362 EEPOKT — 1867. 



tively faint, but not smaller than fifth-magnitude srars. The letter T iu the sub- 

 joined list indicates that the meteor had a train, which was the case with by far 

 the greater number. Observations were made at tlie same time and place with 

 another meteoroscope by Professor Adams and his Senior Assistant Mr. Graham, 

 and it was agreed to divide the heavens into the northern and southern halves. As 

 I took the northern half, my observations are principally iu that portion, the ex- 

 ceptions occurring in the earlier and later obsenatious, and when the north quarter 

 was nearly covered with clouds, (See Table, pp. 304, .3(15.) 



Notes explanatory' of the Calculations. 



The chronometer was 2"" 51'"'82 fast on Observatorv Mean Time at November 

 13th, 11" 28"", and 2™ o2-.3o fast at November 13th, 16'' 49"'. Hence as the Ob- 

 servatory is 22''7'5 east of Clreenwich, 3"" 1.5* has been subtracted from each of the 

 chronometer times to calculate the Greenwich Mean Time to the nearest second. 

 The azimuths are reckoned from the N. point through E. to 360'. Let A represent 

 the azimuth-reading, and z the zenith-distance reading for any star, and let a and f 

 be its true azimuth and zenith distance calculated from its Iniown II. A. and N. P. D., 

 the colatitude of the Obser's atory being 37"^ 47', and the longitude east 22*-75. Also 

 suppose the axis of the instrument to have inclined by the arc .r from the zenith 

 towards the south, and by tlie arc y from the zenith towards the east. Then if m 

 be the index-correction of the zenith-distance readings, and fi the index-correction 

 of the azimuth-readings, we liave the following equations : — 



C — Z=:wi — X cos a-\-;/ sin a, 



a — A=?)+ cot f (z sin a+y cos a). 



The values of A, Z, a and 90°— f are given in the foregoing Table. By using 

 these values, two equations were derived from each of the observations of stars. 

 It should, however, be stated that, instead of using the recorded value of z, I have 

 adopted in each instance a value f/reater by one-fourth of a degree, having found 

 by experiment that the eye was almost necessarily elevated a little above the end 

 of the bar in order to see the opposite end in coincidence with the object. The 

 experiments gave a difference of pointing equal to about 15'. Also the small cor- 

 rection required for refraction has been taken into account to the nearest minute. 

 In this manner the follo^ving equations were obtained for determining the values of 

 7H, n, X and »/ : — 



No. No. of No. of 



of the the equa- the equa- 



Series, (f— Z) tioii. (n— A) tion. 



1. 21°27'*=)H-004f'.^).r-i-0-9989y (I)..-.52°10' =« + 0-8406,r-t-0-0.394y (8) 



3.2125 =>H+0-r494.r-!-0-7fK)4V(2)..-53 Ot=w-(-0-.i337.(-0-4.-5.59(/ (9) 



22. 17 11 =»(-0-805ai-0-5018y (.3)..-.56 37 =«-0-0(i34.i4-0-1093)/ (10) 



40.2121 =w+0-22.30j-+0-9748'!/ (4),,-53 7 =«+l-2205.i-0-2791y (11) 



51. 20 51 =;« + 00.31].r+0-9995y (.5). .—54 13 =w-f-0-.3123.r-0-0097y (12) 



62.19 41 =wi4-0-775.5.c-l-0-8.314y (6)..-55 9 =M-l-0-4760.i-0-5854y (1.3) 



70. 19.50 =w-f-0-227.5.i-l-0-97.38^ (7),,-53 .51 =«-|-0-4704x- 0-1099^ (14) 



Any displacement of the stand would be likely to exhibit itself in discordances 

 of the values of a — A, rather than iu discordant values of f — Z.' The above values 

 of a— A .'ihow that there was no azimuthal change sufficient to affect the values of 

 .r and i/, but that there may have been small changes of tlie index-coiTection n. 

 These changes, must, however, have been too small to ha\e any perceptible effect 

 on the values of f — Z. As there was an inter\-al of only three minutes between Nos. 

 1 and .3, it may be assumed that for these observations both ni and n had the same 

 values. Accordingly, after eliraii-atiug m and n from the equations (1), (2), (8) and 



■••■ Instead of the recorded reading 32° I have used 28°, an error having been apparently 

 committed by mistaking the direction of the graduation. 



t Instead of the azimuth-readinsj LSSl- I have adopted 18.34. a mistake having bsen pro- 

 bably made in reading off or recording. 



