This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Ethmoidal Arteries are two in number; they arise at the inner surface of the optic nerve, and pass between the internal rectus and superior oblique muscles of the eye to arrive at the internal wall of the orbit. The posterior or larger enters the foramen orbitale internum posterius, and sends several delicate branches to the membrane of the posterior ethmoidal cells : others enter the cranium and descend into the nasal fossae with the filaments of the olfactory nerve, to be lost on the mucous membrane of the nose. The anterior ethmoidal artery, smaller than the preceding, accompanies the ethmoidal branch of the nasal nerve, and having entered the anterior internal orbital foramen, is distributed to the mucous membrane of the frontal sinus, and anterior ethmoidal cells and nasal fossae. The posterior branch frequently arises from the lachrymal or supra-orbital.
* Todd's Cyclopaedia.