As mentioned in the Webster 1913 entry for the Gloria (a term more usually employed for the Gloria in Excelsis), the Gloria Patri is a short prayer, often used as a doxology following a psalm.

From the Book of Common Prayer, 1662, 'Of Ceremonies':

And at the end of every Psalm, and of every such part of the 119th Psalm, shall be repeated this Hymn,

Glory be to the Father, and to the Son : and to the Holy Ghost;
As it was in the beginning, is now, and ever shall be : world without end. Amen.

From Breviarum Romanum, 1910, following the long-standing Roman Catholic pattern, the following is the form which gives the prayer its name:

Glória Patri, et Fílio, * et Spirítui Sancto.
Sicut erat in princípio, et nunc, et semper, * et in sǽcula sæculórum. Amen.

NB: That's an a-e diphthong with an acute accent in 'saecula'.