The search pattern used to find the Scorpion was an early application of what's called "Bayesian search theory", which, interestingly, is used today by some email relay software to identify spam, but the general application is to find lost objects.

The first thing you do is formulate some hypothesis as to what could have happened to the lost object. That's important, because some of the hypothesis might involve the object being utterly destroyed, in which case a search is pointless and a probability of zero is assigned.

Next, define an area that you're going to search, and divide that area into a grid.

For each hypothesis, assign to each square in the grid the chance that the lost object would be found in that square of the grid if that hypothesis is true. In the case of looking for a sunk ship, you assign a higher probability of being able to find it in shallow water than in deep water, because it's easier to see things in shallow water, so in the case of a ship, areas of the grid with shallow water get a higher probability if the hypothesis is that it sunk and is still there (i.e. was not hijacked or was not blown to bits so small that it could be swept away by currents or has not slipped into a Bermuda Triangle worm hole etc.).

Now layer the grids for each hypothesis on top of each other and combine their probabilities.

Start searching in the area of the grid that has teh highest probability.

If that area turns up no result, move on to the area of the grid with the next most likely probability, but also do a recaclulation of the combined probabilities of the hypothetical possibility of the object being in each square of the grid by dropping the one you just searched, because if one of the hypothesis was heavily tipping the odds in favor of the area of the grid that you just searched, but was heavily disfavoring an area where the total combined probabilities made an area of the grid, say third, then without that first area's combined probabilities from all hypothesis being included, it might tip the odds so that now the next most likely place to find the lost object is not the one that had been ranked as third most likly, but is now calculated to be the second most likely place to find it, so as you go, the order of the grid areas that are searched might change.

Within each area of the grid, it's a simple sig-zagging back and forth.

Six months might seem like a long time to find the Scorpion, but actually, if people could understand just how vast the possible area was, and if they could understand just how dark it is down there, and how hard it can be to see things, such that there's a limite to how fast one can sweep over an area, they'd realize that six months is pretty darn good.

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