Murray was born at Newry, the eldest son of John Tulloch, a captain in the British army, and his wife, daughter of Thomas Gregorie of Perth, Scotland.

He took home specimens of depreciated coin, had them assayed at the Royal Mint, and got the matter taken up by the secretary at war, John Cam Hobhouse, Baron Broughton, who called on the company for an explanation.

The matter was dropped for a time, but about 1836 it was revived by Tulloch, and Earl Grey, after investigation, compelled the company to make reparation by supplying the army yearly with coffee, tea, sugar, and rice, to the value of £70,000, the amount of the annual deficit.

[2] On his return to England Tulloch entered the senior department of the Royal Military College Sandhurst, and obtained a first-class certificate.

They attracted the attention of Earl Grey, then secretary of war, and he appointed Tulloch, with Henry Marshall and George Balfour, to investigate the subject fully and to report on it to parliament.

Four volumes of statistical reports were the results of their inquiry, which extended till 1840, and the data afforded by the investigation have formed the basis of many subsequent ameliorations of the soldier's condition.

The commissioners did not lay the entire blame on the failure of the home authorities to furnish adequate supplies, but, on the contrary, reprehended the carelessness of general officers with the army in not providing for the proper distribution of stores and in neglecting the welfare of their troops.

Kinglake, in his Invasion of the Crimea, repeated the allegations of the general officers, and accused the Crimean commissioners of having gone beyond their instructions, and of basing their report on improperly digested evidence.