LET

And if, again, the first, third, fifth, . term of each of these series be written in one line, and the se- cond, fourth, sixth, . in another, the same arch will be expre ed thus: t*+ —~fpm + —+ ue ty feta Yaa peat — fe -f . an +f ms + , DEQ iiten exe IMG:tbl024_1.webp:Table (PDF page 24) PR and expre their value in the form given in article 5. we shall have the circumference of a cire cle whose diameter is 3, 4aC t 39D 17.80 25.80 33.80" ad a 6B 24C 32D 21.80 oo 29.80 st, . 47,80 16B 2C 32D 11,86 °° To.80 27.80" 35.80" se 16B 24C 32D 23.80 31.80" 39.80" a operation by them is much facilitated, the division by 80 being exchanged for a division by 10, which is no more than removing the decimal point. These’ series, then, when the factors which are common to both numerators and denominators are expung- ed, will stand as follows (each of which still con« verging somewhat quicker than by the powers of 80), and we shall have the circumference of a cir cle whose diameter is 1, Td AOI sale i rs plate’ va EE.tO uve, Bsc *¢ By which series the’ arithmetical computation will be much more easy than by the original series.” Some curious series for the same purpose have been recently investigated by Mr. Wallace of the Royal Military College, for which we must refer to his ingenious paper on the subject, in the Edinburgh Transactions. 25