[168] 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. [169] _Works_, p. 59. [170] _Ibid._ p. 61. [171] _Works_, p. 63. [172] Alexander Ross (1590-1654) was a believer in centaurs and griffins, in nations of giants and pygmies, and also, of course, in witches. In short, a pretty accurate statement of his intellectual creed might be constructed by turning into the articles of a confession of faith the list of "Vulgar Errors" controverted by Sir Thomas Browne. It is interesting to know that he was probably the last person in Scotland who heard the voice of the water-kelpie. "One day," he says, "travelling before day with some company near the river Don in Aberdeen, we heard a great noise and voices calling to us. I was going to answer, but was forbid by my company, who told me they were spirits, who never are heard there but before the death of somebody; which fell out too true, for the next day a gallant gentleman was drowned, with his horse offering to swim over" (Quoted in _Lives of Eminent Men of Aberdeen_, by J. Bruce). [173] They begin-- "Si cupis ætherios tutò peragrare meatus, Et sulcare audes si vada salsa maris," etc. A friend, who knows "Himself to sing and build the lofty rhyme," has given me the following metrical translation of Ross's verses:--