160 RELATIONS BETWEEN SEVERAL PLACES IN SPACE. [BOOK I. 



and in the same manner, 



[10] = n (0. 0. 2.) D ri ((0. 1. 2) &amp;lt;T -f (0. 1 2) ZX) + n&quot; (0. H. 2) ZX , 

 [11] = (0. 1. 0) D n (0. 1. 1.) Z/ + n&quot; ((0. 1. 2) d&quot;+ (0. l.H.) Z&amp;gt;&quot;). 



By means of these equations the distances d, d , 8&quot;, can be derived from the 

 ratio between the quantities n, n , n&quot;, when it is known. But this conclusion only 

 holds in general, and suffers an exception when (0.1.2)= 0. For it can be shown, 

 that in this case nothing follows from the equations 8, 9, 10, except a necessary 

 relation between the quantities n, n , n&quot;, and indeed the same relation from each 

 of the three. Analogous restrictions concerning the equations 4, 5, 6, will readily 

 suggest themselves to the reader. 



Finally, all the results here developed, are of no utility when the plane of the 

 orbit coincides with the ecliptic. For if (f, /? , /3&quot;, B, B B&quot; are all equal to 0, 

 equation 3 is identical, and also, therefore, all those which follow. 



