6 PREFACE 



found it of advantage. Even so, difficulties arise, but they are 

 much like the troubles the old man spoke about on his death bed 

 as having been very real when they came, but as a matter of fact 

 most of them never happened. Walter Bagehot, in " Physics and 

 Politics," says: " Everybody who has studied mathematics knows 

 how many shadowy difficulties he seemed to have before he un- 

 derstood the problem, and how impossible it was, when once the 

 demonstration had flashed upon him, ever to comprehend those 

 indistinct difficulties again, or to call up the mental confusion 

 that admitted them." 



