62 REMARKS ON APPENDIX.
ber of quotients by the first, that is the number of places in the product less one, will be equal to the Logarithm of the second.
| Number of Places |
||
| 1 | 0 | |
| 1 | 2 | 1 |
| 1 | 4 | 2 |
| 2 | 16 | 4 |
| 3 | 256 | 8 |
| 4 | 1024 | 10 |
| 7 | 1048576 | 20 |
| 13 | 1099511627776 | 40 |
| 25 | 1208925819614 | 80 |
| 31 | 1267650600228 | 100 |
| 61 | 16069379676 | 200 |
| 121 | 25822496318 | 400 |
| 241 | 66680131608 | 800 |
| 302 | 107150835165 | 1000 |
| 603 | 114813014767 | 2000 |
| 1205 | 131820283599 | 4000 |
| 2409 | 17316587168 | 8000 |
| 3011 | 19950583591 | 10000 |
Here we see that if we assume the Logarithm of 10 to be 10, the number of places in the tenth power is 4, wherefore the logarithm of 2 will be 3 and something over. The number of places in the hundredth power is 31; in the thousandth, 302; in the ten thousandth, 3011; and generally the more products we take the more nearly do we approach the true Logarithm sought for. For when the products are few, the fraction adhering to
the
