of Vessel's Astronomical Observations. 21 



The mean of all these twenty determinations is +l"-83, 

 exactly agreeing with the result obtained by Dollond's transit. 



I have stated here the single results, as they may serve for 

 solving the question, whether the axis of rotation of the earth 

 coincides with a principal axis, for which there is, as far as I 

 know, no positive proof founded on observation. If the period 

 of the inequality resulting from this cause, on the supposition 

 of the earth being a spheroid of rotation, be supposed = 337*5 

 mean days, and if the angle of the axis be designated by 3, the 

 observed azimuth of the mark is 



= 15A« + 3 sec. <p (e + t. 1° 4') 

 where t denotes the number of mean days elapsed from the 

 beginning of 1820, and e the value of the argument at that 

 time. The twenty observations compared with this formula 

 give 15 A a = + l"-804 probable error = ± 0"'1226 



3. cos s = +0 -064- =+0-0997 



3. sins =—0-090 =±0-0927 



d = 0-110 =±0-1361 



from which it becomes probable that the angle of the axis does 

 not exceed a quarter of a second. 



Observations of this kind, continued during a longer period 

 or instituted with the sole view to determine 3, might still more 

 diminish the uncertainty ; those which have here been given 

 may, however, satisfy us that the angle of the axes is so small 

 as to have no dangerous influence upon the greatest number 

 of observations. 



Besides these remarks concerning the use of the instrument 

 as a transit, I have to give some explanations on the observa- 

 tions in general. The observations made with the circle may 

 be employed either as polar distances or zenith distances ac- 

 cording as the place of the pole or of the zenith on the instru- 

 ment is supposed to be known ; the former appears to me to 

 be more direct, partly because the result which is required, 

 the declination, is immediately derived from the polar distance, 

 partly because the place of the pole may be found at every 

 period independently of reversing the instrument; whereas 

 the place of the zenith can only be determined by combining 

 two periods. I have therefore constantly referred all com- 

 putations hitherto made to the pole, and give here the deter- 

 minations which have been employed, and which are exclu- 

 sively founded on the two pole-stars which were usually ob- 

 served five times at each passage ; the declinations made use 

 of in these calculations are for « Ursa: Minoris taken from the 

 Ephemeris which Prof. Schumacher and Prof. Struve have 

 published; for 5 Ursa; Minoris they were computed from my 

 tables. 1820. 



