14 ESSAY ON PROBABILITIES. 



The property of this table is, that if we wish to 

 multiply together any two numbers called amounts, we 

 have only to add together the number of years they 

 belong to, and look opposite the sum in the table of 

 years. Thus, 11 and 12, added together, give 23; 

 2048 and 4096, multiplied together, give 8,388,608. 

 The reason is as follows: if 11. in 11 years yield 2048/., 

 and if this 2048/. be put out for 12 years more, then, 

 since II. in 12 years yields 4096/., 2048 times as much 

 will yield 2048X4096/. ; or the amount in 11 + 12 

 years is the product of the amounts in 11 and 12 years. 

 The only reason why the preceding table is not in the 

 common sense of the words a table of logarithms, is, that 

 its construction leaves out most of the numbers. We 

 can deal with 2048 and 4096, but there is nothing 

 between them. The remedy is, to construct a table of 

 compound interest, at such an excessively small interest, 

 that a year shall never add so much as a pound through- 

 out. Certain considerations, by which the table may be 

 shortened, but with which we have here nothing to do, 

 make it convenient to suppose such a rate of interest, that 

 11. shall increase to 101. in not less than 100,000 years, 

 at compound interest. Or we may suppose interest pay- 

 able 1 00,000 times a year, and say, let the whole yearly 

 interest be 1000 per cent, per annum. Taking the first 

 supposition, we have a part of a table of logarithms as 

 follows : 



This is the light in which a common reader may view 

 a table of logarithms. Let 1 increase to 10 at compound 

 interest in 100,000 equal moments, then 1 will become 

 5234 in 371,883 such moments; and so on. We can 

 thus manage to put down every number, within certain 



