Obase.] OOO [Oct. 15 and Dec. 3, 1875. 



These equations are immediately suggestive of the numerous familiar 

 equations between tlie sums of periodic times. The substitution of 'pro- 

 ducts for sums, and powers for products, indicates the early organizing 

 activity of constant forces, acting with reference to given centres, in 

 elastic media. 



The solution of equations (1) to (4) is as follows : — 



(1) 



Log. 30.033865-202798 7.687713 



" 19.18358119-183581-5.20279S 17.936362 



" 5.20279830-o?386 21.511361 



47.135435 



•' 9.07764530-033864-19. 183581 47.148979 



.013544 ^ 49.217441 = .000275 = log. 1.00051 



(2) 

 Log. 30.335515-^2 735 1 8.043068 



" 20.04418320-044183-5.427351 19.030955 



" 5.427351'^o-3355i 22.284102 



49.358125 

 " 9.53885230-3351 + 20.044133 49.346714 



.011411 -^ 50.379693 = .000227 — log. 1.00050 



(3), (4) 

 If log. == 10, the logs, of the assumed masses are : — 



tp (Newcomb, from satellite) 5.712646 



t|; ( " " perturbations) 5.705534 



§ ( " ) 5.645892 



l2 (Bessel) 6.455734 



2/ ( " ) 6.979689 



Substituting these logs, for the aphelion logs, in equation (2), we get 

 for log. \i , by using for log. tp 



Satellite value . (3) 6.458198 



Perturbation value (4) 6.456439 



6.458198 — 6.455734 = .002464 = log. 1.0057 



6.456439 — 6.455784 ~. .000705 ~ log. 1.0016 



