What is the bulge under the engine of the Mirage III and some of its variants?
For the Mirage III, it's a fuel tank (that also allows a camera attachment). See cutaway below (item 157).

Also from Wikipedia:


  The Mirage IIIRS could also carry a centerline pod for conducting photo reconnaissance missions, as well as an integral fuel tank underneath the aft belly; this tank could carry a smaller fuel load, but also allowed for a rear-facing film camera to also be added. When fitted with the reconnaissance pod, supersonic performance was severely diminished.



Source: aviadejavu.ru (composite of two pages: 16-1.jpg and 16-2.jpg; use links for full-res)