Can you use an unnamed namespace to hide constants in a header?

I have some inline functions contained within a namespace in a header file and am not currently in a position to move them into a cpp file. Some of these inline functions use magic constants, for example:

// Foo.h
namespace Foo
{
    const int BAR = 1234;

    inline void someFunc()
    {
        // Do something with BAR
    }
}

However, I want to make these magic constants private - any ideas how? My first thought was to use an anonymous namespace thus:

// Foo.h
namespace Foo
{
    namespace
    {
        // 'private' constants here
        const int BAR = 1234;
    }

    inline void someFunc()
    {
        // Do something with BAR
    }
}

However, this doesn't work and Foo::BAR is available to any cpp file that includes Foo.h? Is there a way to do this without creating an implementation cpp file?