It's 1862 and the self-centering 3-jaw chuck has yet to be invented, so how does one centre a job before turning it? The ultimate way of achieving concentricity is to use a collet (originally called a 'split chuck) drawn by a threaded tube against a tapered socket formed in the front end of the headstock spindle. This method had been invented a few years earlier, in 1857/1858, by Charles S. Moseley but, being patented, took time to be widely adopted - and, no doubt not wishing to pay a fee to use it, other inventors came up with alternative (and always inferior methods). Hence, Jackson's 'chucking apparatus' patent is not the invention of a new lathe, but an example of a rather involved method of achieving the alignment of a job before turning it. Like those proposed by other inventers in the 1800s, including St. John, Shaller, Hopkins and Kesselmeir, it was not an automatic system and required the operator to manipulate the assembly in order to achieve the desired  alignment
An attempt to strip out some of the legalese of the patent text (which is attached in full below) and describe what the inventor intended might read:
To all whom it may concern: Be it known that Gamil Jackson, of Cincinnati, Hamilton County, Ohio, has invented new and useful improvements in watchmakers' lathes. These improvements allow cylinders, shafts, pinions, and other pieces of watch-work to be held on any part of their diameter and then adjusted to run true. Figure 1 is a perspective view of an ordinary watchmakers' lathe with my "faceplate" or "chucking apparatus" attached; Figures 2, 3, 4, 5, and 6 show its various parts, and Figure 7 is a vertical section of these parts.
First Part of the Invention: This involves fastening the work to be turned in the lathe. The 'grasping apparatus' slides on the headstock spindle using two parallel rods to which it is permanently fixed and allows the job to be gripped at any part. When secured, one end of the job projects through the gripping apparatus while the other rests in the head's stationary center.Second Part of the Invention: The involves adjusting the work to run true. The chuck containing the article to be turned moves on the spindle end via a ball-and-socket joint. This ensures the socket center aligns with the lathe's head-center, where one end of the job rests - while the other end is adjusted in line with the spindle. This method of adjustment differs from previous methods in that one end of the job remains stationary while the other end is adjusted.
To help those skilled in turning understand my invention, here's a detailed explanation with drawings.
Figure 1: Perspective view with all its parts in place.
Figure 2: Straight cylindrical chuck, one end of which is tapered and held in a socket in the lathe spindle. The other end terminates in a hemispherical head, double the diameter of the body of the chuck. A portion in the middle is enlarged for a screw, to which the tightening-nut in Figure 4 is fixed. In the enlarged end is a spring-center (a), explained later.
Figure 3: Hollow hemisphere with an inner surface (b) matching the head (c) in Figure 2. It has three parallel holes at right angles to its plane surface, one through its center continuous with opening (b) to allow the job to play freely on the head (c). The other holes are smaller and positioned about the middle of the rim (shown at d d). Tightening-screws (e e) reach holes (d d). The tightening-nut and washer (f g) in Figure 4 tighten on the head in Figure 3, holding it against the spindle head (c) in Figure 2
Figure 5: A thin circular plate fitting into the recess (h) in Figure 3, secured by screws (i i). The center of this plate (k) forms the center of motion of the ball-and-socket joint and is so unaffected by ant motion of the joint
Figure 6: A circular plate with jaws moving from the periphery towards the center. Parallel rods (l l) fastened to this plate to correspond with holes (d d) in Figure 3, through which they slide and secured by thumb-screws (e e).
Figure 7: Vertical section representing a piece of work secured but not adjusted.
Operation of the Lathe:
1. Tighten the nut (f) to hold the head steady while securing the work. Open the holding jaws (m) to allow the job to enter, placing one end of the job (o) in center (k) and the other end through jaw-plate (n). Move the jaw-plate to grasp the job on any desired part and secure it with screws (e e). Bring the jaws together on the job to secure it ready for adjusting, as seen in Figure 7.
2. To adjust, turn back the tightening-nut (f) to allow the head holding the work to move freely on spindle-head (c), held lightly against it by spring-center (ct). With the lathe spindle revolving and a smooth-pointed rod held against the free end of the work, bring it in line with the spindle. Secure it with a turn of the nut (j) ready for turning.
Claims:
1. The arrangement of grasping apparatus on parallel adjustable rods (l l) to grasp the job at any part, with one end resting in a stationary center.
2. The application of a ball-and-socket motion to the head of a lathe, allowing one end of a job to be adjusted while the other end rests in a stationary center.