No. 3.] 



MINOR PLANETS— LEUSCHNER, GLANCY, LEVY. 



143 



Tablu LIII. 

 [5] — {fii (cos ^— e)+f2Hin y!r) 



Umt=l". 



and by eq. (193), 



d-0,=^t 



By inspection it is clear that the periodic part of <S' is of the form 



I Up.,7,Pjj'^ sin A 

 and the secular terms are of the form 



I TJ^.-q-qPri'i-i^nt cos {U-£) +£} + 2"<- '?^i-o cos A 



Expanding cos {{A — e)-\-s}, and collecting coefficients of sin s and cos £, the secular terms can 

 be written 



nt{ Kjicos € — f ) + A'j sin e} 

 where 



/„w 



w , 



K, = I C7p.,>)P>?'»^ cos (.4 -e)-~ U,., cos A 



K, 



'o'J^ . 



2=-Jfv7'ZP,'«|sin(.4-£) 



Introducing this notation, the perturbation can be written in the form of eq. (205). 



The coefTicients Vp.q are given in Table LIV. K, and TT,, which are constants, are tabu- 

 lated in Tallies LV, and LYu, respectively. For a given planet the factors and arguments are 

 known. Therefore /f, and K^ reduce each to a single numerical quantity. 



Since the Bohlin-v.Zeipcl method is based on the fundamental principles of Hansen, the 

 constants of integration are dcternuncd by the condition which must be satisfied when the 



