How can I initialize a const variable of a base class in a derived class' constructor in C++?

I have an abstract C++ class with no constructor. It's supposed to be a base class so other classes can inherit from it. What I am trying to do is to declare a constant variable in the base class and initialize it in each derived class' constructor but nowhere else in each one of those classes. Is it legal in C++? If so, how can I do that?