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 Facial Vein is much less tortuous than the artery, and at the root of the nose and inner angle of the eyelids it communicates with the ophthalmic and with a large vein that descends on the middle line of the forehead, and communicates with its fellow of the opposite side by means of a short branch which passes across the root of the nose: as the facial vein descends, it crosses the cutaneous surface of the parotid duct, being external to the artery. On the body of the inferior maxillary bone, it lies close to the artery, touching its outer surface: it then descends superficial to the submaxillary gland, and either terminates in the external,, internal, or anterior jugular vein.
The facial artery usually gives off eleven branches,— five in its cervical, and six in its facial stage.
The Inferior Palatine Branch is usually small: it penetrates between the stylo-glossus and stylo-pharyngeus muscles to arrive at the superior and lateral part of the pharynx, where it divides into two principal branches, Which are distributed to the pharynx, tonsils, and Eustachian tube.
The Tonsilitic Artery sometimes comes off directly from the facial, and passes between the internal pterygoid and stylo-glossus muscles to its destination.
As the facial artery is passing through the substance of the submaxillary gland, it gives off several small branches, which are distributed to this structure and also to the tongue and mucous membrane of the mouth.