TRANSIT. OR TRANSIT INsTHfMKXT. 



TRANSIT, OR TRANSIT INSTRUMKNT. 



sn 



UM prim* vertical for the purpose already explained ; but ai he bad 

 now a meridian transit circle, with which he could measure declination* 

 with great accuracy, he leenui not to hare followed up this idea. 

 Bevel, in the ' Antronombche Nachrichten,' vol. li. p. 9, showed that 

 the trmnriU of stars over the prime vertical near the zenith might be 

 employed for determining difference* of latitude with great accuracy ; 

 and once that time aereral observatories abroad hare had transit* 

 mated in this position. We shall here briefly show how terrestrial 

 latitudes and difference of latitude may be determined by a transit in 

 the prime vertical. 



Let r be the pole, I the zenith, Kw the prime vertical, which is 

 also the line described in the heavens by the transit, and SMS' part of 

 the daily parallel of a star which passes south of ttu> zenith aud near 

 to it Then if the time at which the star is on the wire at 9 and s' be 

 noted, the angle srs' is the difference of those times, and therefore 

 known. 



In the right-angled triangle I PS, 



tan pz = tan rs x cos spz; 

 [or, cotan f = cotan 8 x coa 4 time elapsed. 



If then the declination of the star U 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 some place, as 

 tan declination = tan latitude x cos 4 time elapsed, and as the time 

 lapsed can be observed with the greatest nicety, the rariaiioni 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 aiie, which gives it an immense advantage over 

 the transit. The level may be applied just as well to one instru- 

 ment as the other (the plumb-line much better to the zenith sector;) 

 ami 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 ii 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 lie detected : but of little consequence in the 

 sector, and easily detected. It must, however, be admitted, in re- 

 turning from this digression, that the zenith sector has not quite 

 equalled the expectations which might be formed of it; and that 

 the modern transit, as it comes from the best makers, is an almost 

 perfect instrument. 



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 lined in the ordinary way. This would possibly suit roost 

 observers best. Ertel of Munich (and many other continunt.il artists] 

 makes an astronomical theodnlet, whieh is particularly adapted to this 

 observaUon : the divided horizontal circle enables you to set the 

 tranxit axis in the prime vertical ; and as the telescope has 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 

 nsrnsMij to warn the unpractised observer that in this problem ho 

 only geU the rxacl latitude at once if the telescope passes through the 

 zenith, or if the axis is truly horizontal. If the north end is lii 

 instance, V, the circle described by his instrument will pass 6" to the 

 south of the true zenith, and he will get by the formula given above 

 aa apparent co-latitude too great by 5*. 



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 ; then the telescope describes a vertical circle passing 

 through r'z w and PI, which bisects s s', will be the co-latitude which 

 result* from the formula. 



If the true sidereal time be known with moderate accuracy, find 

 how much the middle of UM times of the star's transit over the 

 opposed prime vertical, corrected for clock-error, differs from the 

 time at which it actually passes the meridian, that is, from its right 



ascension. This difference is the L I ft, which U consequently known- 

 Mow from right-angled triangle r If 



tan PZ. coe. zpz-ton pr = tan p s x cos. J elapsed time ; 



tan S x cos. z PI 

 or ' tttn *= cos. I time elapsed' 



It would be better to deduce the angle xr:, which is the same for 

 all stars, from a star which does not pass very near to the r.enith, 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 is 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 be easily deduced from the approximate. 



sin i' - oos. approximate latitude. 



SmPZ = rin"p^' orcoalat= cos.ofamuthalerror7 



Lastly, as almost all transits hare vertical circles, which ore or may 

 be tolerably adjusted, the observer may measure the apparent zenith 

 distances, z 8 and z s', pretty nearly, ana half the difference gives z:. 



Then cos p z = cos rt x cos z;, or sin latitude = siu approximate lati- 

 tude x cos of half difference in star'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, nf two stars on the some day in reversed 

 positions, or of the same star on following days in reversed po.- 

 will correct each other, and the mean will give the true latituile, 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 mean*, it would *-em that this 

 is the best method of determining the latitude, and is. th> 

 especially suited to coast surveying. It has been ev 

 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 th.it 

 no motion of theirs while observing can affect the horiioutality of the 

 axis. With this precaution, and such transits as are turned out 

 best workshops here and abroad, a thirty-inch instrument will 

 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, 'In y 

 ought to be true cylinders, having their axes in the same right line ; 

 and BO, no doubt, they ore, very nearly, when the axis is strong and the 

 pivots are turned in a good lathe, using a diamond for - 

 A*little inequality of radius we have shown how t<> n 

 correct for. But if the pivots are elliptical, the fault will not be 

 ,-ho\vu by the level; and its effect will be to give the iuMnr 

 small variable error in azimuth, the period of which is 90. There ore 

 several ways of trying whether the pivots have a correct { 

 error is so small as not to offer much hold to any dii 

 yet, if it does exist, no mass of observations will have any tend. < 

 get rid of it Reversion gives a chance <>f foinpeiiKitiiiK the 

 part; and we think the plan of remlciin.; the object ..< 

 interchangeable is worth considering with a view to correcting ^ 

 error, at least in small instruments. 



The right ascension of the standard fixed stars, as they are pub- 

 lished by the principal observatories, .do not in all instances agree as 

 closely as might be expected from the moss of observations ami tin; 

 apparent accuracy of each. Whether this can be accounted i 

 supposing each catalogue to have a small variable error depend 

 the flexure of the axis of the instrument, or on error in the form of 

 the pivots, in more than we can undertake to say; but it is a i 

 well worthy of investigation in the present state of practical astro- 

 n.'iuy. 



\\ i have deferred our account of the Aitmnomicat O&serrof >>/' until 

 the principal instruments which form its furniture were des< 

 We cannot attempt such a minute delineation as would suffice t- 

 any one who wished to erect such a building. It will l>c enough to 

 state some of the properties which a well-contrived observ, 



