Private functions are meant to be hidden from the outside world and from the derived classes. Although you are overriding the access specifier of the parent's DoSomething and making it private, you are instantiating a base class; so in the first case, you can call base's DoSomething as it is public. This scenario can be used if you want to stop people deriving from your derived class.
In the second case, the private access specifier causes the base's members not to be exposed to the users of the derived class, which effectively makes the derived class useless.
