This section is from the book "Applied Anatomy: The Construction Of The Human Body", by Gwilym G. Davis. Also available from Amazon: Applied anatomy: The construction of the human body.
The arachnoid is a thin fibrous membrane, which passes over the convolutions of the brain and does not dip into the sulci between. It is more marked on the base than on the convexity of the brain. It is not attached to the dura above, and this subdural space, while moist, contains little or no free fluid. Hemorrhages do not occur into this space unless the membranes are torn, because the bleeding from the vessels of the dura is always epidural and the arachnoid derives its nourishment from the pia mater below, so that hemorrhages start beneath the arachnoid, but may rupture through the arachnoid into the subdural space. From its under surface, fibrils of loose tissue pass to the pia mater; the space between the fibrous layer of the arachnoid above and the pia mater and convolutions of the brain below is called the subarachnoid space. This is a lymph space and contains the cerebrospinal fluid. This fluid is normally about 60 c.c. (2 ounces) in quantity, but in injuries to the brain in which the subarachnoid space is opened, the fluid is secreted and discharged very rapidly. As has already been mentioned, the arachnoid sends a prolongation into the internal auditory meatus, hence a fracture through it would open the subarachnoid space. This space communicates with the ventricles of the brain through three openings in the pia mater at the lower back portion of the roof of the fourth ventricle; these are called the foramina of Magendie, Key, and Retzius. The cerebrospinal fluid extends down the spinal canal and can be removed by tapping with a trochar, as is practised in the lumbar region.
The net-work of vessels, with their supporting membrane, . which covers the convolutions of the brain, forms the pia mater. The fibrils of connective tissue supporting the vessels are attached to the fibrous layer of the arachnoid above, so that the pia and arachnoid are in reality continuous structures. The spaces between these fibrils are often quite large and communicate with each other, forming the subarachnoid space. The lower portions of these fibrils are united and form a basement membrane which lies directly on the convolutions of the brain and dips into the sulci. The blood-vessels are intimately connected with this lower pial membrane and not with the arachnoid above. These vessels penetrate into the substance of the brain, carrying with them a covering or sheath of pia mater. This is called the peri-vascular lymph sheath and, of course, communicates with the subarachnoid space above. These vessels nourish the brain. The perivascular lymph sheaths are also said to form capsules around the great pyramidal and large glial cells of the cortex.