190 



EEPORT— 1882. 



On the whole, therefore, if the expression be written in the form 

 0'223 — 'OOo X — "001, the last term being only nsed when x is > 2, no 



error amounting to O'OOl will be made. 



Table XXXV. 



The corrections for the initial points which will be required afterwards 

 are as follows : — 



Table XXXVI. 



Bessel's Method. 

 FurtJie)' Modifications in the Calculations. 



(.31) Having thus described Bessel's method as modified by von 

 Oettingen, it is necessary to indicate some points in which it appears to be 

 susceptible of improvement. 



The most obvious objection is that the scale is corrected by dif- 

 ferent methods in different parts, and with varying degrees of ac- 

 curacy. 



In the first approximation, the middle part of the scale is corrected by 

 observations on all the ten threads, the upper part by observations on 

 three, two, and at last on one only. It is true that in the second approxi- 

 mation the additional measures are introduced, but the corrections for 

 the lower ends of these are of unequal value. Thus the correction 

 at 124° is determined from 9 curves, that at 1.34° is found from 5. The 

 latter must, therefore, be the more uncertain, and this uncertainty will be 

 as it were transmitted to the upper ends of the threads measured at these 

 points in the additional observations. 



At the lower end of the scale matters are still more unsatisfactory. 

 In the opinion of von Oettingen (loc. cit., p. 14), the corrections for 

 the initial points are of the same value as those for the upper ends of 

 the threads. If this be so, only four points are corrected between 98° and 



