ERROR OF COLLIMATION, ETC.] 



ASTRONOMY. 



1005 



It can also be determined by the comparison of the 

 results of the transit of a star observed by reflection and 

 direct vision. A slowly moving star is generally selected 

 for this purpose, four or more wires being observed in 

 each position. The difference of the two results (sepa- 

 rately reduced) is equal to double the level error of the 

 object observed, which can be converted into "error of 

 inclination" for an equatorial star by the proper factor. 

 By comparing this result with the level indication, the 

 value of one division of the scale may be found. 



Lastly, it can be obtained by elevating or depressing 

 the Y's by the proper screw, and finding the effect of a 

 change of level indicative of the transits of a close cir- 

 cumpolar star. The level error may also be obtained by 

 a Bohneberger's eye-piece, an instrument consisting of an 

 ordinary eye-piece, perforated at the side, and so arranged 

 that, by means of a glass reflector, placed near the eye 

 lens, inside the tube, the light of a lamp may be thrown 

 into the instrument. In thi* manner the system of ver- 

 tical and horizontal wires may be seen, by directing the 

 telescope nearly to its nadir position, and placing under- 

 neath the object-glass a trough of mercury. By causing 

 the two images to overlap, by means of the right ascen- 

 sion micrometer (noting its readings), and comparing 

 these with the corresponding readings for the line of 

 collimation of the instrument previously obtained, the 

 level error may be easily deduced. This method is now 

 practised in the use of the Greenwich transit circle. 

 The following form shows the readings of the transit 

 micrometer for coincidence of the central wire, for deter- 

 mination of error of lovel of the axis of the transit circle 

 of 18J1 : 



The azimuthal error may be determined by the transits, 

 above and below the pole, of any close circunipolar star. 

 In observatories, where the adjustments of an instru- 

 ment are sufficiently steady to be relied on, the successive 

 passages of Polaris, or i Ur.-ue Minoris, for several days, 

 are aged for this purpose. But, in small instruments, 

 whose foundations are not BO firm, it is usual to obtain 

 an azimuth error by corresponding observations of high 

 and low stars, or an observation of Polaris, or 6 Ursa 

 Minoris, compared with the transit of a star south of the 

 zenith. Thus, Polaris and Ceti can be used advan- 

 tageously for this purpose, the difference of their right 

 ascension being only thirteen minutes, and their tabular 

 right ascensions being known with sufficient precision. 



Mr. Johnson, in his Oxford Observations, uses certain 

 pairs of stars for azimuthal errors, whose positions have 

 been determined with considerable accuracy. These 

 stars are distributed in such a m.inner, that the observer 

 can have little trouble in finding one transiting above 

 the pole, and another passing below the pole, within 

 a short interval of time of each other. Thus, the result 

 is entirely free from any doubt as to the rate of the 

 clock, or other causes, and the principal error can only 

 arise from the unavoidable uncertainty of observation. 



It is frequently necessary, in the use of a small transit 

 instrument, to have a fixed mark in the direction of the 



meridian, which can be easily referred to for the purpose 

 of determining the error of collimation, and also its 

 deviation from the meridian, in cases when, from clo.idy 

 weather, observations from circumpolar stars cannot be 

 obtained. 



At the distance of 236 feet, a circle of two-tenths of 

 an inch in diameter will subtend an angle of 12" of 

 azimuth. By noting the positions of the central wire of 

 the transit in reversed positions of the axis, an approxi- 

 mation may be made at once to the error of collimation, 

 from its relative positions in this circle. This meridian 

 mark may be frequently verified by observations of cir- 

 cumpolar stars. 



If the instrument be furnished with a micrometer, 

 this method of determining the collimation will not be 

 necessary. 



We will now proceed with the investigation of the 

 formulae for the three preceding errors, and will show 

 the method of application to the results of observations. 



ERROR OF COLLIMATION. The error of collimation is 

 the distance of the middle line from the true line of 

 collimation, east or west. When the middle wire is east 

 of the true line of collimatiou, the transit is observed too 

 soon, and consequently the correction for collimation is 

 additive for stars above the pole, and subtractive for 

 those below the pole. The contrary takes place when the 

 middle wire is west of the line of collimation. According 

 to this, the transit telescope may be supposed to describe 

 a circle parallel to the meridian. Thus, let C S A (Fig. 

 206) be the circle described by the telescope, or the circle 



in whose plane the middle wire is. Then AN, or 8 Jf, 

 is the error of collimation, which is generally expressed 

 in seconds of arc. Let S be the place of a star, P S B 

 a great circle passing through it. We have now to 

 find B E, the corresponding part of the equator ; but 

 SN SN 



= B E in arc, or 



BE in time, 



sin. P S 15 sin. PS 



which is the correction to be applied to the observed 

 transit. In that investigation, stars, however, near the 

 pole, are supposed to transit the middle wire; that is, 

 their distance from the pole is supposed to be greater 

 than the error of collimation. If this were not the case, 

 such stars could not pass the middle wire. 



The correction for the error of collimation is written 

 thus : 



Correction = error X 15 x gin . l r . g N P p- 



CORRECTION FOR LEVEL. The error of level is con- 

 sidered positive when the western pivot is too high. In 

 that position the great circle, passing through the north 

 and south points of the horizon, and which is the circle 

 on which observations are made, lies to the east of the 

 meridian, and the observed time of passage is less than 

 the true time for stars above the pole. 



Thus (Fig. 207), O Z = the error of leveL 

 Z O X cos. S O = S x, and 



UF- -* S!B 



15 sin. N P D 15 sin. P S 



/.BE = 



Z O X cos. zenith distance south 



15 sin. N P D 



AZIMUTHAL ERROR. This error is considered positive 

 when the eastern pivot is too far north. In tliia position, 



