364 
Proceedings of the Royal Society of Edinburgh. [Sess. 
APPENDIX. 
(1 7 \ 
— - , g , 2 , sin 2 h J and 
J’l’ 2 ’ Sin2 2 i ) 
introduced in Section IV. of the foregoing paper have been computed for 
each degree of the quadrant, at the suggestion of the author, by Mr Frank 
Robbins. Their seven-place logarithmic values, with first and second 
differences, were published as an appendix to the author’s paper on “ The 
Computation of Secular Perturbations” in the Monthly Notices of the 
Royal Astronomical Society, vol. lxvii., May 1907, pp. 444-447. 
On the recommendation of the referees, these tables, with the descriptive 
preliminary paragraphs, are here reproduced (with Mr Robbins’s permission), 
so as to facilitate the application of the method described in the present 
paper : — 
In the hypergeometric series F (a /3 y x) in the first case 
a has the value - 
1 
6 
and in the second case 
For convenience of designation the tables are headed Minus F and 
Plus F according to the sign of a. 
Yega’s (1794) ten-figure logarithms, corrected by collation with the 
copy in use at H.M. Nautical Almanac Office, were used, and the natural 
values of the individual terms were taken out to ten places of decimals. 
These were obtained in duplicate for each end of the quadrant, and the 
whole were examined by differencing to the sixth order. Lastly, the 
seven-figure logarithms of the functions were taken from the eight-figure 
table of the Service Geographique de l’Armee (Paris, 1891), reference being 
made to Vega where the eighth figure was approximately five. 
The log Minus F has been increased by 10 as customary, to avoid the 
inconvenience of printing negative characteristics. 
The whole has been examined by Mr J. Abner Sprigge, of H.M. 
Nautical Almanac Office, so as to make it possible to use the tables with 
confidence in their accuracy to the seventh place. 
