From what we have already said, it is evident that where exact time is wanted, the collimation, inclination, and deviation factors are per petually required. The collimation factor is merely a table of secants of declination, and may be taken from any table of natural secants. The inclination and deviation factors should be computed for each observatory to every 10' of declination, and be tabulated for constant use. For the stars often observed, we find it most convenient to have a catalogue in which the log secants of declination, the natural secants and tangents of declination, and the factors for inclination and deviation, are entered in parallel columns with the proper signs. The astronomer royal employs a sliding-rule for these and similar computations. In computing this table for a given latitude, the formulae will be advan tageously transformed thus :— so that having the natural sine and cosine of latitude, and also the log sine and cosine, the computation reduces itself to adding the log tan. declination to these last. The necessary tables may be computed in a few hours as far as is advisable ; for near the pole the change of declination has so large au effect, that it is necessary to use the exact declination.
Great service would be done to amateur practical astronomers by a judicious set of printed forms, in which to enter and reduce their observations; and by a set of tables sufficient for these small com putations, and not containing anything further. This can only be obtained by repeated attempts, and after all most observers would probably prefer a modification of some form to adopting it implicitly. Wo have tried to produce something in this way on which a better attempt may be founded. The astronomer royal published a por tion of the forms used at Greenwich in the volume of the Observa tions for 1840, and we venture to recommend his practice to other observers, in order that their less able brethren may profit by their superior skill and experience.
While lie was employed in the Royal Observatory of Paris, Romer proposed a method of determining the equinox by observing the azi muth of the sun at rising and setting near the time of the equinox, which method ho illustrated by an example. (' Basis Astronomiaa,' p. 107.) He thus got rid of the effects of parallax and refraction, and deduced an accurate declination of the sun without an exact knowledge of the latitude. The method is a very good one, though undoubtedly inferior to that proposed and executed by Flamsteed. Many years after, Romer, on erecting a small observatory in his own country, placed a transit east and west, that is, in the prime vertical. Almost all his papers were destroyed by a great fire at Copenhagen, and it does not seem by Horrebow's account that any use was made of this prime vertical transit. He intended ,probably to observe the sun in
the prime vertical for the purpose already explained ; but as he had now a meridian transit circle, with which he could measure declinations with great accuracy, he seems not to have followed up this Idea. Passel, In the ' Astronomische Nachriehten,' voL IL p. 0, showed that the transits of stars over the prime vertical near the zenith might be employed for determining differences of latitude with groat accuracy ; and since that time several observatories abroad have had transits erected In this position. We shall here briefly show bow terrestrial latitudes and differencea of latitude may be determined by a transit in the prime vertical.
Let r be the pole, z the zenith, zzw the prime vertical, which is also the line described in the heavens by the transit, and axe' part of the daily parallel of a star which lames south of the zenith and near to it. Then If the time at which the star is on the wire at a and s' be noted, the angle ors' is the difference of those times, and therefore known.
aacension. This difference is the I z rs, which is coneequently known. Now from right-angled triangle r z If then the declination of the star is known, the latitude is found ; or if the same star be observed at two places, the difference of latitude may be found with only an approximate knowledge of its place.
Again, if the same star be observed regularly at the same place, as tan declination = tan latitude x cos time elapsed, and as the tune elapsed can be observed with the greatest nicety, the variations of declination can also be measured with great precision. Thus the con stants of aberration and nutation may be determined by a transit in the prime vertical instead of a zenith sector ; but the advan tage appears to us questionable. The telescope in a zenith sector may be of almost any size, which gives it an immense advantage over the transit. The level may be appliedjust as well to one instni ment as the other (the plumb-line much better to the zenith sector;) and though the division by time in the transit is more perfect than division by arc in the sector, the telescopes being of the same power, it is certain that the division is not the failing part of the sector. An error in the form of the pivots would be injurious to the transit, and is not readily to be detected ; but of little consequence in the sector, and easily detected. It must, however, be admitted, in re turning from this digreagion, that the zenith sector has not quite equalled the expectations which might be formed of it; mid that the modern transit, as it comes from the best makers, is an almost perfect instrument.