You need to define static variables in a translation unit, unless they are of integral types.
In your header:
private:
static const char *SOMETHING;
static const int MyInt = 8; // would be ok
In the .cpp file:
const char *YourClass::SOMETHING = "something";
C++ standard, 9.4.2/4:
If a static data member is of const integral or const enumeration type, its declaration in the class definition can specify a constant-initializer which shall be an integral constant expression. In that case, the member can appear in integral constant expressions within its scope. The member shall still be defined in a namespace scope if it is used in the program and the namespace scope definition shall not contain an initializer.