16 ESSAY ON PROBABILITIES. 



second steps, and the sum is nearly the logarithm of the 

 product of all numbers up to the given number inclusive. 

 For still greater exactness, add to the final result its ali- 

 quot part, whose divisor is 12 times the given number. 



EXAMPLE. What is [30] or 1 x 2 X 3 X x 29 



X30? 



log. 30 1-4771213 

 4342945 



Subtract 1-0428268 2)2-2753012 Add. 



30 



. 1 '1376506 Second step. 



Multiply 31-284804 First step. 



1 -137651 Result of second step. 



32-422455 log. of result. 



The result has, therefore, 33 places of figures, of 

 which the first six are (nearly) 264,518 ; or, if this be 

 increased by its 360th (12 times 30) part, or about 

 735, the result is 265,253, followed by 27 ciphers; or 



the approximate result is 



265253000000000000000000000000000 

 The true result is 



2652528598121 91058636308480000000 



and the error is not so much of the whole, as one part 

 out of 500,000. 



In this way, we are able to do with more than 

 sufficient nearness, and in a few minutes, what it 

 would take days to arrive at by the common method, 

 and with much greater risk of error. 



If we wish to find the product of all the numbers, 

 say from 31 to 100, both inclusive, we find [100] and 

 30] approximately, and divide the first by the second. 

 We shall represent this by [31,100] : thus, 



[7,15] stands for 7x8x9x10x11x12x13x14x15 



But, though we can thus simply put the logarithmic 

 computer in possession of a great acquisition of power 

 we can get through much the greater part of our task 

 without such a process, by means of a table of which 



