io Existence and Position of [January, 
that of Neptune being in 46° 6' 39". He placed his unknown 
almost in the middle between Neptune and A, at 6*120 from 
the former at 5*844 from the latter. According to the ex- 
centricity intercalated, between Neptune and A, for the 
Predicted, it moved 3*89 farther, and nearer than its mean 
distance from Uranus. Le Vender placed the mean orbit of 
the Predicted at 16*97 from that of Uranus : Neptune is at 
io’ 85. This reduces the perturbing power in its mean, 
comparing Neptune to the Predicted, — 
16*97 2 -4-10*85 3 =2*46 times. 
This loss of power by distance had to be balanced by mass. 
21. “The search for the value of in' is a very delicate 
point,” says Le Verrier. The mass of Neptune is 1 4- 19360 ; 
Le Verrier made that of the Predicted 1 -4-9322, about 1-4-26 
more than double, but not that of Neptune plus A. Had 
he done this he would have balanced loss by distance by 
mass, for 1-4-13200 + 14-19360 = 1-4-7848 exceeds the mass of 
Neptune 2*46 times. As it was, he attributed to his planet 
only a mass 2*077 times that of Neptune, and left against 
the loss of power by distance an unsatisfied balance of 0*38. 
When we apply the distance and mass attributed to the 
Predicted, we find that it would exercise at its perihelion an 
influence 1*423 times greater, and at aphelion 1*789 times 
less, than that exercised by Neptune at mean distance, which 
is in sum a variation of 1-4-3*212 in the disturbing power of 
the Predicted. 
When we apply the elements of Neptune and A in com- 
parison, the former exceeds A in perturbing power by 
distance 2*i03 2 =4*42 times, and aCts less by mass 1*46 times. 
Neptune therefore exceeds A in this power 3*027 times, which 
gives a difference of only 0*185 with the variation 3*212 of 
power by excentricity of the fictitious planet. 
For such slight differences various causes may exist ; but 
the dominant cause is B, whose perturbing power is 1-4-26 of 
that of Neptune and 14-8*7 of that of A. It moved in 
I 55 years only through about 88°. When B came in con- 
junction with Uranus and Neptune it became a part substi- 
tute for far-off A : the excess of 0*077 ever the 2, in the 
point of mass, may be therefore considered as equivalent of 
the 1-4-26, and the deficiency 0*38 of mass balancing distance 
as more or less representing the absence of A in the time of 
conjunction of the other three planets. 
The disturbance of Uranus by B may be indeed traced as 
