THE PLANET NEPTUNE. 19 



not accord well with the observations. The disturbing 

 body must then be situated beyond Uranus, and at a 

 considerable distance from it, for reasons already given. 

 Now the distance of each of the more remote planets 

 from the sun, is about double that of the preceding one. 

 It is natural, tken ; to conjecture that the disturbing 

 planet may be at a distance from the sun double that 

 of Uranus, and it must move nearly in the ecliptic, be- 

 cause the observed inequalities of Uranus are chiefly in 

 the direction of the ecliptic. Le Yerrier then propounds 

 the following specific problem : 



" Are the irregularities in the motion of Uranus due to 

 the action of a planet situated in the ecliptic, at a distance 

 from the sun double that of Uranus f If so, what is its 

 present place, its mass, and the elements of its orbit ?" This 

 problem he proceeds to resolve. 



If we could determine for each day the precise effect 

 produced by the unknown body, we could deduce from 

 it the direction in which Uranus is drawn; that is, we 

 should know the direction of the disturbing body. But 

 the problem is far from being thus simple. The amount 

 of the disturbance can not be deduced directly from the 

 observations, unless we know the exact orbit which 

 Uranus would describe, provided it were free from this 

 disturbing action; and this orbit in turn can not be 

 computed unless we know the amount of the disturb- 

 ance. Le Yerrier therefore computes for every nine 

 degrees of the entire circumference, the effect which 

 would be produced by supposing a planet situated in 



