IV INTERPOLATION TABLES. 



EXPLANATION OF THE TABLES. 



Pages 1, 2, and 3 contain the products divided by 100 of each number from 

 1 to 99 by 1 to 100. Pages 4 to 77 contain the products divided by 1000 of each 

 number from 1 to 500 by 1 to 1000. Pages 78 to 139 contain the products divided by 

 1000 of each number from 500 to 999 by all numbers up to 1000, but beginning each 

 table with a value of the second factor not greater than that of the first factor. 



The first factor is given on the top horizontal line in clarendon type and 

 is preceded by a decimal point. The number of digits after the decimal point 

 indicate the power of ten by which the products are divided. 



The second factor is given below in the body of the table in ordinary type. 

 Only the first number of the series which produce the same product is given. 



The required product, to the nearest unit, is given in the outside vertical 

 column headed P, in bold-faced type. When the product is greater than 100, 

 its third digit (the number of hundreds) is given, also in bold-faced type, in the 

 next to the top line, opposite the letter P. 



To obtain the product we have the following: 



RULE. Find one factor among the numbers in the top line preceded by a decimal 

 point. Either factor may be taken if both factors are less than 500, but if one 

 or both are greater than 500, then find the smaller factor in the top line. In the 

 column or columns below find the other factor or the number nearest to and smaller 

 than the other factor; then on the same horizontal line with the number last found, 

 either to the right or to the left, in the marginal columns headed P, is the required pro- 

 duct, or the last two digits of the product when it is greater than a hundred; the number 

 of hundreds in the product is found, opposite the letter P, in the next to the top line of the 

 column in which is the second factor, or the number next smaller than the second factor. 



Examples. 1. Required 16/100 of 29. Find .16 in the top line (section 1, 

 page 1), under .16 find 29, then to the right or left on the same horizontal line as 

 29 in the marginal column is 5, the answer. 



Or find .29 in the top line (section 2, page 1), under .29 find 16, then in the 

 marginal columns on the horizontal line with 16 is 5, the answer. 



2. Required 2.3 X 8.9 to the nearest unit. Find .23 in the top line, under 

 .23 find 89 or the nearest number less than 89, in this case 85, then in the marginal 

 columns on line with 85 is 20, the required product. 



3. Required 0.302 X 441. Find .302 on top line (page 33). In the column 

 below the 100 we find 439, the nearest number to 441 and smaller; and opposite 

 439 in the marginal columns is 33, thus 0.302 X 441 = 133. 



Or find .441 on top line (page 63). In the columns below is 301 the nearest 

 number smaller than 302 and opposite 301 is 33; thus .302 X 441 = 133. 



The first three pages are intended for use where the factors are of two digits 

 or less, but they may often be employed advantageously when one factor contains 

 three digits, the other two digits and the product divided by a hundred is desired, by 

 neglecting, at first, the third (or hundreds) digit and adding the partial product thus 

 obtained from the tables to the product of the third digit by the factor of two digits. 

 This is especially convenient when the third digit is unity, in which case the pro- 

 duct from the tables is added to the two-digit factor to obtain the required product. 



All the tables on the first page are given later extended ten times under the 

 same heading but with a cipher attached. Thus on page 1 is given the table for 26 

 hundredths of all numbers from 1 to 100, while on page 26 there is given the table 

 for 260 thousandths (same as 26 hundredths) of all numbers from 1 to 1000. 



Pages 4 to the end are intended for use where the factors are of three digits 

 or less, but they may often be employed advantageously when one factor contains 

 four digits by neglecting, at first, the fourth or thousands digit and adding 

 the partial product thus obtained from the tables to the product of the fourth 

 digit by the factor of three digits. For example, let it be required to find how many 

 feet are in 268 thousandths of a mile. 



.268 X 5280 = 5 X 268 + 280 X .268 = 1340 + 75 = 1415. 



