538 

 ADDENDUM. 



Prof. üK Sitter, to vvlioiii I luive coiiiniuiiicated the above, writes: 

 A precession of 0''.()13 per aiinuivi of course comes well within the 

 reach of observations, since the observed valne of the precessional 

 constant is trustworthy to about ()".0()H). The point is therefore 

 with what accuracy the theoretical value can be com|)uted. Now 

 the liinisolar precession (the planetaiT precession can be taken as 

 completely known) is given bv a formula of the form 



p^={P-^- Qli).H (1) 



where P and Q are known numbers and ft is the mass of the 



moon (ex|)ressed in that ot earth -|- moon as unit) and H = — — — 



depends on the momeiils of inertia of the earth. The uncei-tainty of 

 H causes in />, an uncertainly of about Vsooo of its amount, thus, if 

 H was exactly known, /y, would be uncertain to the extent of 

 db 0",025 or twice the new precession. A better determination of fi may 

 be expected from the opposition of Eros in 1931 M- However the 

 uncertainty of H is of much greater im|)0rtance. In 1915*) I have 

 with the aid of the hypothesis of isostasy, derived the ellipticity s 

 of the earth from H, this latter being determined from p^ by (1). 

 To invert this order it would be necessary, in order to get a p.e. 

 of ± 0".0ü5 in p^, to know e to about Vsoooo of its amount. The 

 direct determinations of e at present do not go beyond about '/too- 

 To increase this accuracy seventyfold would in my opinioti be 

 beyond the forces of geodetical science, at least in the near future. 

 We can determine H witii greater accuracy from the constant of 

 nutation, which is given by 



N = R.fi. H (2) 



where R is again a known number. From (1) and (2j we derive 



p^=:fs + iyN ........ (3) 



where *S' and T are also practically exactly known. The uncertainty 

 of the multiplier owing to the uncertainty of ft is now about \/4,oo 

 01" V5000. '^"tl it will probably be reduced to Vioooo by the new 

 determination of f^ in 1931. 



^) The figure of the earth and some related astronomical constants. The Obser- 

 vatory Aug. 1915, page 322. 



'') On Isoslasy. the moments of inertia, and the compression of the earth. These 

 Proceedings April 1915, Vol XVll, p. 1291. 



