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 Long Perineal Artery arises from the pudic in its third stage, pierces the obturator fascia, then curves under, that is, posterior and superficial to the transversus perinei muscle, and advances in company with the inferior perineal nerve and vein in the triangular space between the erector penis, accelerator urinae, and transversus perinei muscles; being nearer to the ischium than to the raphe or middle line of the perineum. In this course it supplies the two last-mentioned muscles and the sphincter ani and integuments, after which it penetrates the septum scroti and forms a network of vessels, both in the septum and in the subcutaneous areolar tissue of the rest of the scrotum. It anastomoses with the arteries of the spermatic cord and with the external pudic arteries. This artery may possibly escape in the lateral operations for the stone.
In the female this branch is larger in proportion to the other branches, and is the artery of the labium.
The Transverse Artery of the Perineum is a small branch which arises from the pudic at the termination of its third stage; it then pierces the obturator fascia in this situation, and the base of the triangular ligament, and passes inwards and forwards on the cutaneous surface of the transversus perinaei muscle, which it supplies; it then passes to the central point of the perineum, where it anastomoses with the artery of the opposite side. This artery is sometimes a branch of the long perineal: it is necessarily divided in the lateral operations for the stone.