The length of the trough was 46 inches, breadth 14 inches, and depth 8 inches: at each corner was a graduated scale of inches, and pencil-lines drawn round the inside of the trough at every inch. Sea-water was poured into the trough to the height of 5 inches; and the trough was exactly levelled, by means of the pencil-line, at 5 inches: then the block being forced under the water's surface, the fluid, when still, was risen to 6⅓ inches; consequently the magnitude of the block was equal to a parallelopipedon of 46 inches long, 14 inches broad, and 1⅓ inches deep, or to 858⅔ cubic inches.
Now 858⅔ cubic inches are equal to 0.4969 cubic feet.
And a cubic foot of sea-water weighs 64.373² pounds avoirdupoize.
Then 64.373² × 0.4969 = 31.987 pounds.
So that by a quarter inch scale, a model similar to the Royal William weighs near 32 ℔.
But a quarter inch scale is 1/48 of a foot scale.
And the model is to the ship as 1³ is to 48³, or as 1 is to 110592.
Then 3537506 ℔. (= 110592 × 31.987), or 1579 tons, 4 C. 3 qrs. 14 ℔. is the weight sought.
The difference by the two methods amounts to 5415 ℔. or to 2 tons, 8 C. 1 qr. 11 ℔.
Some of the persons present at this experiment read the height of the water at 6⅜ inches: the difference between 6⅜ and 6⅓ inches is 1/24 of an inch; a difference easily to be made by different persons in an experiment of this kind. But observing, that the computation made on 6⅜ inches amounted to near 50 tons more than on 6⅓ inches, I caused the trough to be diminished in its depth to 6½ inches, had one of the ends cut off, and a board fixed on the open side, being desirous of making the experiment with the trough standing on one end: and indeed, in this situation, an error of ⅒ of an inch in the height of the water makes a difference of about 16½ tons in the weight of the ship. Into this upright trough water was poured to the height of 36 inches; and the block being immerged, the water was raised 9⅓ inches: so that the block was equal in magnitude to a parallelopipedon of 14 inches long, 6½ inches wide, and 9⅓ inches deep, or to 849⅓ cubic inches: from whence I find the weight of the ship to be 1562 tons, 1 C. 2 qrs. 16 ℔. And altho' I take this number to be nearest the truth, yet it may be observed, that it is no easy matter to come at accuracy in this subject by any of the methods in common use.