Storing base and derived classes in a vector???

I'm trying to wrap my head around inheritance. The following code
creates three objects, an Animal, a Dog and a Cat. Dog and Cat are
derived from Animal and overwrite Animal's birth() method.

I thought, since Dog and Cat are Animals, I can make a vector of Animals
and store Dogs and Cats in it. There's no problem until I try accessing
the elements of the vector, where they are now all treated as Animals.

I suppose this makes sense, since I created a vector of Animals, that
all the elements in it should be treated as Animals. How do I store a
Dog in an Animal vector and retrieve it as a Dog? Can I even do that?

I'm not even sure of the terminology of what I'm trying to do, so my
Google searches haven't been very successful. Even a hint of what to
search for would be helpful.

Thanks,

JamesW.

#include <iostream>
#include <vector>

class animal {
public:
    animal(){};
    ~animal(){};
    virtual void birth(){
        std::cout << "Gave birth to an animal" << std::endl;
    }
};

class dog : public animal {
public:
    void birth(){
        std::cout << "Gave birth to a puppy" << std::endl;
    }
};

class cat : public animal {
public:
    void birth(){
        std::cout << "Gave birth to a kitten" << std::endl;
    }
};

int main()
{
    animal thing;
    dog max;
    cat lucky;

    std::vector<animal>list;

    list.push_back(thing);
    list.push_back(max);
    list.push_back(lucky);

    for(unsigned char i=0;i< list.size(); i++){
        list[i].birth();
    }

    return 0;
}

Output::
Gave birth to an animal
Gave birth to an animal
Gave birth to an animal