50 



MICHIGAN ACADEMY OF SClKXCi 



If the error of the eccentricity of the circle be calcuhited for every fifth 

 degree, and subtracted from the corresponding error in the table, the 

 errors of the division will be as follows: — 



It is evident that these errors have two regular periods ; one depending 

 on the double angle, the other having itself a period of ten degrees. From 

 the 72 errors, I find the following expression for these periodical errors 

 of the division : — 



—0.603 cos (2x+74° 20')— 0."23 cos 3(Jx. 



The first term shows that the circle has a small ellipticity; the latter 

 very probably arises from the manner in which the division was made. 

 The introduction of these two terms brings the sum of the squares of the 

 errors from 39.7 down to 22.9. 



If we subtract these periodical errors from the errors of the preceding 

 table, we find at last that the errors of the lines with intervals of five 

 degress, considered as merely accidental, become as shown in the following 

 table : — 



c 



5 

 10 

 15 



20 



25 

 30 

 35 

 40 

 45 



50 

 55 

 60 

 65 

 70 



+0.18" 



+0.98 



-0.67 



-0.12 



-0.32 



-0.04 

 —0.39 

 +0.48 

 —0.57 

 +0.11 



+0.05 

 +0.36 

 —0.10 

 +0.49 

 0.00 



75° 



80 



8.=; 



90 



95 



100 



105 



110 



115 



120 



125 



130 



135 



140 ....:. 

 145 



+0.69" 



+0.07 



+0.69 



-().(i7 



40.47 



-0.71 

 +0.16 

 —0.62 

 —0.39 

 —0.21 



—0.45 



+0.25 

 -O.3.; 

 +0.03 

 —0 89 



150 

 1.55 

 160 

 165 

 170 



175 

 180 

 185 

 190 

 195 



200 

 2<i5 

 210 

 215 

 220 



+0.12' 

 +0.80 

 +0 28 

 4 0.12 

 +0.18 



+0.59 

 +0.01 

 -0.23 

 +0.60 

 —0.95 



-0.08 

 —0.52 

 +0.04 

 +0.32 

 —0.30 



The probable error of any line is equal to ± 0."38 ; and therefore the 

 probable error of the mean of four lines which are used in reading the 

 microscopes, is ± 0."19. 



With regard to the numbering of the degrees as given by Dr. Bninnow, 

 he refers, I think, to zenith distances when the circle is in a particular 

 position on the axis. See Publications of the Duiisiiik Observatory, Part 

 IV. ]»;!tre 12, whore the division marks whose eiiois have hoe^^ determined 

 by Dr. IJn'nniow are taken in this way. S(m\ also, llie Abhandlungen of 



