in finding the index error of a quadrant or sextant, and the conjoint effect of those errors will be obviated. First. To find the Error for a Progressive Motion of the Index : Screw the inverting telescope into its place. Slack the index. Turn the tangent screw backward to nearly as far as it will go. Put the nonius of the index about 1:15' to the right of 0 on the arch, and then fasten the index sufficiently tight for observation.-Hold the sextant so that its plane may be parallel to the horizontal diameter of the sun: direct the sight to that object, and turn the tangent screw forward until the limbs of the sun seen by reflection and direct vision make a perfect contact.-Note down the angle and it will express the measure of the sun's diameter to the right of 0 on the arch.-Direct the sight again to the sun, and turn the tangent screw still forward until the opposite limbs are in perfect contact : note down the angle, and it will be the measure of the sun's diameter to the left of 0 on the arch.-Now, if both measures of the diameter are the same, there is no error in the angles shown by the progressive motion of the index; but if those measures do not correspond, half their difference is to be taken as the index error of the instrument, which error will be additive when the diameter measured to the right of 0 exceeds that measured to the left; otherwise, subtractive.-Then, this error is to be considered as a constant quantity (so long as the instrument does not meet with any accident), and to be applied to all increasing angles, either of altitude or distance, which may be taken by the progressive motion of the index. Again. To find the Error for a Retrogressive Motion of the Index : Slack the index. Turn the tangent screw forward to nearly as far as it will go. Put the nonius of the index about 1:15 to the left of 0 on the arch, and then fasten the index sufficiently tight for observation.-Hold the sextant as before; direct the sight to the sun, and turn the tangent screw backward until the limbs of the sun seen by reflection and direct vision make a perfect contact :-note down the angle, and it will express the measure of the sun's diameter to the left of 0 on the arch.-Direct the sight again to the sun, and turn the tangent screw still backward until the opposite limbs are in perfect contact; read off the angle, and it will be the the measure of the sun's diameter to the right of 0 on the arch.-Now, if both measures of the diameter are the same, there is no error in the angles shown by the retrogressive motion of the index: but if those measures do not correspond, half their difference is to be taken as the index error of the instrument; which error will be additive when the diameter measured to the right of 0 exceeds that measured to the left; otherwise, subtractive. Then, this error is to be considered as a constant quantity (so long as the instrument does not meet with any accident), and to be applied to all decreasing angles, either of altitude or distance, which may be taken by the backward or retrogressive motion of the index. Hence it is very probable that two errors may be established for the same instrument; the one for increasing, and the other for decreasing angles. The true values of those errors should be noted down (for the future guidance of the observer,) with a black-lead pencil on the inside of his sextant case in the following manner, viz. :— Error for the forward or progressive motion of the index 0:10" subtractive. Error for the backward or retrogressive motion of the index 1:40% additive. Or whatever the errors may be. And thus the correct values of the index error will be properly determined, whilst the errors arising from the spring and the friction of the bar, together with that proceeding from the contraction of the sun's yertical diameter will be all safely provided against. OF TAKING THE ALTITUDE OF A CELESTIAL OBJECT Since the generality of nautical persons do not appear to be sufficiently acquainted with the manner of applying the necessary corrections to angles of altitude taken by means of an artificial horizon; the author is, therefore, induced to make a few observations touching the direct application of those corrections; in doing which some hints will be thrown out for the guidance of young observers, relative to the nature and use of the astronomical instrument now under consideration. Of the Artificial Horizon. 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 where there is not an open and commanding view of the sea horizon, the observer must, in all such cases, have recourse to an artificial horizon for the purpose of taking the necessary angles of altitude. Although there is a great variety of artificial horizons now extant, yet, for the sake of conciseness, I shall only touch upon the two that are in my own possession. The first of these consists of a plane speculum, or polished plate of glass (4 inches long by 3 inches 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, 3 inches long, and 2 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. 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. Remarks. 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 horizon glass 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 though 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. 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. When an angle of altitude is taken by means of an artificial horizon, its measure on the limb of the sextant will always be the 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." # Now, the double angle of altitude being thus obtained, the true altitude of the object is to be deduced therefrom in the following manner, viz. : First. To apply the Corrections when the Sun is observed : Correct the observed angle for the index error of the sextant, if any ;-to the half of which apply the sun's semi-diameter by addition if the lower limb be observed, but by subtraction if it be the upper limb, and the sun's apparent central altitude will be obtained; from which let the difference between the refraction and parallax corresponding thereto be subtracted, and the remainder will be the sun's true central altitude. Second. To apply the Corrections when the Moon is observed : Find the moon's apparent central altitude in the same manner as if it were the sun that was under consideration; observing to correct her semidiameter by the augmentation contained in Table IV.;-then, to the apparent altitude, thus found, let the correction in Table XVIII. be added, and the sum will be the true altitude of the moon's centre. Third. To apply the Corrections when a fixed Star is observed :— Correct the observed angle for the index error of the sextant, if any; from the half of which subtract the refraction corresponding thereto, and the remainder will be the star's true altitude. Example 1. Let the measure of the observed angle between the lower limb of the sun reflected from the index glass of a sextant, and the upper limb thereof reflected from an artificial horizon be 103:14:40%; the index error of the sextant 3:10 additive, and the sun's semi-diameter 16:18; required the true altitude of the sun's centre? The half of which is the correct observed altitude of the sun's lower limb above the plane of the hor, = Sun's semi-diameter = Apparent altitude of the sun's centre = Refraction answering to ditto 51:39:10 +16.18 51:55:28 0:44") } difference = |