xxx vi SQUARB8 AM> 



A method easily understood by inspection is this : Add to the neg- 

 ative characteristic of the logarithm a number equal to //*/ where r 

 is the index of the desired root and m is a whole number largr 

 enough to make mr larger than or equal to the characteristic, in 

 other words, large enough to extinguish the negative sign of the 

 characteristic. Write this number with a negative sign after the 

 logarithm. Then divide the whole by the index r. The quotient 

 will be the logarithm of the desired root. Usually m = i, i.e. 

 mr = r. 



Example. Desired v/o.oGSjr 

 log 0.06 831 = 2.8345, adding and subtracting 3 gives 1.8345 3 



dividing by 3 gives 0.6115 i = 1.6115 

 .*. >Xo.o6 831 = number corresponding = 4.o88'io~ 1 or 0.4088. 



SQUARES AND SQUARE ROOTS. 



It is common to give separate tables of squares and of square 

 roots by which, respectively, the square or square root of any num- 

 ber may be taken out. Inspection, however, shows that the four- 

 place table of square roots must occupy four pages, the first two 

 containing the numbers from i.o to 10., the second two from 10. to 

 100. ; the corresponding roots ranging from i. to 10. ; while a table of 

 squares would occupy but two pages, containing numbers from i.o to 

 10., the squares ranging from i. to 100. Hence the tabular differ- 

 ences in the table of square roots will be much smaller than in the 

 table of squares. For this reason the table of squares may advan- 

 tageously be dispensed with, and squares be taken out when desired 

 from the table of square roots, as the numbers corresponding (anti- 

 -logarithms) are taken out of a table of logarithms. The smallness 

 of the differences makes interpolation easier and more rapid than in 

 a table of squares, and this more than offsets the slight disadvan- 

 tage of the reverse process of interpolation. The tables at page 30 

 give square roots to four places. As in the logarithm tables, the 

 numbers in the body of the table are printed in stronger type wher- 

 ever the second figure changes, in order to assist the eye in the 

 reverse use of the table. 



In the table of square roots the insertion of the extra section giving i.oo to 

 i.io to four places direct to avoid interpolation is not called for as in logarithms 

 because the interpolation is very easy, and because the squares of terms of the 

 form (i -f- a) are not frequently required. 



