The length of time required for a candle to burn down one inch. Similar units are found in many cultures. In English commerce, however, the phrase had a special meaning: it referred to a type of auction. Worlidge's description  is worth quoting in full (spelling and punctuation have been slightly modernized):
Goods are sold by inch of candle when a merchant or company of merchants, as the East India Company or the like, having a cargo of foreign goods arrived, are minded to make a speedy sale thereof, in which case notice is usually given upon Exchange by writing, and elsewhere, when the sale thereof begins; against which time the goods are divided into several parcels, called lots, and papers printed of the quantity of each and of the conditions of sale, as that none shall bid less than a certain sum, more than another has bid before, etc. During which time of bidding a small piece, about an inch, of wax candle is burning, and the last bidder when the candle goes out has the lot or parcel exposed to sale, and if any difference arise, as it often happens in a good lot that four, five or more bid together, in such case the lot is put up again, until the true buyer can be discovered by the judgment of standers by appointed for that purpose, which buyer is bound to stand to the bargain and to take the lot whether good or bad, at the rate he bought it, being the last bidder.
An eBay of the 1600's.
The selling of commodities by the Candle, is an ancient Custome beyond the Seas, only for such goods, rents upon houses or lands, or the houses also which require a suddaine sale, after they have been one yeare and one day denounced by publication that they are to bee sold; to the end that if any man will lay claime thereunto, they may come in within that time. And these sales are made upon Fridayes in accustomed places by publike authoritie, for the better warrant of the Buyer, the manner of it is thus: There is a waxen candle, or a piece of it, set up in some place easie to be seene, and the standers by are required to make an offer for such goods, or such a house; which being made, another will offer more, as they do in outcryes, having still a regard to the burning Candle: declaration is made how the payment must bee, so that hee who maketh the last offer (upon the going out of the Candle) hath the bargaine. If it doe fall out, that there is confusion of voycies of the offers made, whereby it cannot bee discerned who made the last offer, and the standers by do differ in their iudgement of it, then the Candle is set up againe by those that are in authoritie, and in like manner it is determined accordingly.
The Merchants of the East-India companie do imitate the same, and after publike notice is given in writing upon the Royall Exchange in London, That such a day, such and such commodities will be sold at such a place[.] Merchants and others (knowing the great parcels of Pepper, Indico, and other commodities of Silkes, Calicoes, and such like) will ioyne together to buy the same in severall companies, and so buy the same by the Candle, as aforesaid, although it were a parcell of one hundreth thousand pounds. The time for the payments is foure times six moneths, which is fifteene moneths in one payment, according to which (if you will pay all or part of it in readie money by way of Anticipation) you shall have use allowed you accordingly, after the rate of ten upon the hundreth. But their good orders require a more larger declaration.
Vel Lex Mercatoria, or the Ancient Law-Merchant.…
London: Printed by Adam Islip, 1622.
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