Like her sisters Frances was very musical,and like her father was a linguist.Horace Walpole who had met her some three months after her marriage said “she was infiniety good humoured and good company,and sang a thousand french songs mighty prettily”
She had sung to Fredrick the Great in Greek ,French,Scotch.”she is very merry and easy”
Frances had loved her husband to a dgree ,that she ordered that,she should be buried as near him as possible,wearing her wedding ring and with her husbands letters to her in her coffin.
The Marquess married Lady Elizabeth (or Frances) Carteret, daughter of John Carteret, 2nd Earl Granville in 1748, and had by her four daughters and two sons.

Secretay Of State

John Hay, 4th Marquess of Tweeddale PC (1695 – 9 December 1762) was a Scottish nobleman.
Tweeddale was an able and accomplished statesman, and possessed considerable knowledge of law. He was appointed an Extraordinary Lord of Session in 1721, the last person to hold this office. He was one of the Scottish representative peers from 1722 to 1734 and from 1742 to 1762. On the downfall of Walpole in February 1742, Pulteney, to whom had been entrusted the arrangement of places in the new Government, insisted that the office of Secretary of State for Scotland, which had been in abeyance since 1739, should be revived, and the Marquess of Tweeddale was appointed, and Principal Keeper of the Signet and a Privy Counsellor. Charles Erskine, Lord Tinwald, who at this juncture resigned the office of Lord Advocate, wrote to a brother lawyer—Robert Craigie of Glendoick on 2 March 1742, ‘You have been mentioned to the King by the Marquis of Tweeddale as my successor. You are happy in having to do with a patron who is a man of truth and honour.’. .
The period of four years during which his Tweeddale held the office of Secretary of State was a time of great trouble and anxiety. The English members of the Government were not only grossly ignorant, as usual, of the state of feeling in Scotland, but they were by no means willing to receive accurate information on the subject. They rejected as utterly incredible the idea that a Jacobite insurrection was at hand, and thought it quite unnecessary to make any preparations to resist and suppress it. Tweeddale, who was in London at that time, shared to some extent in their feeling of incredulity, and even after he was aware that the Highlanders had left Perth in their march to the south, he wrote to the Lord Advocate, ‘I flatter myself they have been able to make no great progress.’ On the very day on which this letter was written, Prince Charles entered the Palace of Holyroodhouse.
In February 1746, when the rebellion was still raging, a ministerial crisis took place. On the refusal of the King to admit Pitt to the Government, Henry Pelham, the Prime Minister, along with those members of the administration who supported him, resigned office. Earl Granville and Tweeddale attempted, unsuccessfully, to form a Ministry. On their failure Pelham resumed office; Granville and Tweeddale were left out of the reconstructed Government, and the office of Secretary of State for Scotland was a second time abolished. Tweeddale resigned at this time his office of Keeper of the Signet.
He was Governor of the Bank of Scotland from 1742 and Lord Justice General in 1761 until his death in London in 1762.
The Marquess married Lady Elizabeth (or Frances) Carteret, daughter of John Carteret, 2nd Earl Granville in 1748, and had by her four daughters and two sons. The eldest son died in infancy; the younger, George, became fifth Marquess, and died in 1770, aged thirteen. The title then devolved on his uncle, George Hay.

Marriage