8 



STATEMENT AND EXPOSITION OF 



In the second approximate arrangement which follows, the dependence of the 

 value of one term on that of another is indicated by the brace connecting them, and 

 the power of r in question is also shown ; the half-planetary terms have their names 

 printed in italics; while Mercury's name (in view of the peculiarity of that planet) 

 appears in capitals: other symbols, etc., as heretofore. 



The leading ratio here accepted, after many trials of it and of other ratios, is 

 1.805. 



Second Approximate Arrangement of the Planetary System. l_Value of Leading 

 Batio 1.805]. 



Names and Symbols. 



Law. 



Fact. 



Diff. L.— F. 



s 



(U) 

 h 



(A) 



© 

 (©?) 



2 

 Aph. 5 



Per. 5 



Neptune) ^j ] 

 C Uranus ) ' > *" 



ri <! Limit (U), 



30.05673 

 19.30118 



16.65193 



30.05733 

 19.18336 



— 0.001 

 + 0.118 



(Missing). 

 9.53885 

 5.20280 





Saturn, . 



Jupiter, -J 



I r 

 Limit (A), > 



- r 

 Mars ) , > 

 (Earth I ^ I r 

 r^ j Limit f© 9), > 

 ( ( Venus, [- r 



?• -< f Mercury in Aph. "1 -* 



( "(Mercuey j 



3Iercu7y in Per. 



9.22545 



5.11105 



2.83161 



1.56876 

 1.00739 

 0.86912 

 0.74982 

 0.48151 

 0.41543 



0.30920 



—0.313 

 —0.092 



1.52369 

 1.00000 



+ 0.045 

 + 0.007 



0.72333 

 0.46670 

 0.38710 



0.30750 



+ 0.026 

 + 0.015 

 + 0.028 



+ 0.002 



(11) The approximation of law to fact here shown, though in the main very 

 close, yet exhibits some terms in which the discrepancy is a greater fraction of the 

 whole than seems to be quite tolerable, in view of the accuracy of the other terms. 



Then, too, the last column of the arrangement here shows a tendency in the 

 difference of law from fact to be negative for the first part of the series of terms, 

 but positive afterwards; as though the value of the leading ratio were in excess for 

 the one portion, and thus had given the results in general too small ; but the same 

 value of the ratio having been too small in the case of the remaining terms, had con- 

 sequently given results too large. All this makes it not improbable that the lead- 

 ing factor ?•, from first to last, should regularly increase, beginning below the mean 

 value of 1.805, and ending above the same ; the increase, however, in any event, 

 being very small. 



To ascertain whether this is so, it will be found advisable to institute a separate 

 induction within the narrower limits of the region from Saturn to Mars inclusive. 



