INTERPOLATION TABLES 

 OR 



MULTIPLICATION TABLES OF DECIMAL FRACTIONS. 



BY HENRY B. HEDRICK, PH. D. 



INTRODUCTION. 



These tables are of especial use in any and all problems involving the multi- 

 plication of decimal fractions of two or three digits where the product is required 

 to no more significant figures than are contained in the smaller factor. As set 

 forth later under the heading, Explanation of the Tables, their use may readily be 

 extended to decimal fractions of three and four digits. They are thus of value for 

 many computations in engineering, in military, naval, astronomical, and physical 

 sciences, or wherever the slide-rule, graphical methods, or three or four-place 

 logarithms are ordinarily employed. They are more accurate than the slide-rule 

 or graphical methods, and far more convenient to use than logarithms. 



For the multiplication of whole numbers of two or three figures such tables 

 as those of Crelle or of Cotsworth are well adapted, but where one of the factors 

 is a decimal fraction given only to a certain degree of accuracy or to a certain 

 number of decimal places and the product is desired to the same accuracy, the 

 present tables are more convenient. They give the desired product directly to 

 the nearest unit as far as needed, requiring no pointing off nor consequent ad- 

 justment of the last figure. They give only the first one of the consecutive numbers 

 from which the same product results, thus making their use easier and more rapid 

 not only for cases where one factor remains constant for a series of multiplications, 

 but also where both factors vary. On examining several well-used copies of Crelle's 

 tables, it was very apparent that they were used mostly for the first 100 pages; 

 in the present tables only 14 pages need be used to cover the same factors. 



The arrangement of placing one factor in the top horizontal line, the second 

 factor in a column immediately below, and the required product in the outside 

 columns has many advantages. It permits the eye to travel in one continuous 

 route, first in a column and then along a line to the desired product, instead of 

 having to travel first in one direction and then in another in order to find the result 

 at the intersection of a column and a line as is the case with other tables. The 

 grouping in blocks of five aids in obtaining the product, since the position in the 

 block indicates the unit figure, after a glance to the right or left has determined the 

 block and the figure in the second or tens place. 



These tables are constructed on the principle of multiplication by means 

 of division by the reciprocal. Since one of the factors in interpolation is a frac- 

 tion, or at least may be so considered, its reciprocal is a whole number or a whole 

 number plus a fraction and, in consequence, the same quotient results from several 

 successive values of the dividend. The smaller the fraction, the larger will be the 

 reciprocal or divisor and the greater the change in the dividend for a unit change 

 in the quotient. Advantage is taken of this fact to make the tables more compact 

 and convenient by giving only the smallest value of the dividend from which will arise 

 the desired quotient, or, in other words, by giving only the smallest of the several 

 values of the second factor that will produce the required product. The products 

 are given in the tables to the nearest unit. Where the discarded fraction is exactly 

 a half, and two numbers are therefore equally near, one a half-unit too large and 

 the other a half-unit too small, the even number is always given in the tables. 



Most of the necessary computations in the preparation of the tables were per- 

 formed by Mr. Benjamin M. Hedrick, Mr. Joseph F. Jackson, and Mr. Edmund 

 S. Davenport. 



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