Onyx

Black Onyx with the initials carved in it. The mounting is 14kt. yellow gold. This ring dates to the 1940's. This would be the type of ring worn by a young gentleman. from http://www.renaissancejewelers.com

Scientific:
I did all kinds of research on onyx, and I have to admit that this stone has possibly the most erroneous information available. First of all, there are two kinds of onyx; black onyx and marble onyx. Onyx is something of a catchall term that usually refers to dyed black chalcedony ("black onyx"), but it is also used to describe other colors of dyed chalcedony. More strictly speaking, onyx agate is banded agate displaying straight and parallel bands of alternating colors, which has historically been used to produce cameos. True onyx, however, is a form of calcite, usually used in architecture and ornamental pieces. 

Black onyx is the more valuable of the two. It is a variety of chalcedony, which is cryptocrystalline (crystals too small to be seen even by a microscope) quartz, and is used as semi-precious stones and for ornamental purposes. This type of chalcedony is basically black and white agate. It is different than regular agate only in that the bands of which it is composed are parallel and regular. The name onyx has its origin in the Greek language and means 'fingernail', probably because of its weak transparency. 

A chalcedony with black and white bands is properly called onyx, but this name is often incorrectly used for grayish chalcedonies or agates that have been dyed black or green. When onyx displays bands of sard alternating with either white or black layers, it is appropriately called sardonyx.

Onyx is used in carved cameos and intaglios because its layers can be cut to show a color contrast between the design and the background. Onyx is a layer stone with the combination of a black base and a white upper layer, also called true onyx or Arabic onyx. Sard onyx is a layer stone with a brown base and an upper white layer. Cornelian onyx is a layer stone with a red base and an upper white layer. The layers in agate or chalcedony required for intaglios and cameos are not often found in nature in the colors of onyx, carnelian, or sard. Therefore, such stones are usually dyed. 

Black onyx is found worldwide but is most commonly from Brazil, India, and Madagascar. 

Marble onyx has many names; onyx marble, Mexican onyx, cave onyx, Oriental alabaster, and in some cases travertine. Onyx marble is a limestone formed by the minerals calcite or aragonite. It is incorrect to name this rock onyx without the word marble. Onyx marble is formed from lime containing water by layered deposits (therefore always banded) near warm springs or as stalactites or stalagmites in caves. Deposits are found in Egypt, Algeria, Argentina, Morocco, Mexico and the U.S. 

It is apparently illegal to harm cave formations in the United States. Therefore, all onyx marble that is on the market should be coming from other countries. 

Onyx marble is used mainly for decorative items, some tiles, and has recently begun to be used for jewelry.

Black Onyx
Variety of: Chalcedony 
Chemical Composition: SiO2 Silicon Dioxide
Hardness: 7

Marble Onyx
Chemical Composition: CaCO3 - Calcium carbonate (which can be either calcite or aragonite) 
Hardness: 3.5 - 4

The Arabic name for onyx is el jaza, 'sadness'. The following passage, from The Curious Lore of Precious Stones, offers an illustration of the prejudice against this stone which was said to come from China and the Magreb:

Those who are in the land of China fear this stone so much that they dread to go into the mines where it occurs; hence none but slaves and menials, who have no other means of gaining a livelihood, take the stone from the mines. When it has been extracted, it is carried out of the country and sold in other lands. Those men of the Magreb who are also gifted with any wisdom will not wear onyx or place it in their treasuries. Indeed, no one is willing to wear it, unless he be bereft of his senses; for whoever wears it, either set in a ring or in any other way, will have fearful dreams and be tormented by a multitude of doubts and apprehensions; he will also have many disputes and lawsuits. Lastly, whoever keeps and onyx in his house, or places it in a vessel, or puts it in food or drink, will suffer loss of energy and capacity.

In India, onyx was worn around the neck for the purpose of cooling ardor. This belief is closely related to the idea that onyx provoked discord and separated lovers.