D. P. Todd—Search for a Trans-neptunian Planet. 229 
the next order of distance beyond Neptune as occupied by the 
planet for which we are searching, I assumed, as a first value 
f mean distance, a=46°0: this value seemed to be indicated 
by a fair induction. The periodic time of the planet would 
Adams (first hypothesis) -....--.------- 0°16103 
LOV erties! i 2555 2: POOR PS ee Ore 
Adams (second hypothesis) .....-------- 0120615 
The eccentricity given by investigation of the orbit of Nep- 
tune from observations of the planet was: 
Newcomb ( Tables of Neptune) .---. .--- 00089903 
We should, therefore, expect nothing of any attempt to 
arrive at the eccentricity of an orbit exterior to that of Nep- 
une. 
(3) The longitude of perihelion of the disturbing planet.— 
Much the same remark obtains in reference to this element. 
The several values of longitude of perihelion of Neptune, 
ae from the researches on perturbations of Uranus, are as 
ollow : 
Adams (first hypothesis) ....-..------- 315° 57’ 
LiON OPIGE on an ace pee es ten 284° 45’ 
Adams (second hypothesis) ...-...------ 299° 11’ 
The longitude of perihelion given by observations of the 
planet is: 
Newcomb (Tubles of Neptune) .----- 46° 6’ 39'°7 
Evidently it would not be wise to include this element in 
the investigation. 
: e epoch of the disturbing planet.—If we can obtain 
even a rough approximation to the value of this element, the 
end of the investigation is fully attained. An inspection of 
the outstanding residuals, graphically exhibited, will show. 
without further labor, the epochs of maximum disturbance. 
The best that can be done will be to prepare an approximate 
perturbative curve, the epochs of maximum disturbance of 
which shall be in harmony with the assumption of mean dis- 
tance of the exterior planet. By applying this to the plot of 
outstanding residuals, we may decide at what points the appli- 
