a
point which is perpendicular to the real star; which, of course, will
always be the shortest distance between the real star and the horizon.
Then, the angle indicated by the vernier, and read-off by means of the
microscope, will be the observed altitude of the star's centre. Should
the horizon be ill-defined, and the star not very bright, the telescope
must be dispensed with: in this case the observer's line of vision to the
point of contact is to be guided by the sight-vane.

When the altitude of the star is considerable, some other star, be-
sides the required one, may appear by reflection in the speculum of
the horizon-glass when this happens, the false star may be readily
distinguished by its tremulous motion: for it will dance in the specu-

lum as the index is moved forward: and thus, there can be no danger of its ever being mistaken for the real star; because this will appear to remain stationary about the middle of the fixed reflector.

IV. To take the Altitude of a Planet at Sea.

64. As the diameters of Mars and Saturn are but of small value, the altitudes of those planets may be taken the same as if they were fixed stars, as directed in the last Article :-observing, however, that it is the centre of the object that is to be brought in contact with the horizon. But, as Venus and Jupiter have very sensible diameters, it is the lower limb of either of these that is to be brought in contact with the horizon :—and, although Venus is subject to all the various phases of the moon, yet, in the absence of the sun, it is her enlightened limb that will be always next to the horizon; and therefore it is the altitude of her lower limb that is to be taken at night. However, for the ordinary purposes of navigation, it will, in general, be quite sufficient to bring the centre of the planet down to the horizon of the sea :-then, the angle indicated by the vernier will be the observed altitude of the planet's centre, or of its lower limb, as the case may be.

V. To take the Altitude of a Celestial Object on Shore.

65. Altitudes are taken on shore by means of an artificial horizon. And, in settling the positions of places in-land in an astronomical manner, or in ascertaining the error and the rate of a chronometer on shore, the observer must, in all cases, have recourse to an artificial horizon for the purpose of taking the necessary angles of altitude.— But, as this instrument, unlike the quadrant and the sextant, is not to be found in the hands of all nautical persons, I shall, therefore, make a few observations relative to its description and use.

66. Although there is a great variety of artificial horizons now extant, yet, for the sake of conciseness, I shall only treat of the two that are in my own possession. The first of these consists of a plane speculum, or polished plate of dark glass (4 inches long by 3 broad), fixed in a brass frame, and standing upon three adjusting screws: by means of these and a spirit-level, placed in different positions on its surface, it may be made perfectly parallel to the plane of the horizon: observing that the adjusting screws are to be turned until the air-bubble rests in the middle of the spirit-level on the surface of the speculum.-The other is the common, or quicksilver horizon;-this simply consists of a small wooden trough, about half an inch deep, 34 inches long, and 24 inches broad;-into this trough a few pounds of mercury or quicksilver are

poured; the surface of which assumes when settled, agreeably to the nature of fluids, an exact horizontal plane. To prevent the mercury from being ruffled or agitated by the action of the wind, a roof is placed over it, in which are fixed two plates of glass, the two sides of each plate being ground mathematically plane and parallel to one another: -And, of all artificial horizons an instrument of this description is the very best that can be employed in taking the altitudes of the heavenly bodies.

Of the Use of the Artificial Horizon; that is, to observe the Altitude of the Sun, or other Celestial Object, with a Sextant, and an Artificial Horizon.

67. In taking the altitude of the sun, or other luminary, the observer is to place his artificial horizon betwixt him and the object selected for observation; and at such a convenient distance as to see the image of that object reflected from the middle of the quicksilver as well as the real object in the heavens :-then, having screwed the plain tube, or the natural telescope of the sextant into its place in the socket; and placed one or two of the dark screens, according to the brightness of the sun, to intervene on each side of the horizon-glass; the lower limb of the reflected image of the sun, as seen through the erect or natural telescope, is to be brought into contact with the upper limb of the image reflected from the artificial horizon :-but, if the altitude of the upper limb of the object be required, it must be brought into contact with the lower limb of the image as seen in the artificial horizon. Now, the angle on the arch of the sextant being read off, and the index error, if any, applied to it, the result will be the double of the sun's, or other object's altitude above the horizontal plane: to the half of which, if the object be the sun, let the semi-diameter, refraction and parallax be applied, and the true central altitude will be obtained. This shall be shown hereafter.

68. Since neither the plain tube, nor the natural or erect telescope, can be depended upon in taking observations when rigorous exactness is required; the inverting telescope should, therefore, be invariably made use of, in all cases where angles of altitude are to be measured with astronomical precision :-and here, perhaps, it may not be unnecessary to state that when the inverting telescope is used, the lower limb of the sun, or moon, will appear to be the upper limb, and conversely. Hence, in observing the altitude of the lower limb of the sun or moon, the apparent upper limb of the object, as seen in the horizonglass through the inverting telescope, is to be brought into contact with

the lower limb of the image in the artificial horizon :-in this case the reflected image in the artificial horizon will appear to be uppermost.— Again, in observing the altitude of the upper limb of the sun or moon, the apparent lower limb of the object, as seen in the horizon-glass of the sextant through the inverting telescope, is to be brought into contact with the upper limb of the image in the artificial horizon :-in this case the reflected image in the artificial horizon will appear to be undermost. 69. If an observer be placed as remote from, or as near to, an artificial horizon as possible, the rays of light passing from the sun or other celestial object to his eye, and from that object to the surface of the artificial horizon, will, on account of the immense distance of such object from the earth, be physically equal and parallel in every respect to each other:-hence, it is easy to perceive that it is immaterial whether the artificial horizon be placed high or low, remote or near, with respect to the observer, provided he can but see the object's reflected image therein.

70. When an angle of altitude is taken by means of an artificial horizon, its measure on the limb of the sextant will always be double of the true value thereof above the horizontal plane :-this will appear evident by considering that if a person places himself at any distance before a plane mirror, or common looking-glass, his reflected image will appear just as far behind such looking-glass as he is before it :— and, upon this simple principle it is that the reflected image of the sun, or other object, will appear to be as far below the surface of the artificial horizon as the real object is above it ;-but since the limb of the real object, as reflected from the index-glass of the sextant, is to be brought into contact with that of the image apparently reflected below the surface of the artificial horizon, it is therefore manifest that the contained angle, as expressed on the arch of the sextant, must be equal to twice the measure of the observed angle of altitude above the plane of the horizon :-and from this we may readily perceive that angles of altitude taken in the above manner are not affected by the angle of horizontal depression, commonly called "the dip of the horizon."

71. The principles of the artificial horizon may be more clearly explained in the following manner, viz.—When a ray of light flows from the sun, or any other celestial body, and falls upon the surface of a mirror placed horizontally, it will be reflected in such a manner, that the angle which is contained betwixt the reflected ray and the zenith will be equal to the angle which is contained between the direct ray and the zenith. Hence, let a celestial object be at any degree of elevation above the horizon; the angle of reflection Z CD, will be always equal to the angle of incidence Z CA, as in the annexed diagram.

the direction of C E:-then, by directing his sight to the surface of the quicksilver, the solar image will appear to be transferred to the point B; that is, it will be seen in the line of reflection D E C, continued to B. But when two straight lines cut one another, the opposite angles are equal; therefore, the angle B C N, is equal to the angle Z C D: and since this is the angle of reflection, which is equal to the angle of incidence, therefore the angle B C N, is also equal to the angle of incidence Z C A-Hence, the reflected image of the sun at B, will always appear to be as far from the nadir N, as the real sun at A is from the zenith Z; and, consequently, the reflected sun at B must invariably appear to be as far below the horizon H, as the real sun at A is above it. Now, the true altitude of the celestial object is expressed by the arc HA; but, since the round or well-defined limb of the object at A must be brought in contact with the well-defined limb of the reflected image at B; it is thus manifest that the are A B, is double the value of the arc H A; and, therefore, it is equal to twice the altitude of the celestial object.-Hence, it is clearly evident that an angle of altitude taken by means of an artificial horizon, must, after being duly corrected for the index error of the sextant, be divided by 2, in order to obtain the correct value of the observed altitude.

72. When the altitude of a celestial object exceeds 60 degrees, it cannot be taken by means of a sextant and an artificial horizon; because, in this case, the measure of the double angle of altitude would exceed the limits of the graduated arch of the sextant.

73. In observing equal altitudes by means of an artificial horizon, or