APPENDIX. 289 



This form is given by ENCKE (Berliner Astronomisches Jahrfawh, 1822, page 184.) 

 If we put e = 1 in the coefficient of de it becomes 



dv , kt 



If we substitute the value of dv in the expression for dr given above, it 

 may be reduced to the form 



7 k . i m \ 7 / o k t sin tf . 



\ i 



t&amp;gt; )de, 



41. 



The time t may be found from table II a , by multiplying the value of r cor 

 responding to w by 



J B 



45. 



Table I for the hyperbola is similar to that for the ellipse, and contains 

 log E, and log E r for the formulas 



tan bv = E v -y tan i w 

 r = fi r sec 2 i w . 



The differential formulas of article 40, of the Appendix, can be applied to 

 the hyperbola also, by changing the sign of A and of 1 e in the coefficients. 



56. 



As the solution here referred to may sometimes be found more convenient 

 than the one given in articles 53-57, the formulas sufficient for the use of prac 

 tical computers are given below. 



Using the notation of 50 and the following articles, the expressions for the 

 rectangular coordinates referred to the equator are, 



x = r cos u cos Q r sin u sin Q, cos i 



(1) y = r cosn sin & cose -f-rsin ticos & cos i cose r.smu sin i sin e 

 z = r cos M sin Q sin e -f- r sin u cos Q cos * sin e -j- r sin u sin i cos e 



37 



