Well I must say I have never heard of a dog doing this before, but of course dogs do strange things every now and then. I guess it is fun for him to just run around chasing something or someone that is not there. Lonely children have imaginary friends too and they may pretend to be playing with a friend who is not really there.

There could be something at the other side of the garden producing humanly inaudible sounds, like a motor or a vacuum or sounds of percussion from very far away.

Ha ha ha, that's adorable! There have been times that I've wondered if dogs truly see something that we can't. My English Mastiff, Pandora, will bark at corners around the house. She has done it since she was a puppy. I always wondered if she is schizophrenic and can see things that we can't. My German Shepard is more similar to your Russell, chasing invisible people around the garden constantly.

I think with George it's because he does the same thing when there is a bird in the garden, the exact same response and he likes chasing birds, so if there aren't any birds he just pretends and chases them anyway.

Hahaha! I have to say that you've got a cute and lovely dog with the way you analyzed the whole scenario. However, I have to say that she is making some fun with imaginary situations and using that as a way to keep the excitement going on. I love such dogs for there will be no dull moments when they are around you.

All dogs chases invisible enemies including mine. Dogs like to run very fast as if they are chasing something or enemy. I have watched it countless time but still haven't understand why they are doing it.