382 Astronomical and Nautical Collections. 



differences divided by their number shows the error of the 

 outer arc so compared, and thence the value of each inner arc, 

 to vphich it has been compared, is ascertained. 



In this method the number of measures, really necessary to be 

 taken, is the same as before, but they occasion considerably 

 more trouble than so many taken in one position of the instru- 

 ment, from the necessity of placing the circles at anew point of 

 coincidence previously to each measurement. 



In my examination, however, I did not limit myself to the mere 

 comparison of a single arc, but in each position I measured the 

 errors of each aliquot part, so that, in fact, the number of mea- 

 sures actually taken, in an examination by 5ths, 6ths, 8ths, and 

 9ths, was 5* + G'' + 8'^ + 9*, the mean of which ensures greater 

 accuracy in the results. Tlie total amount of the errors on 22 

 points, obtained by this estimate of the divisions of this circle, 

 after correction for common and central error, was found to be 

 78 seconds, or about 3i seconds, on an average, for each 

 division. 



By subsequent examination of another set of points, begin- 

 ning from 12° (instead of 0) in the same manner, I found a total 

 of errors 95", or 4| on an average ; so that the mean of both exa- 

 minations shows this engine to be liable to an error of about 

 four seconds on each division. 



In consequence of the discovery of a difference between the 

 inner and outer circles, it became necessary to re-examine the 

 circle divided by Allan, but the measurements that I have taken 

 do not invalidate our former result as to the comparative merit 

 of his mode of constructing his dividing engine. The total 

 amount of errors, in a set of 22 points, did not exceed 42", 

 making the average error of his engine less than two seconds. 



The greatest error discovered on Allan's circle was 6J seconds, 

 while the greatest by Ramsden's engine is as much as 11". 



