Eliza Taylor Spottiswoode was the eldest daughter of William Urquhart Arbuthnot, a member of the Council for India. In 1861 she married William Spottiswoode (1825-1883), mathematician, physicist and president of the Royal Society. Their son William Spottiswoode FCS (1864-1905) was a partner and later director of the publishers Eyre and Spottiswoode.
The Spottiswoodes appear to have been keen collectors and hosted regular salons at their London house in Grosvenor Square. She may have known JW in the mid-seventies, when her name appears in an address book (#12714).
UK census 1881, from http://www.familysearch.org (accessed 2004); Dictionary of National Biography, on-line edition (accessed 12 August 2004); Kelly's Directory of Chelsea, Pimlico and Belgravia "Buff Book" 1887, London 1887.