Dreyer — A Surcey of the Spiral Nebula Ifessier 33. 7 



liitions round tlie central notch, the mean value of tlie interval being 

 found = 0''-2615 = 94'8'-4. Using Bessel's nomenclature/ the following 

 values were found : — 



a - 0-00200 

 f3 = -r 0-00073 

 a' = - 0-00081 

 ft'= - 0-00043, 



so that the correction for periodic error to the reading ic is 

 = - 0-00200 i:osu -r 0-00073 sinw - 0-00081 tos2tc - 0-00043 sm2u. 



Applying the difference between the correction for 0-26 and 0-00, 

 &c., to the excess of the individual sixty values of the interval over 

 the mean value 0*26 15, the following residuals were found, the minus 

 sign referring to the revolutions to the left of the notch, the plus sign 

 to those to tlie right : — 



Rev 





•0 





•i 







•3 



•4 





•5 



•6 





•7 





•8 



•9 



o 



+ •0020 





0010 



-■0031 



+•0010 



+ •0004 





0000 



-•0029 



+ 



0023 



+ 



0008 



-•0019 



-1 



+ 



13 





00 



- 31 



+ 



07 



- 23 





10 



- 19 





19 





05 



- 15 



-0 



+ 



07 



f 



20 



+ 13 



+ 



17 



- 13 



_ 



17 



- 12 



+ 



09 





22 



- 12 



+ 



+ 



07 



+ 



07 



- 07 



+ 



20 



00 





00 



4- 25 





07 



+ 



02 



- 19 



+ 1 



+ 



13 



+ 



04 



- 14 



+ 



20 



+ 30 



+ 



23 



- 12 



+ 



06 



+ 



05 



- 15 



+ 2 





10 





06 



- 24 





17 



00 



+ 



06 



- 09 



+ 



26 



+ 



08 



- 12 



These residuals represent i)rogressive errors, and, of course, also 

 errors of observation. If and u are expressed in revolutions and 

 decimals of revolutions from zero (here three revolutions to the left of 

 the notch), the progressive errors are found by the equations 



X {ill - fi) -r y {ui' - U-) = residual. 



The sixty equations of this form gave 



+ 0-00040, y = - 0-00003, 



so that the error depending on the number of revolutions from the 

 beginning of - 2'' is 



+ 0-00040r - 0-00003r2 



^ Eessel, Astron. Unteisuchungen, II. p. 79 ; Abhandlungen, II. p. 143. 



