( 879 ) 



Prom these v.aliies fonniihie were derived, wliieh after a traiis- 

 forination in oi'der to bring the zero-e|)()ch on 1868.5 beeonie : 

 h=z^ ()".45 ~ r.Wsh/ [KiTM + 20° (^—1868.5)] 

 /• = + ()".-2(; + 1".4(5 cos [I4ir.a + '20" (/— 1868.5)]. 



II' w (' assume that the anipliliidc and the argunu'iil of the two 

 periodie terms musi he ecjual, tiie formnkic become: 



h = Jf- ()".45 — 1".37 .vm [L57\7 + 20' (#—1868.5)] 

 /• = + 0".26 + 1".37 cos [157^7 + 20° (/— 1868.5)]. 



The objeet of tlie seeond operation was to derive from the obser- 

 vations 1895 — 1902 the most reUable value of jV for the mi(Ulle- 

 epoeh, assuming its annual variation to be 20°. Starting fi-om tlie 

 8 X 18 vahies of r and assuming as known only the values of c, 

 (as found from the solution of the equations for eaeh year) and those 

 of hr and Zv (as found aboxe), 1 lirst subtracted the c from the r 

 and then freed the latter from the intluence of A, and /v- 



The residuals must then be of the form: 



r' = — « sl)i jSfshig -}- a cos N cos g = « cos {g -\- No -\- 1 y, 20") 

 and now it is clear that the 8 X 18 residuals correspond with only 

 18 ditferent values of the argument i\^„ -f-// ~f" ^ X 20\ Consequently 

 these residuals could be combined in 18 values, for instance the 

 / ÏOYg = W in 1895 could be combined with that for 7 = 350° in 

 1896, with that for ^ = 330^ in 1897 etc. 



Having due regard to the weights, the following mean values of 

 !•' were derived. The arguments g hold for 1898 i.e. for 1898.5. 



These values are represented by the formula: 



— 0".42 sing + 1".51 cos g = + 1".57 cos {g + 15°.5j. 

 and 15"^. 5 will be a i)retty accurate normal value of jV for 1898.5. 

 For the derivation of a similar normal value from each of the two 

 series of Nkwcomb I chose a less direct but simpler method. In each 

 series I reduced the JSJ' derived from each year to a mean epoch by 

 means of the annual variation 20° and then combined them with the 

 weights as given by Nevvcomb ^). I did not however use the iV of 



^) Applying the same method to the observations 1895—1902 I should have 

 found for iV, 16°.9 instead of l5^5. 



