Note 168 — Chapter IV

The subject of logarithms is perhaps one of those things which the ordinary render might safely be presumed to know something about. In these days of higher education for women, it would be an act of impertinence to provide information on this point for that class of our readers. The following explanations are, therefore, intended for those members of the inferior sex whose education on the mathematical side has been neglected. The idea of logarithms arose in the mind of Napier from the wish to simplify the processes of multiplication and division, by making addition and subtraction take their place. To effect this, connect together a series of numbers increasing by arithmetical progression with a series increasing by multiplication or by mathematical progression.

Thus: 0. 1. 5. 32. 10. 1024.

1. 2. 6. 64. 11. 2048.

2. 4. 7. 128. 12. 4096.

3. 8. 8. 256. 13. 8192.

4. 16. 9. 512. 14. 16384.

To multiply, say, 64 by 256, that is to find the products of the 6th and 8th powers of 2, we must take the (6+8)th or 14th power, which from the table is 16384. To divide 8192 by 256, or the 13th power of 2 by the 8th, we must take the (13-8)th or 5th power, which from the table is 32. By means of this principle calculations can by made by persons whose business it is to do so, and stored up apart for use. The vast saving to mental labour by this simple and beautiful adjustment of numbers may be estimated by a glance at any collection of tables of logarithms. In a science like astronomy, progress would be terribly impeded if calculations had to be conducted by the ordinary methods.