On the whole, the ordinal use is perhaps the more common.
The last of these was that of Louis Agassiz (1807-1873), who, whilst surveying all previous classifications, propounded a scheme of his own (Essay on Classification, 1859), in which, as well as in the criticisms he applies to other systems, the leading notion is that sub-kingdoms, classes, orders and families have a real existence, and that it is possible to ascertain and distinguish characters which are of class value, others which are cnly of ordinal value, and so on; so that the classes of one sub-kingdom should on paper, and in nature actually do, correspond in relative value to those of another sub-kingdom, and the orders of any one class similarly should be so taken as to be of equal value with those of another class, and have been actually so created.
C. Fabricius, who proposed for them the ordinal name of Odonata 11775).
This relation-number is the ordinal number corresponding to n; let it be symbolized by it.
In reality there is a transition from a cardinal to an ordinal system, but to an ordinal system which does not agree with the original ordinal system from which the cardinal system was derived.
In short, the English reformers knew very well that the ordinal and communion office which they drew up could not satisfy the requirements of medieval theology.
The ordinal was not attached to this Prayer Book at its first appearance, but it was added under another act of parliament in the following year, 1550.
To see this, we may represent ordinal numbers by the ordinary numerals I, 2, 3,..
The definition of the ordinal number requires some little ingenuity owing to the fact that no serial relation can have a field whose cardinal number is 1; but we must omit here the explanation of the process.
No ordinal name used in the class has had so many varying meanings given to it by different authors.