are left behind for each of the 360 first days; therefore, this additional process divides the whole annual amount equally among the 365 days. Now, 5 parts out of 365 is one out of 73, or the 73d part of the first result must be subtracted from it to produce the true result. Unless the daily sum be very large, the 72d part will do equally well, which, as 72 farthings are 18 pence, is equivalent to subtracting at the rate of one farthing for 18 d. , or ½ d. for 3 s. , or 10 d. for £3. The rule, then, is as follows: To find how much per day will produce a given sum per year, turn the shillings, &c. in the given sum into decimals of a pound (221); subtract one-third; consider the result as pence; and diminish it by one farthing for every eighteen pence, or ten pence for every £3. For example, how much per day will give £224. 14. 0¾ per year? This is 224·703, and its third is 74·901, which subtracted from 224·703, gives 149·802, which, if they be pence, amounts to 12 s. 5·802 d. , in which 1 s. 6 d. is contained 8 times. Subtract 8 farthings, or 2 d. , and we have 12 s. 3·802 d. , which differs from the truth only about ¹/₂₀ of a farthing. In the same way, £100 per year is 5 s. 5¾ d. per day.
- The following connexion between the measures of length and the measures of surface is the foundation of the application of arithmetic to geometry.
Suppose an oblong figure, a, b, c, d, as here drawn (which is called a rectangle in geometry), with the side a b 6 inches, and the side a c 4 inches. Divide a b and c d (which are equal) each into 6 inches by the points a, b, c, l, m , &c.; and a c and b d (which are also equal) into 4 inches by the points f, g, h, x, y , and z . Join a and l, b and m , &c., and f and x , &c. Then, the figure a b c d is divided into a number of squares; for a square is a rectangle whose sides are