TRANSIT-INSTRUMENT. 



jufted by means of ihe (crew S. Fig. 8. reprefents the 

 ftand, telekope, and level, difplaying the pofition in which 

 they are ufed;_/^. 12. for placing the tranCt in the meri- 

 dian. Of the verifications of this inftrument, tvpo are com- 

 mon to every conitruftion ; one only is peculiar to this. 

 The line of coUimation is adjufted by looking direft at fome 

 diftant fmall point (the cover being turned over the lateral 

 aperture), and turning the telefcope gradually round on, its 

 axis, and moving the fcrew of the wires, if neceffary, till 

 the fpot is in every pofition covered by the interfeftion of 

 the wires. The axis is brought to a horizontal pofition, 

 and the level is in the fame mode adjufted by reverfing the 

 telefcope or level, and correfting half the error by the level- 

 fcrew, and half by the vertical fcrew of the Y, in the ufual 

 mode. The verification peculiar to this inftrument is that 

 of the mirror, and perhaps the beft mode of doing this is 

 by the pole-ftar, when nearly in an eaftern or weftern pofition 

 from the pole ; its motion in azimuth is then fo flow as to 

 give ample time for the adjuftment. Bring the pole-ftar to 

 the vertical wire (the line of collimation having been pre- 

 vioufly adjufted) ; then reverfe the telefcope in its Y s ; and 

 if the ftar is ftill on the wire, the mirror is in adjuftment : 

 if not, correct half the difference by the mirror-fcrew, and 

 half by the horizontal of the Y, till the error vanifhes. 

 This adjuftment may alfo be performed, by fetting up a 

 board with two parallel perpendicular lines drawn on it, 

 diftant from each other exaftly the fpace between the pofi- 

 tions of the mirror when the telefcope is reverfed in its Y s. 

 If the vertical wire be brought to cover one of the marks, 

 and on being reverfed, the wire covers the other mark, it is 

 right : if not, the error muft be made to vanifti by cor- 

 recting it half and half, as before direfted, for the adjuft- 

 ment by the pole-ftar. The following method of placing 

 the inftrument correftly in the meridian, is equal if not 

 fuperior to any that has yet been devifed. Let Z {Jig. 12.) 

 be the zenith ; P, the pole; H O, the horizon ; Z P I, the 

 meridian circle ; Z K, a circle of altitude, diftant from the 

 meridian by a fmall quantity I K (fuppofe a degree) ; 

 If 2, 3, 4, the diurnal circle of the pole-ftar, whofe radius is 

 l°45' nearly ; and let the altitude of the pole be 51° 3c'. 

 Then when the pole-ftar is on the northern meridian, its alti- 

 tude 3 I will be 49° 4j', and its zenith diftance Z 3 = 40° i ;' ; 

 and A C D be a part of the diurnal arc of a ftar whofe 

 polar diftance is 46° 30*, and N. meridian altitude 5°. Now 

 fuppofe the tranfit-inftrument, whofe axis is accurately le- 

 velled, and of courfe in the meridian at Z, to point at the 

 l)orizon to K (it is obvious from its conftruftion the tele- 

 fcope's axis will be at right angles to the meridian line^ in- 

 ftead of I, the true meridian ; then at 3 (the altitude of the 

 pole-ftar under the pole) it will point at B, and the arc 

 3 B will be to I K, as the cofine of the altitude 3 I to 

 radius ; but 3 B, meafured on the diurnal circle of the 

 pole-ftar, will be the fine of its diftance from the meridian to 

 the radius P 3 or P B : and, as in fmall arcs, the arc of 

 a great circle, or of a fmall circle, or their fines, are nearly 

 coincident, we (hall have very nearly, as Z 3 (the zenith 

 diftance) is to P 3 (the polar diftance), fo is the value of 

 3 B, in degrees of the pole-ftar circle, to its value in degrees 

 of a circle whofe radius is Z 3. And as the radius Z 3 is 

 to P 3 very nearly as 23 to I, the error of the tranfit- 

 telefcope at the altitude 3 I, will be meafured by a fcale 

 (if it may be fo called) 23 times as great as itfelf. Now, 

 let there be another ftar A, whofe northern meridian alti- 

 tude is as fmall as it conveniently can be, for example 5°, 

 whofe polar diftance is, therefore, 46" 30', and whofe 

 right afcenfion is the fame as that of the polar ftar ; then, if 

 the tranfit-telefcopc be in the meridian, both thefe ftars 



will pafs tlirough it at the fame time ; but if it be out of 

 the meridian by the quantity I K, the ftar A will pafs 

 through it when it comes to C, but the polar ftar not till it 

 comes to B, when the ftar A has got to D, in its diurnal 

 circle. The value of A C being therefore found, by mul- 

 tiplying I K by the cofine of its altitude A I, that value, 

 being reduced to the angular value from the radius P A, 

 will give the time of the ftar A paifing through the tranfit- 

 telefcope, after the time of its pafling the meridian ; and 

 the fame operation being performed for the pole-ftar as 

 before direfted, the difference of tliefe times will be the 

 error in time of the tranfits, anfwering to the given devia- 

 tion I K of the tranfit-telefcope. And tables having been 

 previoufly conftruAed for fuch ftars as ftiall be thought 

 convenient, the tranilt-telefcope mav, in a very ftiort fpace 

 of time, be fet to the 'meridian, with a degree of precifion 

 unattainable by any other method. It the ftar A precede; 

 the pole-ftar in its paffage under the pole, no tables are re- 

 quifite, nor any thing neceffary to be known but the exaft 

 difference of the right alcenfion between the two ftars; for 

 having obferved the tranfit of the ftar A, (the inftrument 

 being previoufly brought neai" the meridian, fuppofe half a 

 degree,) then elevate the telefcope to the pole-ftar, by 

 moving the horizontal adjuftment of the axis ; keep the 

 pole-ftar on the middle wire, till the due interval of time 

 between their tranfit is elapfed ; the inftrument will then be 

 extremely near its true pofition ; and, by repeating the ob- 

 fervation once more, will be bro\ight to a perfeft cxaftnefs. 

 Or, if another ftar, following the pole-ftar in its paffage, be 

 obferved on the fame evening, if the times elapfed between 

 their tranfits are equal to the tabular difference or their right 

 afcenfions, which will probably be the cafe, the accuracy of 

 the firft placing the inftrument will be immediately afcer- 

 tained. Other ftars near the pole may be made ufe of in 

 the fame manner as is here defcribed for the pole-ftar, but 

 with proportionally lefs advantage as the polar diftance is 

 increafed. It is alfo obvious from the figure, that the 

 tranfit of the pole-ftar above the pole may be alfo ufed, and 

 that with nearly, though not quite, the fame advantage as 

 the tranfit below the pole. The fame method may alio be 

 applied with equal eafe, if the fecond ftar A pafs the 

 fouthern meridian inftead of the northern. 



" The flownefs ot the pole-ftar's motion, though it renders 

 its tranfit uncertain to a few feconds, cannot materially affeft 

 the accuracy of this method, as an error of ten feconds in 

 time, in the eftimation of its paffage, which is certainly 

 more than can be committed, would not caufe an error of a 

 third of a fecond of time in tlie paffage of ftars near the 

 equator. 



" Example of the computation with the numbers given 

 above. 



Sin. I K 

 Sm. Z A 



Sin. Z 3 

 Sin. PA 



Sin. A PC 



Star A. 



8.241855 

 9.998844 



9.810316 

 9.860562 



8.379663 

 1° 22' -"-^'' 

 In time 5" 



'20" 

 294 



Sin. 

 Sin. 



Sin. 

 Sin. 



Sin. 



Pole-fiar. 



I K 8.241855 

 AC 8.240199 



3B 

 P3 



3PB 

 3PB 

 In time 



8.052171 

 8.484848 



9.567328 

 21^40' 10" 

 l"" 26" 40 J' 



" The error of a degree, therefore, in the pofition of the 

 tranfit-telefcope at the horizon, caufes the ftar A to pafs 

 through it 5™ 29P in time later than it ought ; whereas 

 the fame error caufes the tranfit of the pole-ftar to be 

 l*" 26™ 4c I' later than it ought ; and the difference between 



thefc 



