DETERMINING OOLLIMATION. ] 



ASTRONOMY. 



1013 



COMPLETION Of AN IMPERFECT TRANSIT OF A PLANET. 



Planets, N.P.D. = 70 22" s. 



I = variation in B.A. in Ih. = + 12 92 

 Wires observed : 



A 



B 



C 



D 



+ 38-511 

 + 25-711 

 + 12-840 

 -002 



4) + 77-060 

 + 19-265 



Log. 19-265 ........ + 1-28477 



LO-. co. sec. planets, N.P.D ..... -02601 



3600 + I 

 -3600- 



L. No. 20-53* 



FORMULA FOR DETERMINING COLLIMATION. In the 

 operations of the Brussels Observatory, the following 

 formula for the determination of the colliination, inde- 

 pendently of the other errors of the instrument, is used. 

 The investigation is to be found in M. Lingre's memoir, 

 8ur lei Corrections de la Lunette Me-ridienne one of the 



prize essays of the Brussels Academy, vol. xviii. , 1844 

 '45. The stars best suited for this method are, one 

 near the pole, another near the zenith, and a third of 

 south declination. The example aud lui-.uuU are as 

 follows : 



ft Corvi 



<y Ursffi Majoris 



Polaris S.P. , 



Example. Greenwich Observations, 1842, May 10th. 



h. m. >. h. m. . ' " o 



H = 12 25 39-53 RA = 12 26 8'86 p = 112 31 39 



H=ll 45 3-88 RA=11 45 33 '11 p = 55 22 39 



H' = 13 1 30-42 RA' =13 2 6-52 y' = 1 31 69 



Observer 

 Henry. 



0=-D 



Calculation of the Collimation. 

 sin. p" cog. $ (p - p 7 ) j_ TV _ sin, p* cos. $ (p - 



p) 



2sin.i(p-jj)8in.i(p -/) 2sin. i (p -/,') sin. 



D = 15 [(H + R A) (H + R AVJ = 1* -50. 

 D' = 15 f(H + R AT (H' + R A)J = + 101" -40. 

 ') = 57 1' 49' : i (p j>) = 38 33' 0* : \ (p p) = 18 28' 49* 



Log. D 3 



Lo^. sin. p" . 

 Log. cos. i (p - p') . 

 AT. co. log. 2 ... 

 Ar. co. log. sin. ^ (p j> e ) . 

 AT. co. log. sin. \ (j> - p') . 



. -0-17609 

 9-76317 

 9-73516 

 9-69897 

 0-20537 

 0-49897 



-0-07773 

 1st Number = - 1-"20 



A similar calculation, made on May 13th, 1842, 

 using ft Corvi, 7 Ursse Majoris, and Polaris, gave C = 

 + 2* -67. This agrees very satisfactorily with the pre- 

 ceding result. 



The error determined (by reversal of the instrument in 

 the usual way practised at Greenwich) was found to be, 

 on April 6th, - + 1*-51, which is a very good agree- 

 ment. 



The Astronomer Royal, in the Cambridge Observations, 

 1828, proposed a method, nearly similar, for determining 

 k errors, and the errors of collimation and 

 azimuth, but was obliged to discontinue it on account of 

 the imperfect places of the star catalogues, and the diffi- 

 culty of making observations sufficiently accurate. The 

 following is the investigation : " Let x, y, z, be the 

 clock error, and the errors of collimation and deviation 

 (the clock being supposed slow). O, O 7 , O", the observed 

 times of transit corrected for the error of level and the 

 clock rate ; T, T", T*, the true sidereal times at which 

 they piiss the meridian ; Y, Y', Y*, the respective multi- 

 pliers of the error of collimation, which give results 



Log. D' . . . . 

 Log. sin. ff . 

 Log. cos. J (p - p) . 

 Ar. co. log. 2 ... 

 Ar. co. log. sin. (p p') . 

 Ar. co. log. sin. \ (j/ p) . 



2-00604 

 . - 8-42738 

 989324 

 9-69897 

 0-07626 

 . - 0-49897 



+ 0-60086 



2nd Number . + 3-99 

 1-20 



C 



2-79 



transits ; Z, Z', Z" 

 Then the following 



the 

 equations 



additive to the observed 

 for the error of meridian. 

 subsist : 



O +SB+YV -fZz =T 



W + x + Y'y + Z'z = T 



O' + x + Y"i/ + Z"z = T 



And subtracting the 2nd from the 1st, and the 3rd from 

 the 2nd 



(Y' - Y" ) y + (Z' - Z") z = (T' - O ; ) - (T" - O") 

 " The catalogued R. A. and the observation of the 

 transit must be extremely accurate, in order that any 

 result worthy of confidence may be obtained from these 

 equations. The most favourable stars are Polaris, a star 

 below the pole, and a, star above the pole, whose N. P. D. 

 is considerable." 



METHOD OF FINDING THE TIME, The method of find- 

 ing the time given in the following pages is capable of so 

 many useful applications to travelling astronomers, that, 

 in a treatise on this subject, it would be unwise to ueg- 

 lect it. 



