On the outbreak of the Revolution in 1789, she left France and for 12 years traveled abroad, to Rome, Naples, Vienna, Berlin, St. Petersburg, and Moscow, painting portraits and playing a leading role in society. In 1801 she returned to Paris but, disliking Parisian social life under Napoleon, soon left for London, where she painted portraits of the court and of Lord Byron. Later she went to Switzerland (and painted a portrait of Mme de Staël) and then again (c. 1810) to Paris, where she ceased painting.

Vigée-Lebrun was a woman of much wit and charm, and her memoirs, Souvenirs de ma vie (1835-37; "Reminiscences of My Life"), provide a lively account of her times as well as of her own work. She was one of the most technically fluent portraitists of her era, and her pictures are notable for the freshness, charm, and sensitivity of their presentation. During her career, according to her own account, she painted 877 pictures, including 622 portraits and about 200 landscapes.

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Marie  Louise Elisabeth Vigee-Lebrun 1755-1842 
Marie Antoinette 1787 oil on canvas 9'x7'
Versailles

In the self portrait the artist has chosen a neoclassical looking garment and the texture of the background is undefined.  In the portrait of Marie Antoinette, the queen is dressed in fairly expensive clothing however the clothing is not terribly ornate or ostentatious.

Iconography:  In both images, the artist has chosen to portray the female as a "good mother" in the manner that Rousseau advocated.  In Rousseau's point of view the role of individuals was predetermined by their innate nature and that in order for an individual to fit into society as a whole one must live in accordance with this nature.  In the case of females, this role was to have children and be good mothers.  Both of these images subscribe to this point of view because these images were meant to be almost advertisements or a form of propaganda that would present a persona to the world.

Context:  By 1789, accusations of impropriety and adultery had destroyed her public reputation.   This self portrait was an attempt to portray herself as a moral and upright Frenchwoman.  The same was true for Marie Antoinette.  In this painting Marie Antoinette is being depicted in modest clothing to defend against accusations of excessive spending and she is also portrayed as the good mother who had also lost a son.  On the right is her brother, Louis, Le Dauphin gesturing toward the empty crib which indicates her loss.

The last portrait of thirty that Vigee Le Brun painted of the doomed queen. The picture shows Marie Therese Charlotte de France, Madame Royale, and her brother, Louis, Le Dauphin.  Louis died of natural causes early in the year that the revolution began. The next younger child, also called Louis then became the second Dauphin. After his father had been guillotined he became known as Louis XVII . This Louis may have been murdered, or may have died of other causes while imprisoned in the temple, but he may also have survuved after having been exchanged for another sickly child. This painting still hangs at Versailles.
http://www.batguano.com/vigeemagallery.html#F

Stele of Hegeso
c.410-400 BC, Marble, 5'9"
Athens. Classic Greek

The picture plane is arranged in a sculptural frieze like band that takes its cue from antique sculptural friezes such as those found on the Ara Pacis and the Parthenon.  Like its classical counterparts, the image is constructed so that most of the figures are placed in the foreground and even though there is the creation of deep space, the background is not as important as the figures. 

Stokstad goes into the specific story of the Cornelia and the Gracchii and so this next section will be dedicated to some other aspects of the image.

The use of classical imagery, such as the togas and columns, and a story that deals specifically with self sacrifice for the generations of the future.  The classical clothing and arches referred to a tradition that was considered more dignified than the light classical themes expressed in paintings like Watteau's.

The lighting and the frieze like placement of the figures are equally a part of the iconography of this image because these formal elements directly refer to those classical traditions.  Compare Watteau's style of painting and see how the formal qualities of each actually are part of the iconography.

The individuals being represented are also all physically beautiful and this refers to the classical concept of kalos (Greek for beautiful and moral.)

In a twist on the classical vocabulary found in the Stele of Hegeso, Kauffman corrects the iconography and updates it.  The prescribed role of woman is specifically expressed in this image as that of a mother rather than a selfish woman who cares only for jewels.  This philosophy is very much in keeping with Rousseau's ideas concerning that of the "happy mother" and in her depiction of Cornelia she is almost changing the meaning of the image found on the stele.

Context: According to WebGalleries,

This fine painting combines the 18th century attributes of loving and attentive mother with Roman classicizing elements. Kauffmann presents us with the narrative subject of "exemplum virtutis" or example of virtue. Here a wealthy women sits showing off her jewels. When she asks Cornelia to present her jewels, Cornelia raises her hand to bring forth her sons, Tiberus and Gaius, saying "These are my jewels". The subjects are clothed in roman dress and set against a roman background. An interesting comparison can be made to Jacques Louis David's "Oath of the Horatii".

A child prodigy, Kauffmann produced her first commissioned work before the age of 13. After the death of her mother, she traveled through Austria and Italy with her father, painter Joseph Johann Kauffmann. She assisted him by painting in the backgrounds of his works, but she also received her own commissions and soon established a solid reputation in her own right. She was influenced by Correggio and the Carracci and copied their works in the galleries as part of her artistic training. Later her style reflected a neoclassical flavor influenced by Benjamin West, Sr. Joshua Reynolds and the classicizing elements at Herculaneum.

In 1766 Kauffmann was invited to London. She produced many portraits and decorative painting but preferred history painting which was considered the highest artistic genre and reserved only for her male colleagues. Despite her inability to secure a formal artistic education or study the male nude, Kauffmann produced paintings which depicted classical mythology, history and allegory. She received commissions from the Royal courts in Naples, Russia and Austria. While often dismissed by traditional art history as a mere decorative or sentimental artist, she was successful enough to purchase her own home from earned commissions and live a comfortably stylish life. Another testament of Kauffmann's success was that she was one of the founding members of the British Royal Academy in 1768. 
http://www.webgalleries.com/pm/colors/kauffman.html