EXPLANATION AND USE OF THE TABLES, 



TABLE I. 



1. To find the log. of any given number. 



If the given number be under 100, its log. is found in tlip first page of 

 the Table, immediately opposite to it. Thus log. 66 is 1.819544. 



If the No. consist of three figures, find the given number in the column 

 under N, and opposite to it in the next column, marked at the top, is 

 the decimal part of the logarithm required, before which put an index, 

 which is always less by unity than the number of integral figures in the 

 natural number. Thus log. 448 is 2.651 2"8. If the number should con- 

 tsist wholly of decimals, the index of the log. is then negative, and it is 

 indicated by the place occupied by the first figure in the decimal. Thus 

 the index of the Jog. of .04 is 2 ; of .006 is - 3. But to avoid the con. 

 fusion that might arise by the addition and subtraction of negative in- 

 dices, it is customary to take the arithmetical complement or the nega- 

 tive indices, and to consider these complements as positive; thus 8 is put 

 as the index of .04 ; 7 as the index of .006. 



If the No. consist of four figures, the three first are to be found as be- 

 fore in the side column under N ; and under the 4th at the top will be 

 found the logarithm required, to which prefix the index as befoie. Thus 

 log. 7-218 is 3.858417. If the No. be odd, and /. not contained in the 

 Table, take the difference of the logs, of the Nos. next greater and less 

 than the given one; and add % this difference to the less log. Ihus if 

 log. 7217 were required, we have by Table 



Log. 7-218 3.858417 



Log. 7216 3.858297 



120 



the y 2 of which, or CO, added to 3.8582-7 gives 3.858357, the log required. 

 If the No. consist of 5 figures or more, find the difference between the 

 logs, answering to the first four figures of the given No., and the next 

 immediately following ; multiply this difference by the remaining figures 

 in the given number, strike oft' as many figures from the right band as 

 there are in the multiplier ; and the remainder added to the log., answer- 

 ing to, the first 4 figures, will be the log. required nearly. Thus if log. 

 100176 were required, we have by last case, 



Log. 1001 000434 



1002 OOOSfiS 



434 



.". 434 X 7"6 is 32984. From this cut off two figures, and it becomes 329.84 

 or 3SO nearly. Whence to 000434 add 330 and supply the index, and we 

 have the required leg. = 5.000764. 



2. To find the natural No. corresponding to any given logarithm. 

 Look in the different columns for the decimal part of the given log. ; 

 but if you cannot find it exactly, take the next less tabular log., and in a 

 line with the log. found in the col. on the left marked N, you have three 

 figures of the number sought, and at the top of the column in which the 

 log. is, you have one figure more, Avhich annex to the other three. As, 

 however, the Table contains only the logs, of the even Nos., it should be 

 observed that if the given log. falls between any two of the tabular logs, 

 and differs considerably from both j in that case we must find the log. of 

 the intermediate odd No. as directed above, and compare it with the given 

 one ; by which means the 4th figure of the No. sought (whether it be 

 even or odd) may be correctly ascertained. The number of integers is 

 always one more than the number expressed by the index. Thus the 



