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Greville plants, and made before he was nineteen between one and two hundred careful drawings of British species. Being intended for the medical profession, he went through a four years' curriculum in London and Edinburgh; but, circumstances having rendered him independent, he did not proceed to a degree. In 1816 he married a daughter of Sir John Eden, bart., of Windlestone, Durham, and settled in Edinburgh in order to study anatomy under Dr. Barclay. In 1819 he joined the Wernerian Society, before which and the Botanical Society of Edinburgh he read many papers, especially on Algae and other Cryptogamia. At this period, too, he commenced those excursions with W. J. Hooker, Robert Graham, and other botanists, in which he exhibited both critical skill as an observer and great endurance as a pedestrian.

In 1823 Greville began the publication of his 'Scottish Cryptogamic Flora' in monthly parts, with plates drawn and coloured by himself, which was dedicated to Hooker, and was 'intended to serve as a continuation of "English Botany,"' especially with reference to the fungi. It extended to six yearly volumes, containing 360 octavo plates. While this work was still in progress he published in 1824 the `Flora Edinensis,' dealing with both the flowering and the flowerless plants of the district. This work, a single 8vo volume, dedicated to Robert Graham, is arranged on the Linnæan system, and contains four plates by the author illustrating details of cryptogamic structures. In 1821 he was elected fellow of the Royal Society of Edinburgh, and in 1824 LL.D. of Glasgow University. At this time he was in the habit of giving popular lectures on botany in Edinburgh, and he formed extensive collections, not only of plants, but also of insects, marine crustacea, and land and fresh-water mollusks. Of the latter he got together the finest Scottish collection ever made. In 1829 he began the publication, in conjunction with Hooker, of 'Icones Filicum,' two folio volumes, completed in 1831, containing 240 plates drawn and coloured by himself, the ferns being mainly those sent from India by Wallich (to whom the work is dedicated) and by Wight, and from the West Indies by Lansdowne Guilding, and others. Again with a large serial work in progress, he produced a valuable independent work, his `Algæ Britannicæ,' published at Edinburgh in 1830, with nineteen coloured plates executed by himself. He commenced a work on the 'Plant Scenery of the World,' in conjunction with J. H. Balfour, and drew some forty or fifty plates for it; but abandoned the scheme for want of competent lithographers. Though he thus accomplished a large amount of descriptive work, he was not merely a herbarium botanist. In 1834 he made a tour through Sutherlandshire with Selby and Jardine; and in 1837, with Brand and Balfour, he collected no less than fifteen thousand specimens in the highlands for the Botanical Society of Edinburgh. As late as 1862 he was awarded the Neill medal of the Royal Society of Edinburgh, more especially for his papers upon `Diatoms.' His large collections of this group of Algae were purchased for the British Museum; his insects for the university of Edinburgh; his flowering plants by Professor J.H. Balfour (they are now at the university of Glasgow); and his other Cryptogamia for the Edinburgh Botanic Garden. The last collection, with that of Professor Balfour, amounting to fifty thousand species, represented by about ten times as many specimens, formed the nucleus of the Edinburgh university herbarium. An outdoor naturalist, fond in his younger days of his rod and his gun, he was a man of many-sided culture, agreeable in society, musical, with an artist's eye, and considerable literary taste. He took an active interest in various philanthropic and social matters. In 1830 he issued a pamphlet entitled 'The Drama brought to the Test of Scripture and found wanting,' and between 1832 and 1834 he edited, in conjunction with Dr. Richard Huie, the three volumes of 'The Amethyst, or Christian's Annual,' to which he contributed several religious poems. In 1832 he wrote the botanical portion of the three volumes on British India in the 'Edinburgh Cabinet Library,'and in 1839 that in the three volumes on British North America.

Greville was an active opponent of slavery, and an advocate of temperance. In 1833 he served as an anti-slavery delegate from Edinburgh to the colonial office, and then as chairman of the committee, and in 1840 as vice-president, of the Anti-Slavery Convention. In 1834 he published 'Facts illustrative of the Drunkenness of Scotland, with Observations on the Responsibility of the Clergy, Magistrates, and other Influential Bodies.' He was for four years secretary of the Sabbath Alliance, and in 1850 addressed a letter to the Marquis of Clanricarde, postmaster-general, on the desecration of the Lord's day in the post office, with an appendix on its 'legalised desecration' by railway companies and dealers in intoxicating liquors. Himself an episcopalian, he compiled in 1838, with the Rev. T. K. Drummond, 'The Church of England Hymn-book.' He was also connected with various missionary societies, ragged schools, and refuges, and in 1856 was elected M.P. for Edinburgh.