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I'm puzzled by this description of a British ruse; what was the machine that "threw a reflection"? It's an extract of a letter written by Private A. Anderson (2,008), 1st Scots Guards, and was printed in the Burnley Express of 3rd February 1900.

"It is very dull here. Since we had our reverse at Magersfontein we have done nothing but trench work and play tricks on the Boers. Last week our officers worked a ruse that worked up to perfection, and caused the Boers to waste a large quantity of ammunition on empty air. It was worked with the Kimberley and Modder River searchlights. They were made to shine on some kind of a machine that threw the reflection of a battalion of men with fixed bayonets advancing towards the Boer trenches. The Boers took the bait, and fired thousands of rounds of ammunition at what they thought were British soldiers, but what was in reality only a shadow. The same thing has acted three times."

Makes you wonder if it wasn't a variation of a projector that used glass lantern slides to some effect.

You could well be right, magic lantern shows were very popular at that time. Whoever came up with the idea in this particular situation was a genius.