As to the accuracy of the estimated distance—one mile—that, to be sure, was a much more uncertain quantity; though officers of war vessels are, and were then, well trained to estimate distances on the water, as otherwise they could not determine the range of their cannon and arms. Altogether I had every reason to suppose, barring variations in the compass and individual errors, that the location assigned was reasonably accurate. At any rate I decided to start my investigation with the assumption that the assigned location was accurate, and to work from the designated point as a centre; it would then be easy, as I proceeded, to allow for error in all directions without the chance of multiplying it in any particular direction.

In my little box of drawing-tools was a small brass protractor—a semi-circle divided into one hundred and eighty degrees, with half-degree marks. This would be convenient in the work I was about to do, though not absolutely necessary, as in its absence I could have easily constructed one that would answer my purpose. The first thing to do was to establish a true north and south line. That night the stars shone brightly, and I easily found the pole star by the pointers in the Great Bear, or “Dipper.” In the sand at the north cape I drove an upright stake made of a stout cane. Then taking another straight piece I placed it in a notch on top of the upright and sighted along its length adjusting it until it pointed straight at the north star. To secure it in this position I drove a short notched stake at the butt of the inclined cane and tied the cane firmly to both. I was now sure that the two uprights were in a true north and south direction from each other, and the work for that night was finished, as the remainder could be better done by daylight.

The next thing I wanted was a standard of measurement; unfortunately my drawing instruments did not contain the usual ivory rule. But this did not occasion me much uneasiness, as I hoped to be able to deduce the standard inch by a comparison of my belongings. If I once got the true inch it would be easy to get from that the foot, the yard, the rod, the mile. I had my photograph plates as one guide; these I had every reason to suppose were cut quite accurately to the dimensions of five inches by seven. Then there was the brass protractor. It is true there were no inches marked on this; but the workman who made it would naturally follow some standard, and the chances were very great that the diameter of this instrument would be found to be an exact multiple of the inch, and as I conjectured, exactly four inches. To test this matter I laid the protractor on the short side of one of the plates, and taking the difference between the two found, as I had expected, that this difference was one fifth of the width of the plate, and one seventh of its length. This proved satisfactorily to my mind that the plate was accurate in dimensions, that is to say, five by seven inches, and that the difference between the length of the straight side of the protractor and the width of the plate was the standard inch. From this starting-point I constructed a foot measure, and cut me a light pole exactly a rod in length.

Returning now to the cape where my north and south direction rod was fixed, I proceeded to set a peg, which to avoid confusion we will designate as A, in the sand in a prolongation of the line, and with the protractor got the true east by north, marking this line by a second peg. Then I turned about and marked a line which made an angle of one hundred and twenty degrees with the east by north line, and which would lead down the beach.

I now proceeded to plant in the sand three poles about fifteen feet in height: one at the central point A, one in a prolongation of the east by north line, which pole we will call B, and the third in a prolongation of the angle line down the beach, which latter pole we will call C. The next thing was the measurement of a base line from the pole A, through C down the beach for a mile. This I did as accurately as I could with my rod measure; but it was a sort of work highly conducive, as you may imagine, to the backache, especially as I went over it three times to eliminate as much error as possible, taking the average of the three measurements. Nor was the third measurement completed much before it was time to go home.

Only one thing now remained to be done, and this I did the next morning. At the end of the mile line on the beach I erected a tall pole, which we will call D, and from it as a centre laid off a line thirty degrees from the base to intersect the east-by-north line or its prolongation, and marked the direction by a second tall pole which we will call E. Now, according to a simple problem in trigonometry, it will be seen that if I should sail out in my boat east of north from the cape, guiding myself by the two poles A and B, when I had brought the poles D and E into line having A and B in line at the same time, I should be a mile away from A in a true east-of-north direction.

Although I now went out every day to try the water, it did not grow clear. Finding the guide-poles barely visible, especially the more distant pair, I mounted a gourd on the top of each one, after which I had no further difficulty in seeing them. As it was some little trouble to take the bearings constantly, I rigged a buoy and anchored it at the spot where theoretically the galleon lay. I found the water about sixty feet deep; and the buoy—a large gourd attached to a line with a stone for an anchor—floated easily on the swell, with eighty feet of line. After this buoy was anchored I took down the guide-poles, marking their places with pegs, in case I should require to use them again. This I did out of a superabundance of caution, not that I believed any one else than myself—had there been any one else—could have read the riddle they told to me.

Every day for three weeks I went out to the shoal near the buoy and examined the water. It was getting gradually clearer; but had it not been for my recollection of the first visit made, before I had the water-glass, and of the appearance of the water at that time, I should have doubtless given up the attempt in despair. The remembrance, however, of the clear water, and the gleam through it of yellow sand, was not to be forgotten, and it kept up my hopes to the last.

The weather grew oppressively hot, and there came on one day a terrific thunder-storm followed by a gale of wind from the northeast which lasted two days and was followed in turn by fair weather, with a gentle southwest wind. When I went out again I found the water quite clear. I was very impatient to test the glass, so much so that I would not wait to make any trials until I had reached the neighborhood of the buoy. Here I lowered the sails and put the glass over.

I could see the bottom quite plainly. It was of clean sand and strewed with shells. Here and there was a fragment of sea-weed, sponge, or other ocean growth. A shoal of silver-sided mackerel dashed by, and numerous strange fishes came into view. One sort there was with long streamers extending from the tail, and a body banded with rainbow hues. I looked long and intently at the strange panorama unfolded to my view, and found when I raised my head that the boat had drifted half a mile to the northeast of the buoy. Then I hoisted the sail and ratched back beyond the buoy, and drifted again, with the glass over the side, watching the bottom for signs of the galleon. This manoeuvre I repeated as long as there was light enough to see. I found that I could not see the bottom after four in the afternoon, nor before nine in the morning.