LOGARITHMS. XXXI 



the small saving in time effected by this means is an equivalent 

 t<> tlit- slight additional mental rfi'ort incident to the employment in 

 alternation ,!' tables different ly arranged. may be questioned. Wlirrr 

 many antilogs are to be taken out in succession, tin- Lrain is, however, 



i>le. 



Example. To find by the table of Autilogarithms tin* antilog 2.4857. 



Taking the mantissa first, we find on line .48, column 5, the next small. -r 

 number 3.055 with a tabular difference of 7. lit n. .-. antilog .485 = 3.055. Hut 

 - will be 0.7 of the way from that of .485 to .486. The amount to be 

 added then for interpolation is 0.7 x 7 = 5. 



antilog .4857 = 3.055 + 0.005 = 3- o6o 

 2.4857 = 3.060- lo 2 = 306.0. 



rpolation tables are provided whose method of use is suftirirntly 

 obvious. 



Cologarithms = Logarithms of Reciprocals. The colo^ of any 

 number // is the logarithm of the reciprocal of the number. 



It is therefore log i logp = o log/). 



In substitution in a formula such as x= , which is the product of 



c*a*" 



st-vrral numbers (one or more) divided by the product of several others 



tin- iliivrt jn-'MM-ss w.nild l>r t take tin- sum of tho logarithms of the 

 in tin- nunuTat'T. and to subtract from this the- Mini of the l>p< "f the 

 factors in t! 



Example. i = 1.2543 logc = 3.8642 



log b = 3.8766 5-jui 



loge = 2.1345 



Numcrat c.r sum =1.1309 R >minat"i sum = 1.2108 



.in.itnr sum = 1.2108 



Difference = 3.9201 



nding = 8.320-iQ- 8 , or 0.008320. 



If process may be simplified by rmpl.yiii.i: the oolog, It ilu-n becomes 



loga = 1.2543 



log 6 = 3.8766 



colog = 4.1358 



.^^ = 4.7879 



x = number corresponding = 8. 320-10-* 



> process is thus reduced to the simple mi - <f numl)era. 



Til-- it M| the usual log tabl< 



mental!] 



