In the observations already described, and for lunar distances, a stand for the sextant will indeed add greatly to the accuracy of the observations, but is not absolutely necessary for a practised observer ; so far as our own experience has gone, good observations of the stars can scarcely be made without a stand. By lying on the ground, and resting the edge of the sextant on a book or some convenient support, the observation may undoubtedly be made ; but in most situations and in many climates this would expose the observer to more incon venience and risk than he can prudently encounter. With a stand, and a little experience in setting it up, the observation of a star is just as accurate as that of the sun. The time is noted when the images form a figure like this ", parallel to the horizon ; and stars of the third magnitude, or even lower, are quite bright enough for the pur pose. We have observed Polaris very tolerably with a snuff-box sex tant when the instrument rested on a book ; the telescope, though of extra size for the instrument, was of much smaller aperture than those attached to ordinary sextants. It is rather steadiness which is required for these observations than light. Equal altitudes of the same star give the moment of its meridian passage by the chronometer without computation ; and as this is the R.A. of the star, the error of the chro nometer, if it be sidereal, is obtained at once; if it should be a solar chronometer, the computation is very easy, that is, merely computing the mean solar time of the star's transit of that day from the R.A. of the star and the longitude of the place. The computation of circum meridian altitudes of a star for the latitude is rendered more simple by using a sidereal chronometer, for the hour angles observed with the solar chronometer must be reduced to sidereal time before taking out the corrections to the meridian from the Tables of Reduction.
There are certain faults either usual or inevitable in the sextant, which are now to be pointed out, and the mode of eliminating their effect from the final result. First, the determination of index correction is always somewhat erroneous, and this error runs through all the abso lute observations, and affects the mean with its whole amount. Again, if the telescope be not parallel to the Oahe of the instrument, or if the contact be not made exactly midway between the wires, the angle read off is too large, and exceeds the true angle, and there is no prin ciple of compensation ; this class of errors has always the same sign. Finally, as sextants are now divided, there is no certainty that the axis of the index is exactly concentric with the divided arc. It is difficult to say within what limits this error is confined, but we think it amounts not unfrequently to 10", 15", or even 20" in the total arc." This is not, however, proportional to the arc, though it is generally smaller in the smaller arcs. Hence if this effect of excentricity lie tho same way as the other errors, as it easily may, the most careful ob server will make a considerable mistake in measuring a large angle. If we further suppose the error of the lunar tables to be in the same direction (the best meridian observations show that the moon is not un frequently from 10" to 15" out of her tabular place), it will be seen that the longitude, determined as it generally is by distances between the moon and sun, or the moon and a tingle star, may differ much more from the truth than lunar observers usually think possible.t
Mere instrumental error is got rid of by combining those observa tions which they affect in contrary ways. Thus in equal altitudes, the fixed errors, such as index error, excentricity, bad division, inclination of the glasses or telescope, have contrary effects on the morning and afternoon sights, and therefore no effect on the mean. Making the contacts out of the middle of the wires is a casual error, and just as likely to happen in the morning as in the evening observations ; so that as the angles are the same in both cases, errors of this kind will have pretty much the same influence on the mean of several pairs.
Hence the great excellence of the method of equal altitudes for determining the time, so far as instrumental error is concerned ; it is an additional advantage that nn error in the auppoaed Latitude is also without sensible influence. Again, if time is deduced by absolute altitudes of a star rising in the met, the result will be affected one way by the errors above described ; if a second star be observed at nearly the same altitude setting in the west, the altitude will be affected to the same amount ; and if the stars have declinations which do not widely differ, the exult deduced from the second Mar will be affected to the same extent, but ih a contrary way from the first ; a mean of the two results will be nearly free from any error, except the casual error of observation. A latitude by the aun or a Mar to the south, which is erroneous from the above-mentioned causes, will be balanced and corrected by a star of nearly the Pante altitude to the north ; or a star to the north may be balanced by two to the south, one of higher and the other of lower altitude. It is scarcely credible how nearly the time or latitude may be thus determined. We have a series of such latitudes with an 8-inch sextant, observed by Mr. Lassell at Liverpool, which scarcely differ more than 2" or 3" from each other, though deduced from different groups of Greenwich stars. When the longitude is to be obtained from lunar distances, a consider able number of observations should be taken from the objects cast and thaw west of the moon. If a pair can be selected on different sides of the moon, and nearly at the same distance from her, the result will be liable to the effect of casual error only, and to the error of the lunar tables. This latter error cannot be got rid of at the time of observation ; but after the Greenwich, Cambridge, Edinburgh, Cape of Good Hope, and Oxford observations for the year have been pub lished, it will generally be possible to find the error of the moon at the time of observation with considerable accuracy. This must be done whenever a sure longitude is to be deduced from lunar distances, and lunar observations must be taken in great numbers, so as to destroy casual error, nice points in geography.