APPENDIX. o!9 



logr&quot; . . 0.47447 



log sin ( A&quot; D C&quot;) . . 9.84253 



log sin d&quot; 0.05770 



log of reduction 0.37470 



Reduction =0.013653 



Observations. Corrected Times. Intervals. Logarithms. 



I. July 30. 361080 



IJ. Sept. 6. 236691 37.875611 1.5783596 



in. Oct. 14. 119260 37.882569 1.5784395 



Hence the corrected logarithms of the quantities &, 6&quot; become 9.8140209, 

 and 9.8139410. 



We are now, according to the precept of Art. 146, to commence the determi 

 nation of the elements from the quantities/, /, r&quot;, (3, and to continue the calcula 

 tion so far as to obtain rj, and again from the quantities /&quot;, r, /, 6&quot; so as to 

 obtain ij&quot;. 



log*? 0.0011576 



log 77&quot; 0.0011552 



logP .... 9.9999225 

 log &amp;lt;/ .... 9.6309476 



From the first hypothesis, therefore, there results X == 0.0000251, and 

 Y= 0.0029648. 



In the second hypothesis, we assign to P and Q the values which we find 

 in the first hypothesis for P and $. We put, therefore, 



x = log P 9.9999225, 

 y log $=9.6309476. 



Since the computation is to be performed in precisely the same manner as in 

 the first hypothesis, it is sufficient to set down here its principal results: 



. 7 59 34&quot; 98 



&amp;lt; 5 43 56&quot; .10 



c.j + a 7 49 1 .97 



log (Jcsmoi 0.9142633 



log/ 0.4749037 



log n - 0.7724177 



