custom him to make those efforts of , mind, and to hear 

 that tension of thought, the necessity for which is the 

 distinction between a problem of geometry, and one of 

 ordinary algebra. 



The considerations contained in this volume have, in 

 my opinion, a species of value which is not directly de- 

 rived from the use which may be made of them as an 

 aid to the solution of problems, whether pecuniary or 

 not. Those who prize the higher occupations of intel- 

 lect see with regret the tendency of our present social 

 system, both in England and America, with regard 

 to opinion upon the end and use of knowledge, and the 

 purpose of education. Of the thousands who, in each 

 year, take their station in the different parts of busy life, 

 by far the greater number have never known real mental 

 exertion ; and, in spite of the variety of subjects which 

 are crowding upon each other in the daily business of 

 our elementary schools, a low standard of utility is gain- 

 ing ground with the increase of the quantity of instruc- 

 tion, which deteriorates its quality. All information be- 

 gins to be tested by its professional value; and the know- 

 ledge which is to open the mind of fourteen years old is 

 decided upon by its fitness to manure the money- tree. 



Such being the case, it is well when any subject can 

 be found which, while it bears at once upon questions 

 of business, admits, at the same time, the application of 

 strict reasoning ; and by its close relation to knowledge 

 of a more wide and liberal character, invites the student 

 to pursue from curiosity a path not very remote from 

 that which he entered from duty or necessity. Such a 

 subject is the theory of life annuities, which, while it 

 will attract many from its commercial utility, can hardly 

 fail to be the gate through which some will find their 



