Hi all. Do const member functions call only const member functions?

class Transmitter{
  const static string msg;
  mutable int size;
  public: 
    void xmit() const{
    size = compute();
    cout<<msg;
  }
  private:
   int compute() const{return 5;}
};

 string const Transmitter::msg = "beep";

 int main(){
   Transmitter t;
   t.xmit();
   return EXIT_SUCCESS;
 }

If i dont make compute() a const, then the compiler complains. Is it because since a const member function is not allowed to modify members, it wont allow any calls to non-consts since it would mean that the const member function would be 'indirectly' modifying the data members?