1895-96.] Professor Tait on Centrobaric Shells. 
117 
Note on Centrobaric Shells. By Prof, Tait. 
(Read February 3, 1896.) 
It is singular to observe the comparative ease with which 
elementary propositions in attraction can be proved by one of the 
obvious methods, while the proof by the other is tedious. 
Thus nothing can be simpler than Newton’s proof that a 
uniform spherical shell exerts no gravitating force on an internal 
particle. But, so far as I know, there is no such simple proof 
(of a direct character) that the potential is constant throughout 
the interior. 
On the other hand the direct proof that a spherical shell, whose 
surface-density is inversely as the cube of the distance from an 
internal point, is centrobaric is neither short nor simple. (See, 
for instance, Thomson and Tait’s Elements of Natural Philosophy , 
§ 491.) But we may prove at once that its at external 
points is the same as if its mass were condensed at the internal 
point. 
For if an elementary double cone, with its vertex at S, cut out 
areas K and E, we have 
E K 
