ION 



ASTRONOMY. 



[LEVBL or ixsrmnscErrs. 



The error of horiiontality of the axil u generally de- 

 termined by the apph. ,i:i-u of a spirit level to tho pivots. 

 Hut it must bo previously known whether t!n- punu are 

 perfectly circular, and of equal diameter. Fur thu pur- 

 pose, careful tone* of levelling* are taken iu reversed 

 position* of the axu of the traunt instrument. If we 

 assuuM the Y' to be perfectly horizontal, but that on 

 application of the level, the same pivot shows a quantity 

 ii;li ia reversed positions of the axis, it U evident 

 that thin pivot U the larger of the two ; and it is equally 

 evident that if the Y'B are not perfectly horizontal, .we 

 can determine the difference of the pivots from level 

 reading* in reversed positions of the axis. The following 

 example, from the Ojcford Obtcmtiont, 1840, page v., 

 will illustrate the whole process. The sign + is used 

 when the west end of the axis ia highest ; when the 

 cast end is highest : - 



"From these it results, that when the lamp is east 

 the west end of the axis is highest, and when the lamp 

 is west the east end is highest ; thus they show that the 

 olid pivot is larger than the perforated one. 



.ngle of the level's Y's is the same as that of 

 the pivot's if*, both being rectangular, or very nearly 

 so : therefore the difference of thn radii of the pivots 



DifT-rmr* o 



. Pn*ilinn of lhi> 



" The column E W shows the difference of the level 

 readings, the arithmetical mean of which - 5*- 445 ; 



6*'446 

 therefore 6 ^ - 0*-962 is the mass of the radius of 



the solid above that of the perforated pivot, and 0*-962 

 1"-3U1 in the correction to be applied to the 

 level reading* to obtain the inclination of the pivot 

 centre*. This correction is to be added algebraically to 

 the level readings when the lamp U west, and subtracted 

 ! M the lamp u tatt." 



A careful series of levelliugs at different elevations of 



tli- object-glass, showed that there was no appreciable 



' o in the circularity of the pivots, as the reader 



will oW-rro by reference to the descriptions of the. 



Altazimuth and Transit Circle in the GrttMoich Oluena- 



ont, 1847 and ls.12, for tho method adopted by tho 



Astronomer Royal to insure perfect circularity of the 



pivots. 



Dr. Oudcmaus, in his e*say on the Transit Instru- 



ment, give* the following formula for the correction of 

 tin- level indication caused by unequal ili.imetors of the 

 pivots. The error of level In-in^ determined after fre- 

 quent reversals of the transit instrument, this correction 

 may be easily deduced. 



Let 2 g be the angles between the planes of the Y 7 *, on 

 which the pivots are placed ; 2/, the angle* between thu 

 feet of the level, by which it is placed on the pivots ; 

 u, the difference of inclinations observed iu Inith posi- 

 tions of the axis ; r and r', the two radii of the pivots ; 

 L, tho distance between the points, where tlio tuo pivoU 

 rest on the planes of tho Y's. Now g, /, u, ami L I 

 known, the difference of the radii r and r' u i 

 known by the following formulae : 



,, sin. o sin. 

 ''.- 



He then gives a determination of the values before :m 1 

 after reversal, and finds an arithmetical moan of tho 

 differences, or of u - + 4* -15. Since this value of 

 fouml will depend on one unequal breadth of the ex- 

 tremities of the axis, the correction of any inclination 

 can be obtained by the level. 



, sin, g 



* sill, g + sin. f 

 In his transit circle, 2/=9S 40", 2 0=91 25'; therefore 



B. 



s - j^ x 0-4854 X 4* -15 - I'-Ol = 0-(i7. 

 Iu order to eliminate any errors in the level itself, it 

 is the practice to reverse it several times, or to take a 

 scries of readings in one position, and then to turn it, 

 end for end, and to take a set of iea.lin_> in an opposite 

 position. The following is an example : 



ROYAL OBSEBVATOBY, GREENWICH. 



The value of one division of tho level scale may be 

 determined by tho application of the level to a vertical 

 circle, moving it so as to produce changes in tho circle 

 reading, and iu the position of tho bubble. Thus,. in tlio 

 Orermrich Observations, 1830, Introduction, pages xvi. and 

 xvii., "on January 27, the level of the transit instrument 

 was bulled to Trougliton's circle, and the circle being 

 moved till the bubble was alternately near the eml <>f one. 

 Mid the other scale, the microscopes A and 1! w< i< n ;i.l. 

 This operation was repeated sixteen times. The mean of 

 the results gave 2' 0"-03 - 112-18 parts at oue em), 

 108-93 parts at the other end of the scale ; the mean 

 value of one part being, therefore, l*-0tk>." 



