His father, William Law, according to communications made by an agent of the family, was great-grandson of James Law, Archbishop of Glasgow from 1615 to 1632, and second son of James Law of Brunton in Fife, by Margaret, daughter of Sir John Preston of Prestonhall, Baronet. He followed the profession of a goldsmith in Edinburgh, a business, at that time, partaking more of the nature of a bankers than of that to which the name is now restricted, with such success as enabled him to purchase the lands of Lauriston and Randleston. This property, extending to upwards of 180 Scotish acres, stretching along the south shore of the Firth of Forth, in the parish of Cramond and county of Edinburgh, was acquired by him from Margaret Dalgliesh, only child and heiress of Robert Dalgliesh of Lauriston, relict of Lewis Craig of Riccartoun, with consent of Thomas Craig of Riccartoun, her eldest son, by disposition dated 14th June, 1683.