\Vhcn the objects arc seen very distinctly, so that no doubt whatever remains about the contact in both sights being- perfect, the above may safely be relied on as a complete set ; but if, from the haziness of the air, too much motion, or any other cause, the observations have been rendered doubtful, it will be advisable to make more : and if, at such times, so many readings should be deemed troublesome, six observations, and six readings, may be conducted in the manner following. Take three successive sights forwards, exactly as is done with a sex tant ; only take care to read them off on different branch es of the index : also make three observations backwards, using the same caution ; a mean of these will be the dis tance required. When the number of sights taken for wards and backwards are unequal, a mean between the means of those taken backwards, and those taken for wards, will be the true angle.
It need hardly be mentioned, that the shades, or dark glasses, apply, like those of a sextant, for making the objects nearly of the same blightness ; but it must be insisted on, that the telescope should, on every occasion, be raised or lowered, by its proper screw, for making them perfectly so.
The foregoing instructions for taking distances, apply equally for taking altitudes by the sea or artificial hori zon, they being no more than distances taken in a verti cal plane. 'Meridian altitudes cannot, however, be taken both backwards and forwards the same day, because there is not time : all therefore that can be done is, to observe the altitude one way, and use the index-error ; but even here, you have a mean of that altitude, and this error, taken on three different sextants. Both at sea and land, where the observer is stationary, the me ridian altitude should be observed forwards one day, and backwards the next, and so on alternately from day to day; the mean of latitudes, deduced severally from such observations, will be the true latitude ; but in these, there should be no application of index-error, for that being constant, the result would in some measure be vi tiated thereby.
\Vhcn both the reflected and direct images require to be darkened, as is the case when the sun's diameter is measured, and when his altitude is taken with an artifi cial horizon, the attached dark-glasses ought not to be used : instead of them, those which apply to the eye end of the telescope will answer much better; the for mer having their errors magnified by the power of the• telescope, will, in proportion to this power, and those errors, be less distinct than the latter.
In taking distances, when the position does not vary from the vertical above thirty or forty degrees, the han dles which are attached to the circle arc generally most :onveniently used ; but in those which incline more to the horizontal, that handle which screws into a cock on one side, and into the crooked handle on the other, will be found more applicable.
When the crooked handle happens to be in the way of reading one of the branches of the index, it must be re moved, for the time, by taking out the finger-screw, \Ville!) fastens it to the body of the circle.
If it should happen that two of the readings agree with each other very well, and the third differs from them, the discordant one must not on any account be omitted, but a fair mean must always be taken.
It should be stated, that when the angle is about thir ty degrees, neither a distance of the sun and moon, nor an altitude of the sun with the sea horizon, can be taken backwards ; because the (lark-glasses at that angle pre vent the reflected rays of light from falling on the index glass ; whence it becomes necessary, when the angle to be taken is quite unknown, to observe forwards first, where the whole range is without interruption ; where as, in that backwards, you will lose sight of the reflect ed image about that angle. But in such distances Ivhcre the sun is out of the question, and when his altitude is taken with an artificial horizon, (the shade being applied to the end of the telescope.) that angle may be measur ed nearly as well as any other ; for the rays incident on the index-glass will pass through the transparent half of the horizon-glass, without much diminution of their brightness.
The advantages of this instrument, when compared with the sextant, are chiefly these : The observations for finding the index-error are rendered useless, all know ledge of that being put out of the question, by observ ing both forwards and backwards. By the same means the errors of the dark-glasses are also corrected; for, if they increase the angle one way, they must diminish it the other way by the same quantity. This also perfect ly corrects the errors of the horizon-glass, and those of the index-glass very nearly. But what is still of more consequence, the error of the centre is perfectly correct ed, by reading the three branches of the index ; While this property, combined with that of observing both ways, probably reduces the errors of dividing to one-sixth part of their simple value. Moreover, angles may be measured as far as one hundred and fifty degrees, conse quently the sun's double altitude may be observed when his distance from the zenith is not less than fifteen de grees ; at which altitude the head of the observer begins to intercept the rays of light incident on the artificial hori zon; and, of course, if a greater angle could be mea sured, it would be of no use in this respect.