This is called the trapezoidal or **chordal** area, and will be denoted by C1.

The - - 4X + g tangential area may be expressed in terms of **chordal** areas.

If we write CI for the **chordal** area obtained by taking ordinates at intervals Zh, then T i =2CI-C I.

Some of the formulae obtained by the above methods can be expressed more simply in terms of **chordal** or tangential areas taken in various ways.

2um) Now, if p is any factor of m, there is a series of equidistant ordinates uo, up, 142p, um - p, um; and the **chordal** area as determined by these ordinates is ph (2uo + up + u2p +.

The following are some examples of formulae of this kind, in terms of **chordal** areas.

The general method of constructing the formulae of § 7 0 for **chordal** areas is that, if p, q, r, ...

The following are the results (for the formulae involving **chordal** areas), given in terms of differential coefficients and of central differences.