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The two pneumogastric nerves are the right and left vagus nerves, the tenth cranial nerves: mixed sensory, branchial motor and parasympathetic pathways from the medulla oblongata to the neck, thorax and abdomen. A useful description separates their apparent origin at the surface of the brain from the origins and terminations of their component fibres.

Rootlets emerge in the groove behind the inferior olive, between the glossopharyngeal nerve above and the accessory rootlets below. Branchial motor fibres arise chiefly in the nucleus ambiguus; preganglionic parasympathetic fibres arise in the dorsal motor nucleus of the vagus and, particularly for cardiac control, the nucleus ambiguus. Visceral sensory fibres have their cell bodies chiefly in the inferior vagal ganglion and terminate centrally in the nucleus of the solitary tract; somatic sensory fibres associated with the superior vagal ganglion project to the spinal trigeminal nucleus. Consequently a sensory fibre is not accurately described as originating in a motor nucleus simply because its peripheral nerve emerges nearby.^[ref]

Each vagus nerve leaves the skull through the jugular foramen, with the glossopharyngeal nerve and accessory nerve. It bears the small superior vagal ganglion at the foramen and the larger inferior vagal ganglion below it. Connections include communications with adjacent cranial nerves and the cervical sympathetic nervous system. Traditional descriptions assign fibres joining the vagus nerve from the cranial part of the accessory nerve to the latter peripheral nerve; their modern classification is more nuanced and does not change the peripheral branches being described. In the neck the vagus nerve descends in the carotid sheath, behind and between the internal jugular vein and the internal, then common, carotid artery.

Its meningeal and auricular branches supply small sensory territories of the cranial covering and external ear. Pharyngeal branches contribute to the pharyngeal plexus, supplying much of the soft palate and pharynx; the stylopharyngeus muscle belongs to the glossopharyngeal nerve and the tensor veli palatini muscle to the mandibular division of the trigeminal nerve. The internal branch of the superior laryngeal nerve supplies sensation above the vocal folds; its external branch supplies the cricothyroid muscle. The recurrent laryngeal nerve supplies the other intrinsic laryngeal muscles and sensation below the vocal folds. The right recurrent laryngeal nerve loops beneath the right subclavian artery; the left loops under the aortic arch beside the ligamentum arteriosum. Both return towards the larynx near the groove between trachea and oesophagus.^[ref]

In the thorax, both vagus nerves pass behind the roots of the lungs, contrasting with the anterior course of the phrenic nerves. Cardiac branches join the cardiac plexus; pulmonary branches join the pulmonary plexus. The trunks break up into the oesophageal plexus, then collect principally as an anterior trunk derived from the left vagus nerve and a posterior trunk derived from the right. Through the oesophageal hiatus they reach the stomach; hepatic and coeliac branches distribute to abdominal viscera. Their parasympathetic territory includes foregut and midgut derivatives, extending into the proximal colon, rather than every abdominal and pelvic organ.^[ref] This extensive distribution explains why the level of experimental section is indispensable information.

The main consequences of section can be organized by the interrupted functions:

A discriminating historical experiment would record respiratory movements and heart rate before and after section, distinguish unilateral from bilateral section, and compare an intact airway with an airway bypass. A tracheal cannula can separate obstruction at the glottis from changes in the respiratory rhythm, while the central-versus-peripheral stimulation comparison separates incoming reflex traffic from outgoing motor effects. Later separate-lung recordings confirmed that a change following unilateral section could affect both lungs, supporting a central reflex interpretation rather than simple local paralysis.^[ref] The gastric distinction is also borne out by measurements of persistent acidity after surgical vagotomy, despite major reductions in stimulated gastric acid secretion.^[ref]

The fourth ventricle is the cavity of the hindbrain between the dorsal surfaces of the pons and upper medulla oblongata anteriorly and the cerebellum posteriorly. It is continuous above with the cerebral aqueduct and below, at the obex, with the central canal of the spinal cord. Its floor is diamond-shaped when viewed from behind, while its roof rises dorsally towards the fastigium.

The floor, the rhomboid fossa, consists of an upper pontine triangle and a lower medullary triangle. Its upper apex points towards the cerebral aqueduct; its lower apex is the obex; the two lateral angles continue into the lateral recesses of the fourth ventricle. A median groove divides it into right and left halves. On each side, the medial eminence lies medial to the sulcus limitans, which separates predominantly motor territories medially from sensory territories laterally. The striae medullares of the fourth ventricle cross the floor near the junction of its pontine and medullary portions; their extent varies.

Several surface features identify deeper relations. In the pontine part, the facial colliculus overlies the abducens nucleus and the internal looping course of fibres of the facial nerve; it is not the exposed facial motor nucleus. The upper part of the sulcus limitans has the superior fovea, and near its rostral lateral region lies the locus coeruleus. Laterally, the vestibular area overlies the vestibular nuclei. In the lower triangle, the hypoglossal trigone overlies the hypoglossal nucleus, and the vagal trigone, lateral to it, overlies the dorsal motor nucleus of the vagus. The area postrema lies still farther caudolaterally, separated from the vagal trigone by the funiculus separans. These are landmarks and underlying relations, not claims that the cranial nerve nuclei lie loose within the cavity.^[ref]

The upper lateral boundaries are formed by the superior cerebellar peduncles. The lower lateral boundaries relate to the inferior cerebellar peduncles and adjacent dorsal medullary margins. The lateral recess on each side curves around the inferior cerebellar peduncle towards its external opening near the flocculus.

The roof has superior and inferior slopes. Superiorly the thin superior medullary velum spans the superior cerebellar peduncles, with the lingula of the cerebellum on its dorsal surface. Inferiorly, the roof relates to the inferior medullary velum, nodule of the cerebellum and thin tela choroidea. Vascular folds of the tela choroidea carry the choroid plexus of the fourth ventricle, with median and lateral extensions. The cavity has an ependymal lining; the choroid plexus has its specialized epithelial covering and produces cerebrospinal fluid.

There are three important exits to the subarachnoid space: one median aperture of the fourth ventricle through the inferior roof, opening towards the cisterna magna, and two lateral apertures of the fourth ventricle at the ends of the lateral recesses of the fourth ventricle. These must be distinguished from the inlet through the cerebral aqueduct and the inferior continuity with the central canal of the spinal cord. Most cerebrospinal fluid leaving the fourth ventricle reaches the subarachnoid space, not the narrow adult central canal of the spinal cord.

The three-dimensional arrangement explains the method of examination: reflecting the cerebellum and opening the delicate roof exposes the rhomboid fossa, but destroys part of the structure one is trying to describe. Studying an intact roof, then the exposed floor, and using a median section to locate the fastigium avoids interpreting a dissected cavity as naturally open behind. The modern nomenclature is useful here; not every fine landmark or physiological interpretation in this account should be read as an assertion about what an 1867 examiner required.^[ref]