He was born in Wemyss Castle on 11 July 1858, the eldest son on James Hay Erskine Wemyss and Augusta Millicent Anne Mary Kennedy Erskine, youngest daughter of the Honourable John Kennedy Erskine of Dun in the County of Forfar. He was tutored at home by Revd. John Thomson; minister of St. Adrian's church in West Wemyss, until he entered Eton College in 1873. Randolph married twice. Firstly Lady Lillian Mary Paulet, daughter of John Paulet, 14th Marquess of Winchester and the Hon. Mary Montagu, on 18 July 1884. There were two children:
Mary Millicent Erskine-Wemyss, 15 May 1885, married Ernest Caswell Long on 30 April 1917
In January 1900 he embarked on the steam yacht "Vanadis" for a honeymoon cruise to Egypt and South Africa. The honeymoon, however, was interrupted by the outbreak of the Boer War. Wemyss donated the yacht to the war effort as a hospital ship and he was promoted to the rank of Captain and on 4 September 1900 travelled to Mafeking with Charles Cavendish, 3rd Baron Chesham. He returned from South Africa in July 1901.
Business
Following the early death of his father in March 1864, he inherited the Lairdship and the estates. Day to day management was carried out by his mother until he reached the age of twenty-one. The principal activity on the estate was coal extraction centred on West Wemyss, under the Wemyss Coal Company. A new wet dock was opened in 1872 at a cost of £10,000. Railway schemes were developed to assist the business, and construction of the Wemyss Private Railway from Thornton to Buckhaven began in 1879, and was completed in 1881 at a cost of £25,000. After his service in the Boer War, business continued in the coalfields on his estates, the docks at Methil and the creation of the Wemyss and District Tramways Company from Leven to Kirkcaldy. As a benevolent landlord, he provided improved housing for workers. He oversaw the developments at East and Coaltown of Wemyss, and a new village at Denbeath. He personally spent around £75,000, on housing in the parish.
Death
Following a death in November 1907 at the Lochhead and Victoria of a miner, Wemyss, assisted with the underground rescue operations, and developed symptoms from shock and exposure. He never recovered and died on 17 July 1908. He was buried at Wemyss in the Chapel Garden. In a speech in the House of Commons on 21 October 1909, James Falconer MP for Forfarshire said:-
“Mr. Wemyss had taken all the risks in developing his property at a cost of £1,000,000. He has provided employment for thousands of men, had provided them with travelling facilities and built dwelling houses which were a model to everyone. The rates paid in respect of the enterprise amounted to £8,000 to £9,000 a year. I know no instance which is so much to be commended from the point of view of anyone interested in the development of the country. It is a real romance of enterprise, which has not been equalled in my time in Scotland.”
