The base of a tax is the thing or phenomenon upon which the tax is assessed. The base is not always the source. Thus a tax based on property is generally paid out of income or revenue, which comes sometimes from the property, sometimes from some other source. The direct taxes are almost always called by the name of the "base."

The tax-rate is the amount of the tax falling on each unit of the base. The base is generally expressed in units of values ; as for example \$100 worth of property. It may, however, be some other unit, as one person, one ox, one acre, one yard, one ton, etc. Sometimes the unit of the base is very complex. For example, in Vermont the rate is so much, say \$1.50 on each \$1.00 in the " Grand List." But only 1 per cent of certain kinds of property is entered in the grand list. This arose, originally, from the custom of fixing a definite uniform value for each piece of property, as so much per acre of land, so much per head of cattle, so much per horse, irrespective of the actual value, and then fixing the rate upon this artificially constructed base.

The rate may be proportioned, apportioned, progressive, degressive, or regressive.

When the rate is proportioned, it is the same per cent of all property. When it is apportioned, the total amount to be raised is ascertained and then distributed, share for share, on each unit of the base.

A tax is progressive when the rate increases more rapidly than the base ; that is, when a higher per cent is assessed upon the higher values than upon the lower. This progression may be regular and start from the very smallest base, or one unit. For example, the rate may increase in some geometrical ratio, while the base increases in an arithmetical ratio. Of course any set of ratios may be chosen. The progression may be irregular in several different ways. Thus the progression may go by stages ; i.e. between certain limits, in arbitrarily fixed groups, the rate may be proportional, but increase gradually with each higher group. Or the progression may affect only certain parts of the base. That is, a certain minimum may be taxed proportionally, then a certain part taxed progressively, and the proportional rate may set in again after a certain high point has been reached. Again, a certain minimum may be altogether exempt, and the rate after that progressive.

The rate is degressive when the progression grows smaller as the base increases. There are various ways of accomplishing this. The most common is to exempt a certain moderate amount of the base and deduct that amount from all larger sums, while a nominally proportional rate is levied on the remainder. In this way a proportionally increasing burden is laid on the larger amounts of the base ; but the ratio of increase" grows gradually less, until, when the base reaches a very large amount, the increase in rate is practically nil, and the rate becomes practically proportional. For example, we may have an income tax in which the rate is 3 per cent on all income in excess of \$500. The man who has \$1000 pays 1.5 per cent on his whole income, while the man who has \$10,000 pays 2.85 per cent, and the rate approaches but never reaches 3 per cent by ever decreasing amounts. So that the man with an income of \$100,000 pays only 0.0015 less than three per cent. Another method is to make a deduction for the incomes below a certain amount only, the rate above that being proportional. A degressive rate is properly an irregular form of progression. Both progressive and degressive taxes are sometimes called graduated.

A regressive rate is just the reverse of a progressive or of a degressive rate. In this case the rate decreases as the property increases, and a heavier burden is laid on the smaller amounts. The regressive rate may be irregular in as many ways as the progressive. That is, it may vary in the reverse of any of the ways in which the progressive rate may vary.

Assessment is the name applied to the whole process of ascertaining the amount of tax due from each person or property. It consists of two steps, (1) the valuation of the property or income, or the listing of the things taxed ; (2) the levying of the rate or tax, that is fixing the amount each unit is to pay.

The tax list or roll contains the record of the amounts assessed and levied. In some European countries these lists are, for certain taxes, elaborate, permanent, or partly permanent records which serve various legal purposes as well as the fiscal, as for example the record of titles, and are called cadastres.

Impost is a general term for any tax, but there is a tendency to make it synonymouswith indirect taxes.

Customs duties are indirect taxes levied on the goods imported into or exported from certain territories. Excises (English) or internal revenue taxes (American) are indirect taxes levied on goods produced or consumed within certain territorial limits.                            Toll was originally a general term for many taxes, but it has come to have a special meaning, and applies only to the charges for passage over roads, bridges, canals, etc.

A tax is sa id to be shifted when the tax-payer reimburses himself from some one else. The final incidence of the tax is the falling of the burden upon some person who does not shift it.