No. 8.) 



MINOR PLANETS— LEUSCHNER, GLANCY, LEVY. 



Taiile XXVI He. 

 [(l-cco8£)TrV'] 



111 



Unit— 4tb decimal of a radian. 



Table XXIX. 



[(l-«C08£)(r3-¥V')] 



Unl^4th decimal of a radian. 



These developments cover the function W within the extent of our tables. This does not 

 mean that W is always inclusive of all these terms, but that these terms occur in one or more of 

 the tables. With the exception of [(1 — e cos e) W], which contains W,— W,", Wis to be under- 

 stood to mean ^_ y^^ ^ '^y^, ^ [ ^y^-^ ^ ( ^^,, + w," + W,") 



^^^ w= w,+ F,'+nig + (tF/'+ w,"+w,"). 



The ascending powers of w, -q, -q' , f are selected independently in each function. 



To avoid along series which is analogous in construction to T^, the function W^" + TF," + W/' 

 is not tabulated. The sum of this function and Tables XVII, XVIII, XIX, XXIIa gives W. 

 Since W is so long and we only need W, it is not tabulated. The function 



IS given m Table XXIXa. 



It is convenient to collect here [(1 — e cos e) If], which is required later. The function is 

 given by the sum of Tables XM^, XX, XXI, XXVIII, and XXIX, and is tabulated in Table 

 XXIX6. 



Wc shall also need the function S 



H = x + 2,y = E.+H/ + [S,] + (S,"+H3"+E/') 



Evidently E can be written by inspection if Wis tabulated. If the double headings are retained in 

 the construction of E the mass- factors and ranks are explicit as in the construction of W. If W 

 is not given, we can write by inspection E, (previously required in the computation), Ej' and 

 [Sj] from TF,, TF/, and [W^], respectively. The remainder, namely, ^2" + ^3" + 'ZJ' , can 

 be written from F/'+ F,"+ F/', i. e., by inspection of Tables XXIH, XXIV, XXV. The 



function 5^ S is given in Table XXIXc. 



