These are invaginations of the ectodermal cells of the skin forming olfactory sacs in fishes or lining of a part of the nasal passages in tetrapoda.
The olfactory organs have a lining of olfactory mucous membrane or Schneiderian membrane made of basal cells, supporting cells and elongated neurosensory cells.
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Neurosensory cells are bipolar neurons, they are produced at their free ends into hair-like processes or sensory hairs.
The structure of sensory hairs is like that of cilia with two central fibrils and nine double peripheral fibrils enclosed in a protoplasmic sheath.
Image Source: classes.midlandstech.edu
Backward growth of neurosensory cells forms fibres of olfactory nerves which join the olfactory lobes.
The neurosecetory cells are covered with mucus which is not only protective but also dissolves substances for smelling.
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The olfactory organs open to the exterior by external nares, the olfactory organ is single in cyclostomes with a single naris but it has two olfactory nerves.
In gnathostomes the olfactory organs are paired. In Dipnoi and tetrapoda each olfactory organ communicates with the mouth cavity by an internal naris.
In mammals the sense of smell is very acute, they have elongated nasal passages containing folded turbinal bones called ethmoturbinals, maxilloturbinals, and nasoturbinals.
The turbinals are covered with Schneiderian epithelium which is not olfactory over the maxilloturbinals but only moistens and warms the inhaled air, on the ethmoturbinals it is olfactory, on the nasoturbinals it is only some neurosensory cells.
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Organ of Jacobson or vomeronasal organ: In many tetrapoda there is a pair of vomeronasal organs which are sac-like chambers lying below the nasal cavities but above the buccal cavity, they have a pigmented epithelial lining like that of the olfactory organs. Each opens by a short duct into the olfactory organ in amphibians, but in others the duct opens into the buccal cavity.
The organ of Jacobson receives nerves from the nervous terminalis, a branch from the olfactory nerve, and a branch from the trigeminal nerve. The organ is believed to aid by smelling the recognition of food held in the mouth, and in lizards and snakes it appreciates the scent introduced into it by the tip of the tongue.
The organ of Jacobson first appears in amphibians as anevaginations of the olfactory organ, in the frog it lies in the anterior portion of each nasal cavity, but it is best developed in Sphenodon, lizards, and snakes, it is also well formed in monotremes, marsupials, insectivores, and rodents.
But in turtles, crocodiles, birds, and many mammals such as Primates and Cetacea, it is found only in the embryo and is absent in the adult.