40 



The accompanying are two very compendious Logarithmic Tables, in which 

 I have endeavoured to combine the minimum of size, with the maximum of 

 utility. — By Capt. Shortrede. 



The mode of using these Tables is so similar to that of the Tables in 

 common use, that it is almost needless to give any particular directions 

 on the subject. 



It is to be understood that every number in the body of each Table 

 is supposed to consist of 5 figures ; the single figure on the left in 

 columns and 5 being common to the succeeding columns on the 

 same and following lines. These leading figures increase progressively 

 by unity, and nine changes occur in each Table. To mark this change, 

 when it occurs any where not at the beginning of a line, the numbers 

 subsequent to the change are put a little lower than their usual place, 

 in order to indicate that their first figure is to be supplied from that on 

 the lower line, besides which, the first following zero is printed black to 

 distinguish it as a change figure. 



The Table of common Logarithms (neglecting at present those be- 

 yond 1000) has in its first column marked Nat. Num. the natural 

 numbers from 10 to 100, and immediately adjoining in the column 

 headed are the corresponding Logarithms, (for numbers between 1 

 and 10, the Logarithms are opposite the tenfold number) : for numbers 

 for three figures the two first being found in the first column, the 3rd is 

 to be found among those at the top, and in the body of the Table is 

 seen the corresponding Logarithm. For numbers of more than 3 figures 

 the Logarithm is found by adding to that in the Table the proportional 

 part for the 4th and subsequent figures, (allowing, if need be, for the dif- 

 ference between the proportional part in that and the next line according 

 to the distance of the 3rd and following figures from the middle of 

 the line.) 



Example. 



Required the Log. of 33952. 

 for 339 the Table gives, . . 53020 

 for 5 Propl. part gives, .... 65 

 for 2 Propl. part gives, 2*6 



Log. Required, 5 3087 '6 



The 3d and subsequent figures 

 of 33952 being about midway 

 between 3345 and 3445, the pro- 

 portional parts should be the half 

 of those given in lines 33 and 34. 

 Instead of 65, the proportional 



