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 Lachrymal Artery is the first and one of the largest branches of the ophthalmic: it arises at the outer side of the optic nerve and passes forwards and outwards between the origin of the superior rectus muscle and the superior head of the external rectus: it supplies both these muscles, and is conducted by the superior margin of the latter towards the lachrymal gland: in this part of its course it sends a branch through the malar bone into the temporal fossa, which anastomoses with the anterior deep temporal artery. More anteriorly it gives off a number of branches which pass above, and sometimes round, the lachrymal gland to penetrate between its lobules, and to supply its interior. Lastly, the terminating branches are lost in the upper eyelid, in anastomosing with the superior palpebral and anterior temporal arteries.