In determining the latitude by the portable transit, it is easy to place the instrument with sufficient accuracy, for the error must be considerable to affect the result very sensibly. An object-glass may be inserted in one pivot, and wires and an eye-piece into the other, and the telescope be directed upon a mark placed in the meridian by the instrument used in the ordinary way. This would possibly suit most observers best. Ertel of Munich (and many other continental artists) makes an astronomical theodolet, which is particularly adapted to this observation : the divided horizontal circle enables you to set the transit axis in the prime vertical ; and as the telescope hes a prism at the centre of the axis, to reflect the rays down the transit axis itself, the observer looks horizontally wherever the stars may be. It may be necemery to warn the unpractised observer that in this problem ho only gets the exact latitude at once if the telescope passes through the zenith, or If the axis is truly horizontal. If the north end is high, for Instance, 5", the circle described by his instrument will pass 5" to the mouth of the true zenith, and he will get by the formula given above an apparent co-latitude too great by V.
If the axis is very incorrectly placed with respect to the meridian, the co-latitude will be sensibly too small. Let the axis point to the east of the north ; than the telescope describes a vertical circle passing through z'z w and which bisects s a', will be the co.latitude which result from the formula.
If the true sidereal time be known with moderato accuracy, find bow much the middle of the times of the Mar's transit over the supposed prime vertical, corrected for clock-error, differs from the time at which it actually passes the meridian, that is, from its right tan P z. ooe. z ratan it= tan r 8 X cos. elapsed time ; tan 8 x cos. z rz or, tan cp= cos. time elapsed ' It would be better to deduce the angle z r:, which is the same for all stars, from a star which does not pass very near to the zenith, as the passage is more easily observed, but the length of time which elapses between the two passages of such a star is inconvenient. If the time ia well known, one such passage will do.
, If the observer has any means of determining the error in azimuth by a reference to known objects in the horizon, the correct latitude may bo easily deduced from the approximate.
sin cos. approximate latitude.
Sin PZ cos hat = sin rzz cos. of azimuthal error.
Lastly, as almost all transits have vertical circles, which are or may be tolerably adjusted, the observer may measure the apparent zenith distances, z s and z a', pretty nearly, and half the difference gives zr.
Then cos P Z = cos rz x cos zz, or sin latitude =sin approximate lati tude x cos of half difference In stir's altitude east and west.
By reversing the instrument., any error of collimation or inequality of pivots „will produce exactly a contrary effect on the latitude. Observations, therefore, of two stars nu the same day in reversed positions, or of the same star on following days in reversed positions, will correct each other, and the mean will give the true latitude, that is, as nearly as the declination of the star is known. We have dwelt the longer and more minutely on this problem, because where great accuracy is required with but moderate means, it would seem that this is the best method of determining the latitude, and Is, therefore, e.speidally suited to coast surveying. It has been extensively used in the Russian navy, and by many travellers, German and Russian. There is one caution which the users of this method must not dis regard, and that is, that the position of the instrument be so stable that no motion of theirs while observing can affect the horizontality of the axis. With this precaution, and such tranaits as are turned out of the best workshops here and abroad, a thirty-inch instrument will give, we conceive, the latitude within 1' or 2", without any particular skill on the part of the observer.
There Is one word more to be said on the subject of pivots before concluding. By the mode in which they are turned and finished, they ought to be true cylinders, having their axes in the same right line ; and so, no doubt, they are, very nearly, when the axis is strong and the pivots are turned in a lathe, using a diamond for steel pivots. A'little inequality of radius we have shown how to measure and correct for. But if the pivots are elliptical, the fault will not be shown by the level; and its effect will be to giro the instrument a small variable error in azimuth, the period of which is 90*. There are several ways of trying whether the pivots have a correct form, but the error is so small as nut to offer much hold to any direct method ; and yet, if it does exist, no mass of observations will have any tendency to get rid of it. Reversion gives a chance of compensating the error in part; and we think the plan of rendering the object and eye end interchangeable is worth considering with a view to correcting such an error, at least in small Instruments.
The right ascension of tho standard fixed stars, as they arepula Balled by the principal observatories, ado not iu all instances agree as closely as might be expected from the mass of observations and the apparent accuracy of each. Whether this can be accounted for by supposing each catalogue to have a small variable error depending on the flexure of the axis of the instrument, or an error in the form of the pivots, is more than we can undertake to say; but it is a matter well worthy of investigation In the present state of practical astro nomy.