You're simply mistaken about this. The source you provided does not claim that the spirit level works due to a difference in gravity acting on two points merely an inch apart. This would be miniscule.
A level line is a line in a level surface. A level surface
has all points perpendicular to the direction of gravity and hence is curved.
https://link.springer.com/chapter/10.1007%2F978-1-4757-1188-2_6For, if one imagines holding a spirit level near the intruding mass,
its extra gravitational pull draws the fluid of the level toward the mass thus forcing the bubble away.
https://history.nasa.gov/SP-4211/ch11-4.htm“Level Surface …A level surface is a curved surface,
every point on which is equidistant from the centre of the earth”
https://books.google.com/books?id=0fUIAAAAIAAJ&pg=PA72&lpg=PA72&dq=%22spirit+level%22+gravity+surveying&source=bl&ots=xhQKkEEHpa&sig=ACfU3U2MFyw7M0Z2wHWi6XpKaCDIZpFxHQ&hl=en&sa=X&ved=2ahUKEwiJpMKEztPkAhWP9Z4KHVD1DqkQ6AEwDXoECAsQAQ#v=onepage&q&f=false
Such a reference height is a level line or
level surface and is defined as a surface on which all points are normal to the direction of gravity as defined by a suspended plumb bob. Since the surface of the Earth is curved, level surfaces are also curved, as shown in figure 2.1.
https://link.springer.com/chapter/10.1007/978-1-349-07348-1_293. Level Surface- A level surface is a curved surface which at
every point is perpendicular to the direction of gravity…
https://books.google.com/books?https://books.google.com/books?id=G6UEAAAAMAAJ&pg=PA72&lpg=PA72&dq=all+points+equal+level+gravity+%22spirit+level%22&source=bl&ots=s6YXL10XzT&sig=ACfU3U1667EJZea_0bTNuyvlioZUPsam4w&hl=en&sa=X&ved=2ahUKEwic1frR5tPkAhU0Pn0KHaF8D_YQ6AEwDnoECAYQAQ#v=onepage&q&f=falseI'll make this as simple as possible. When all points are perpendicular to gravity, all points are the same distance to the center of gravity and therefore all points are subject to the same gravitational pull. When all points are not perpendicular to gravity, some points are closer to the center of gravity and are therefore subject to more gravitational pull. Since fluids will respond to any force acting upon it, and fluids are more sensitive to gravitational pull than solids, a fluid will be pulled lower when it is closer to the center of gravity due to the increased level of gravitational pull.
Knowing this, we can apply basic classical mechanics to estimate the time the bubble would take to traverse the 2.5cm tube if this, and nothing else, were the factor responsible for the bubble's movement.
I have no idea what those calculations are supposed to prove. Gravity doesn't move the bubble at all. Gravity determines where it falls when it is stationary and not subject to any other force. Have you ever even used one? An external force must be applied to move the bubble.
For, if one imagines holding a spirit level near the intruding mass, its extra gravitational pull draws the fluid of the level toward the mass thus forcing the bubble away.
To counter this effect the end of the level nearer the mass must be tipped up to recenter the bubble. In other words, the level surface tips upward as one approaches the mass.
https://history.nasa.gov/SP-4211/ch11-4.htmA fine-pitch tilting screw
is turned manually to center the bubble in the vial of the spirit level. Compensator instruments depend on a: pendulous reflecting component, the compensator, within the optical system of the telescope.
Responding to the attraction of gravity automatically renders the line of sight horizontal.https://www.ngs.noaa.gov/PUBS_LIB/GeodeticLeveling_Manual_NOS_NGS_3.pdf (page 3-11)
The bubble should sit between the graduation marks.
Where the bubble sits over or out of the graduation marks, adjust the left or right side. When the left side is too high the bubble will sit on the right side of the graduation marks and vice-versa for the opposite side. Using this as a guide, you can now make the necessary adjustment to create a perfectly level project
https://www.home-dzine.co.za/diy/diy-spiritlevel.htmThe only direction the bubble can move is along the axis of the tube.
Once that axis is perpendicular to gravity, gravity does no work on the liquid, so the bubble stays in a fixed location. https://forums.anandtech.com/threads/so-how-exactly-does-a-level-work.1745763/To use a spirit level, set the body against the surface that you want to level. Since liquids naturally seek their own level, the air bubble in the capsule will be perfectly centered between the marks on the capsule when the spirit level is level.
If the bubble floats to the left, raise the right side, and vice-versa.
https://everything2.com/title/Spirit+level The reason "up" is in the centre of the tube when the spirit level is level is the curvature of the tube.
The bubble shows "up" whether it is in the middle of the tube or not. It is always sits at the highest point of tube but only when it is level is the curve the highest point. If the level is tilted down to the right, the highest level will be slightly to the left of the curve and vice versa.
The reason "up" is in the centre of the tube when the spirit level is level is the curvature of the tube.
So UA causes things to move side to side? That is the only direction the bubble moves. As I pointed out above...it is always at the top of the tube and only moves side to side along the axis of tube, but it always at the top of tube. A spirit level with a barrel vial doesn't even have a curve.. the bubble only moves side to side along the axis of the tube.