SECT. 3.] PLACES IN ORBIT. 131 



log ... 3.5500066 esin^ = 31932 / .14 = S52 12&quot;.14 



f log a . . . 0.6336584 esmJE = 27455 .08 = 7 37 35 .08 



2.9163482 Hence the mean anomaly for the 



logif . . . 1.3411160 first place 32944 27&quot;.67 



4.2574642 for tne secon d = 334 45 58 .73 



Difference 5 1 31 .06 



Therefore, the mean daily motion is 824&quot;.7989. The mean motion in the time 



t is I809i&quot;.o7 = 5 rsr.07. 



II. In the other example we have 



/= 3127 3S&quot;.S2, 01 = -21 50&quot;.565, 1= 0.08635659, log mm= 9.3530651, 

 or the approximate value of h = 0.2451454 : 



to this, in table n., corresponds logyy = 0.1722663, whence is deduced 



= 0.15163477, x = 0.06527818, 

 yy 



hence from table ITT. is taken I = 0.0002531. Which value being used, the cor 

 rected values become 



h = 0.2450779, logy y = 0.1722303, = 0.15164737, x = 0.06529078, 



I = 0.0002532. 



If the calculation should be repeated with this value of , differing, by a single 

 unit only, in the seventh place, from the first ; h, logyy, and x would not suffer 

 sensible change, wherefore the value of x already found is the true one, and we 

 may proceed from it at once to the determination of the elements. We shall 

 not dwell upon this here, as it differs in nothing from the preceding example. 



III. It .will not be out of place, to elucidate by an example the other 

 case also in which cos/ is negative. Let v v = 224 0&quot;, or /= 112 0&quot;, 

 log r = 0.1394892, log / = 0.3978794, t = 206.80919 days. Here we find 

 w = + 4 14 43&quot; 78, L = 1.8942298, log MM = 0.6724333, the first approximate 

 value of log-5^ 0.6467603, whence by the solution of equation 15* is obtained 

 Y= 1.591432, and afterwards x = 0.037037, to which, in table III., corresponds 

 = 0.0000801. Hence are derived the corrected values log H= 0.6467931, 

 F= 1.5915107, x 0.0372195, \ = 0.0000809. The calculation being repeated 



