SECT. 3.] PLACES IN ORBIT. 12 J 



2 tan 2 w / pp n s 



i / -, = e sin F sin/ 



cos 2 03 V rr 



2 tan 2 &amp;lt;u /- jr T? 



- = tan tp sin tr sin / tan a&amp;gt; sin / sm 7 . 

 cos 2 o&amp;gt; 



Lastly, the mean motion and the epoch of the mean anomaly will be found in the 

 same manner as in the preceding article. 



97. 



We will resume the two examples of article 87 for the illustration of the 

 method explained in the 88th, and subsequent articles : it is hardly necessary to 

 say that the meaning of the auxiliary angle w thus far adhered to is not to be 

 confounded with that with which the same symbol was taken in articles 86, 87. 



I. In the first example we have /= 3 47 26&quot;.865, also 



log ^ = 9.9914599, log tan (45 -f- w) 9.997864975, a = 8 27&quot;.006. 



Hence, by article 89, 



log sin 2 i/ . . . 7.0389972 log tan 2 2 w . . 5,3832428 



log cos/. . . . 9.9990488 log cos/ . . . 9.9990488 



7.0399484 5.3841940 



= log 0.0010963480 = log 0.0000242211 



and thus /= 0.0011205691, | + /= 0.8344539. Further we have 



log** . . . . 9.5766974 

 21ogjfc* . . . . 9.1533948 

 C.flogr/ . . . 9.0205181 

 C. log 8 cos 3 / . . 9.0997636 



log mm ... 7.2736765 

 log (| -I-;) . . . 9.9214023 



7.3522742 



The approximate value, therefore, of h is 0.00225047, to which in our table II. 

 corresponds logyy = 0.0021633. We have, accordingly, 



log m m = 7.2715132, or mm = 0.001868587, 

 3 yy yy 



17 



