Mike,
Re Macdonald's mathematical precision, what do you make of this quote about the 10,000 loads of good soil. He put three caveats on that number - "Roughly", "I think" and "probably". Perhaps he wasn't quite so mathematically precise as you thought. I think the 200 -300 yards was just an estimate because he didn't remember the precise number or he never measured a precise distance because it really wasn't relevant.
We obtained an option on the land in November, 1906, and took title to the property in the spring of 1907. Immediately we commenced development. In many places the land was impoverished. These had to be top dressed. Roughly speaking, I think we have probably put some 10,000 loads of good soil, including manure, on the property. We did not have enough money to consider building a club-house at once, so our intention was to have the first hole close to the Shinnecock Inn, which had recently been built by the Realty Company. The old saying, “Ill blows the wind that profits nobody,” is quite apropos here, for the Inn burned down in 1909, which drove us to building a club-house.
MacDonald, Charles (2014-05-01). Scotland's Gift: How America Discovered Golf (Kindle Locations 2311-2319). Midpoint Trade Books. Kindle Edition.
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David,
How do you suppose he measured the cape hole to know it was a 240 yard carry? It was as you say, largely either swampy or under water. Would he have surveyed it to get the distance (since it couldn't be paced off), and if so when? Or, was the 240 yards initially in his mind a distance that he would want to design the hole to be. He could, after all, build the green at any distance he wanted since it was going to be concrete walls and fill.