MATHEMATICS 25 



ended steel columns. The area of the cross-section A 

 = .7854 (df rfa 2 ), d\ and dz being the outside and inside diam- 



eters, respectively; 7 = 20X12 = 240 in.; and G* = ^~?*. 



Substituting these values in the formula, 



SA 150.000 X .7854(142-112) 

 * 2402 



__ 

 25,000 



16 



150.000X58.905 ^8.835.750 



1 + .1163 " 1.1163 - 7 - 915 - 2111b - 



INVOLUTION AND EVOLUTION 



By means of the table on pages 3148 the square, cube, 

 square root, cube root, and reciprocal of any number may be 

 obtained correct always to five significant figures, and in the 

 majority of cases correct to six significant figures. 



In any number, the figures beginning with the first digit 

 (a cipher is not a digit) at the left and ending with the last 

 digit at the right, are called the significant figures of the 

 number. Thus, the number 405,800 has the four significant 

 figures, 4, 0, 5, and 8; and the number .000090067 has the 

 five significant figures 9, 0, 0, 6, and 7. 



The part of the number consisting of its significant figures 

 is called the significant part of the number. Thus, in the 

 number 28,070, the significant part is 2807; in the number 

 .00812, the significant part is 812; and in the number 170.3, 

 the significant part is 1703. 



In speaking of the significant figures or of the significant 

 part of a number, the figures are considered in their proper 

 order, from the first digit at the left to the last digit at the 

 right, but no attention is paid to the position of the decimal 

 point. Hence, all numbers that differ only in the position of 

 the decimal point have the same significant part. For example, 

 .002103, 21.03, 21,030, and 210,300 have the same significant 

 figures 2, 1, 0, and 3, and the same significant part 2103. 



The integral part of a number is the part to the left of the 

 decimal point. 



