The Court of Exchequer was first erected by William the Conqueror, for the trial of all causes relating to the revenues of the crown; and here are also tried matters of equity and law between subject and subject.

Mogg's New Picture of London and Visitor's Guide to it Sights, 1844

Leaving the Court of Queen's Bench, and elbowing through a throng of customers blockading the apple-stall, we enter at the second side door in Westminster Hall, and find ourselves in the Exchequer Court. The Exchequer Court exercises functions extra-judicial, and keeps up the observance of certain traditionary customs and rites which are worth mention in this place. Thus, it regulates the election of Sheriffs. On the morrow of St. Martin's, November 12, a privy Council is held to receive the report of the judges, of the persons eligible in the several counties to serve as sheriff. On the bench sits the Chancellor of the Exchequer in his figured silk gown trimmed with gold ; next are the members of the Privy Council, the Lord Chancellor, and Judges of the Queen's Bench and Common Pleas ; below sit the Judges and Chief Baron of the Exchequer, and on the left the Remembrancer of the Court. The judges report the names of three persons eligible for sheriff in each county, when excuses for exemption may be pleaded. The list being considered by the Privy Council, the names are finally determined on the approval of her Majesty in council, which is done by her Majesty pricking through the names approved on a long sheet of paper called the Sheriffs' Roll. The Sheriffs of London and Middlesex are, however, chosen by the Livery, but are presented on the morrow of the Feast of St. Michael, in the Court of Exchequer, accompanied by the Lord Mayor and Aldermen, when the Recorder introduces the Sheriffs and details their family history, and the Cursitor Baron signifies the sovereign's approval; the writs and appearances are read, recorded, and filed, and the sheriffs and senior under-sheriffs take the oaths, and the late sheriffs present their accounts. The Crier of the Court then makes proclamation for one who does homage for the Sheriffs of London to "stand forth and do his duty;" then the senior alderman below the chair rises, the usher of the court hands him a bill-hook, and holds in both hands a small bundle of sticks, which the alderman cuts asunder, and then cuts another bundle with a hatchet. Similar proclamation is then made for the Sheriff of Middlesex, when the alderman counts six horse shoes lying upon the table, and sixty one horse-shoes lying upon the table, and sixty one hob-nails handed in a tray; and the numbers are declared twice. The sticks are thin peeled twigs, tied in a bundle at each end (of course with red tape); the horse-shoes are of large size, and very old ; the hob-nails are supplied fresh every year. By the first ceremony the alderman does suit and service for the tenants of a manor in Shropshire, the chopping of sticks betokening the custom of the tenants supplying their lord with fuel. The counting of the horse-shoes and nails is another suit and service of the owners of a forge in St. Cement Danes, Strand, which formerly belonged to the City, but no longer exists; while, as to the manor in Shropshire, even a century ago no one knew where the lands were situated, nor did the city receive any rents or profits from them. It is in the Court of Exchequer that, on the 9th of November, the oaths are administered to the new Lord Mayor : at the same time the late Lord Mayor renders his accounts, and the Recorder invites the Barons to the banquet at Guildhall.
    The chamber in which the Exchequer Court sits differs very little from that of the Queen's Bench, save that it wants the refectory antechamber and its shrivelled Pomona, and that, though of equal size, its interior is less pretentious on the score of architectural display. It is equally thronged with professionals and spectators, and the same respectful silence is in keeping with the same obscurity that pervades the place. Baron South is to-day the deciding judge, and the case which the counsel at the moment is elaborately explaining is one of considerable interest to the tax-paying community. The plaintiff is lessee of a brick-field, which he rents for the purpose of digging the clay and burning the bricks. The assessors of the income-tax have levied upon him the full tax upon the land and the produce of his industry in working it, and he claims a deduction against his landlord in respect of the tax he has paid, on the ground that the landlord derives not only rent, but a royalty on the bricks, and sundry other advantages. The question is a complicated one, is mixed up with a good many stiff covenants and a deal of stiffer clay, and even after all the arguments are gone through, pro and con, the decision, like the plaintiff's instruments of trade, sticks in the mud. The judge, who is wisely given to deliberation, will not pronounce without carefully weighing the matter, and therefore he informs the parties to the suit that he will "take time to consider." 

The Leisure Hour, 1858