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XX. — Account of the New Table of Logarithms to 200 000. 

 By Edwakd Sang, Esq. 



(Read 20th February 1871.) 



The essential character of all tabular aids to computation is, that the results 

 of many operations are recorded in some systematic way for easy reference, 

 and that thereby the computer is spared the toil of obtaining these results for 

 himself. 



In many cases this constitutes almost the whole advantage of the table. 

 Thus when, instead of extracting the cube root of some number, we take it 

 from a printed book, we are merely using another's labour. The gain to the 

 calculating community is, that the oft-repeated extraction of the same root is 

 avoided. We also gain by the facility of systematic calculation ; the labour of 

 computing a series of successive results being in general only a small fraction 

 of that which would have attended the same work performed in a desultory 

 manner. 



The possession of a table of the corresponding values of two connected 

 magnitudes enables us to perform the inverse operation, that of finding the 

 argument from its function, an operation generally much more difficult than 

 that of finding the function from the argument. Tables special to his own 

 pursuits are thus indispensible to every investigator. 



But tables of logarithms possess advantages of a peculiar nature. Except 

 in a few rare speculations, no one desires to know a logarithm for its own sake ; 

 nor, in general, would that knowledge be of any use to us. The ability to 

 compute the logarithm belonging to a number, or the number belonging to a 

 logarithm would, of itself, be almost barren of useful result. If, in order to 

 apply the neperian process to ordinary multiplication, we had to compute the 

 logarithm of each factor, add these together, and thence compute the corre- 

 sponding number, we should have expended a hundred times the labour of the 

 ordinary process. Viewed abstractly, Napier's process is ridiculously cir- 

 cuitous ; its whole advantage is and was intended to be derived from tabula- 

 tion ; so much so, that the mechanical operations of paper-making and printing 

 enter among its constituent parts almost as essentially as the arithmetical 

 computation itself. Napier's original concej^tion was of a table to subserve 

 certain ends, and his efforts were directed not to the discovery of a single 

 logarithm, but to the construction of a logarithmic system. Here the table is 

 everything. 



vol. xxvi. part in. 6 u 



