_Fourth._ From the prepared dividend, 11298, we cut off the last figure 8, and multiply this by the current multiplier, 22. The product, 176, is added to the truncated dividend, 1129, and gives 1305 for the first modified divisor. The whole operation is shown thus: 1 8 8 3 6 ------- 1 1 2 9|8 1 7 6 - ----- 1 3 0|5 1 1 0 - ----- 2|4 0 8 8 --- --- |9 0 ----- 1 9|8 1 7 6 - ----- 1 9|5 1 1 0 - ----- 1 2|9 1 9 8 - ----- 2|1 0 2 2 --- 2 4 We stop at this point because 24 was a previous modified dividend, written under the form 240 above. Our two infinite numbers (which need not in practice be written down) are, with their difference: . . 10,958,904,058 . . 10,958,904,109.5890410958904 ---------------------------- . . 51.5890410958904 . . Hence the quotient sought is 5.158904109. _Example 2._ Find the reciprocal of 333667. The whole work is here given: 3 3 3 6 6|7 |7 2 3 3 5 6 7 - 1 6 3 4 9 6|9 2 1 0 2 1 0 3 - ------------- 2 2 6 5 5 9|9 2 1 0 2 1 0 3 - ------------- 2 3 2 8 6 6|2 4 6 7 1 3 4 - ----------- 7 0 0 0 0 0 . . _Answer_, 0.000002997. _Example 3._ Find the reciprocal of 41. _Solution._-- 4|1 |9 ----- ----- 3 7|9 3 3|3 - 1 1 1 - ----- 1 4|4 1 4 8 - ----- 1 6|2 7 4 - --- 9 0 . . _Answer_, 0.02439. C.S. PEIRCE. * * * * * [SCIENCE.] EXPERIMENTS IN BINARY ARITHMETIC.