What we're talking about here is the topsail halyard (or halliard). More precisely, the tackle consisted of at least two ropes, called the tie (or tye) and the halyard of the tie. (The lifts are different lines; they run from the topmast head to the ends of the yards.) That photo is hard for me to read, at least on my not-very-big monitor.
James Lees's The Masting and Rigging of English Ships of War, 1625-1860, shows several methods of rigging the tyes and halyards. Lees says the typical arrangement for the period after 1810 included four large, single blocks, two hooked under the topmast trestletrees and the other two stropped to the yard, a few feet on either side of the center. The tye in the accompanying drawing is looped around the topmast head just above the crosstrees, with both ends leading down in front of the foremost crosstree. One end of the line goes through each of the blocks on the yard, then up to the block under the appropriate trestletree. A single or double (depending on the size of the ship) was seized in each end of the tye, and a tackle was set up between that block and one hooked to an eyebolt in the channel, inboard of the deadeye for the second topmast backstay. I can't tell whether that arrangement matches the one in the photo exactly - but it seems close.
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