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Frank Reed you wrote: The problem here is the idea of tracing a line down to the horizon and then stopping there. It just does not work! Don't do it. Don't do it with the horns of the Moon. Don't do it with the Orion North Arrow. It fails dramatically for the horns of the Moon, as you can see in the image below .....

Frank

You left the Moon’s altitude on your picture.  In your example, you’re using an altitude of 7 degrees.  How high was the Moon 6 hours earlier when its hour angle was nearer zero, and where did the straight-line point to on the horizon then?  To be fair on the bloggers, the better-quality ones at least, they do say it works best when the Moon is high in the sky and that the line becomes progressively more inaccurate the lower the Moon is in the sky.  Otherwise, I agree with you.  Over the last year, I’ve not been able to help looking at Moon’s Horns every time I see them, and at times I’ve seen the line way off south.  That’s what got me interested in the first place.  Myth busting should be our business. 

Re: The problem here is the idea of tracing a line down to the horizon and then stopping there.  I'm afraid that's as far as the average outdoor enthusiast is prepared to go.  DaveP