Pit saws come in three forms. In addition to the frame and open pit saws shown in Sloane, there is also a version more or less like a really big turning saw. I've seen photos of this third form in use in Egypt and in East Asia.
American made open pit saws (the whip saw) were coming into California as early as the 1840s. These are more convenient to use, as the "box" is easily removable, making it less of a problem to start the next cut. I believe it is Sloane who shows a close up of the box arrangement, the box being held in place with a wedge.
It was kinda confusing, the term whip saw, because some of the two man cross cuts, the ones with really narrow blades, were also called whip saws.
The saw in your picture is a cross cut for use by one or two men. The handle on the end is not what that saw came with, but came off one of the two man cross cuts. The proper handle stands at 90 degrees to the back of the blade, and can be placed at the end to allow two men to operate it, or placed just in front of the tote for more control if only one man is using it. You'll notice a hole just in front of the tote of the one in your picture.