690 SCHULTZ-STEINHEIL, THE ARGUMENT X,n- 



After introduction of A and the expressions for p and q 

 found frora (6) "vve find: 



u 

 cos i 



— Tr^'^Z + Ä^'H [cos mTt sin l — el — 



— ^^f '^ + ^m\ ^°^ *?^ ^°^ "*^ ^*^^ ^'' "^ pei'iodic terms. 



Here we must bear in mind that no quantity caiculated is 

 afterwards enlarged by small di visors, but many are diminished 

 by the divisor i. Moreover no quantities are formed by the 

 difference of two large quantities, and thus we get them more 

 accurately than otherwise would be possible and we need not 

 begin the calculation with so raany decimals. In many cases it will 

 be sufficient to consider the greatest terms, and thus in K,n, S,r, 

 and Cm only those in which small divisors occur, and in the peri- 

 odic terms for those which are of the highest degrees with respect 

 to e] under such circumstances the determination of nöz, 2v and 



, for a certain epoch will be easily made. If thev have to be 



cos l 



determined with great accuracy we may bring the periodic tern.is 



to the form 



A{i) cos iL + B{{) sin i'k 



where A{i) and B{i) raust be determined for each half revolution 

 and it would not be so easily performed to determine nöz, 2v and 



. for a Single value of 2, but if we had to determine these 



cos i 



quantities for many successive values of X within the same half 

 revolution (the same value of in) — the quantities A(i) and B(i) 

 once caiculated — this would not take long to make, and an 

 ephemerid would thus by this method be easily performed. I am 

 now calculating the planet (263) Dresda after this meted and 

 hope soon to arrive at a result. The formulas here given are 

 not always developed to a degree convenient for numerical cal- 

 culation, but I have considered it better to make those develop- 

 ments in connexion with the application of the formulas on a 

 numerical example. 



