348 Astronomical and Nautical Collections. 



5. It was then inferred, that since each point of the inner circle 

 must have moved through a space equal to the first aliquot 

 part of the outer, the intervals or errors measured must be the 

 differences of each arc of the outer circle from the first ; and 

 since the sum of all the arcs is always exactly 360°, the result 

 of all the errors of the arcs additive and subtractive must be 

 0, and the sum of the differences divided by the whole number 

 of aliquot parts, must give the error of the first arc, which being 

 deducted from the several differences measured, gives the errors 

 of the respective arcs ; and the sums of the successive errors 

 of the arcs give the true errors for each point. 



6. It was thought sufficient to carry this examination as far as 

 ^, making the series 2, 3, 4, 5, 6, 8, 9, which determines 22 

 points, at the distances 0°, 40°, 45°, 60°, 72°, 80°, 90°, 120°, 

 135°, 144°, 160°, 180°, and their supplements; many of these 

 points being ascertained by several different measurements. 



7. Where the errors were observed to increase in approaching 

 to a particular division, it was inferred that they were partly 

 owing to a defect in the centring of the instrument ; and an 

 allowance was made, in proportion to the cosine of the interval 

 from the apparent maximum, to such an amount as would give 

 the most favourable result. 



8. It had hitherto been supposed that the zero was free from 

 error in relation to the mean of the other divisions ; but if it 

 appeared that after the correction for the central error, the 

 particular errors remained mostly positive or mostly negative, 

 a quantity was deduclcd as a common error, such as to render 

 the positive and negative errors nearly equal ; and this error 

 was considered as that of the zero itself. 



