Solution of a Problem in physical Astronomy. 93 



And the constant logarithms to be used in these calculations 

 are the following, which are respectively set down to as many 

 places of figures as are requisite. 



L. 2 = 0-3010,300, L. 1 = 7-5740,3, L. f = 1796, 



L. I =7-8239,087, L. | = 0-1249,4, L. ?- = 0-4971,499; 



L. f = 1-1653,0, L. i = 1-1217,2, L. 1 == 1; 1859,1, 



•L.-^ =7-910, L. T =7-910, L.-y =7-939. 



By comparing this Art. with Art. 13 of the first Appendix, 

 it will appear, that the number of logarithms used in the new 

 formula is very considerably less than the number used in those 

 from which they were derived ; and still fewer will suffice, since 



the term— ^-, which occurs in the second theorem, is most easily 



derived from — -/* the first term in the first theorem, the loga- 



2 



cc 



2 2 



rithms of — , — , and cc, being there ready calculated ; so that 

 L. ± needs not be used in the computation. 



12. Let us now compute A and B by the first and third of 

 these new formula, when Venus and the earth are the two 

 planets. 



• See Art. 1 1 of the first Appendix, 



