Born: 28 May 1710 in Basel, Switzerland
Died: 17 July 1790 in Basel, Switzerland

Johann(II) Bernoulli was one of three sons of Johann Bernoulli. In fact he was the most successful of the three. He originally studied law and in 1727 he obtained the degree of doctor of jurisprudence.

He worked on mathematics both with his father and as an independent worker. He had the remarkable distinction of winning the Prize of the Paris Academy on no less than four separate occasions. On the strength of this he was appointed to his father's chair in Basel when Johann Bernoulli died.

However, quoting [1]:-

... thereafter his mathematical production dwindled to occasional academic papers and a treatise, although he lived to almost as old as his father. His shyness and frail constitution did not, however, prevent him from engaging in extensive scientific correspondence (about 900 items) and from furthering thepublication, in four volumes, of his father's Opera Omnia. He personified the mathematical genius of his native city in the second half of the eighteenth century.

Johann(II) Bernoulli worked mainly on heat and light.

1. J O Fleckenstein, Biography in Dictionary of Scientific Biography (New York 1970-1990). 
   http://www.encyclopedia.com/doc/1G2-2830900408.html

Books:

1. H Bernhard, The Bernoulli family, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).

Articles:

1. M Hürlimann (ed.), Die Mathematikerfamilie Bernoulli, Grosse Schweizer (Zürich, 1942), 112-119.