DISCONTINUOUS FUNCTIONS. 257 



change which was principally effected by the 

 labours of the celebrated Professor Woodhouse, 

 we feel convinced that our continental neighbours 

 will not much longer have to boast, over the 

 country which gave birth to the immortal Principia, 

 in almost every department of abstract science. 

 In proof of this we need only advert to the recent 

 struggle for the greatest astronomical discovery 

 which has ever been made, taking into consider- 

 ation the circumstances by means of which it has 

 been effected. 



(16). Suppose the earth to be a hollow sphere, 

 it is known that the attraction of a spherical shell 

 upon a point outside of the shell is proportional 

 to _ ; and when the point is in the shell, the 



attraction is proportional to ^r ; and when the 

 point is in the inside of the shell the attraction is 

 nothing. 



Let a and b be the distances of the shell to 

 the inside and outside respectively ; .r equal to 

 the distance from the centre to the attracted point, 

 and Y equal to the attraction. 



We must have Y = 0, when d' < a ; and Y 

 l1 



