Applicable Mathematics in the 18th Century: An Example from the Textile Trade

摘要

One of the first mathematical societies in England was set up by the Huguenot silk weavers of Spitalfields in London. Towards the end of the 18th century their trade began to decline rapidly, due to competition from other parts of the textile trade, in particular the cotton trade. Originally cotton could only be spun into coarse yarn, which was unsuitable for fashionable clothes, but eventually it became possible to produce cotton yarn that was both fine and cheap in relation to silk. I shall discuss an application of mathematics that arose essen-tially because it was important to control accurately the fineness of the yarn. The fineness of cotton (and woollen) yarn was expressed in a way that appears clumsy to us nowadays, because it was based on centuries of trade practice, rather than scientific principles. This inevitably led to complicated calculations. One way of avoiding the difficulty was to use a specially-designed instrument, such as the bent-lever balance. The theory of this instrument was discussed by William Ludlam in 1765, using mechanics, trigonometry and cal-culus. His analysis is a good example of the 'Newtonian' style and, despite appearing strange to the modern reader, it was fit for the purpose of designing an efficient and accurate instrument.