"Under conditions of poor seeing, large instruments are relatively disadvantageous because the influence of air currents increases with the square of the entrance pupil diameter."
However, this is just a statement. I am missing an explanation why this should be so. Do you or someone else have an idea?
Why are larger scopes more affected by bad seeing?
It has to do with the coherence of the atmosphere above the objective. Generally, the coherence length is fairly small on the order of a few inches or more. When this coherence length is the same or larger and a given aperture, then that aperture defines resolution - not the atmosphere. In this case, the small aperture is providing diffraction limited images. This equates to about 8/10 Pickering or better.
Under those same seeing conditions, a larger aperture captures more of the varying coherence in the atmosphere - incorrectly called "seeing cells". This begins to disrupt the image (along with capturing more atmospheric tilt.) However, with a larger aperture this image is also smaller. So, the effect is seeing is a little worse in a larger aperture, but resolution is not entirely reduced. Up to a point, it will still outperform a smaller aperture provided a full blown speckle pattern has not erupted.
For example, say a 5" scope is operating in 8/10 Pickering. It is delivering diffraction limited images produced by the aperture most of the time. Here, the coherence length (R0) and the aperture are pretty much the same where the ratio D/R0 ~ 1. A twice larger aperture of 10" would experience something on the order of 6/10 seeing. The ratio of the aperture (D) to atmospheric coherence (R0) is D/R0 ~ 2. Conceptually, aperture is twice the diameter of the "seeing cell." In this realm, seeing begins to influence resolution but the smaller Airy pattern is still basically intact and very close to Lambda/D resolution is still possible. By 3 times the aperture, around 15", the speckle pattern begins to form grossly exaggerating the size of the image well into 2" to 5" arc, depending on the severity of the speckle pattern.
Larger scopes loose much of their resolution when the speckle pattern forms, otherwise they keep most of their advantage over small apertures during short exposures. With a given amount of tilt, smaller apertures will cause the star image to jump around pretty much in tact. In larger scopes beyond 3x the smaller aperture, it forms the ugly speckle pattern.
For example, a 5" scope in 8/10 Pickering will be diffraction limited and provide FWHM of Lambda/Dmm ~0.9" arc. A 10" scope, now with resolution influenced by those same seeing conditions, will have a (short exposure) resolution influenced by the coherence (R0) and FWHM of approximately 0.7 Lambda/R0 ~ 80/127mm ~ 0.63" arc. (Note: seeing FWHM is Lambda/R0, not Lambda/D.) This 0.63" arc is not as good as 10" FWHM Lambda/D ~ 0.45" arc found in 8/10 Pickering or better. However, it's still better than the more consistent and "pleasing" 0.9" arc 127mm can deliver in 8/10 Pickering. This is what Eddgie was saying.
I tried to keep the empirical math out of it but failed.
Edit: eyeballing your chart above, it looks like my 150mm aperture can do 50x/inch when seeing is better than 0.5" arc. This makes some sense because the diffraction limited FWHM is larger than that at about 0.7" arc in radius. However, it's limited to about 190x in 1" arc seeing. That's just beyond diffraction limited seeing putting it in about Pickering 7/10. That would put the seeing influenced FWHM at about 0.83" arc, maybe a bit larger. Since visual acuity is involved here, have to think about what they mean by that. I can easily see the Airy disc at 150x, thereabouts, so I should be able to see something enlarged by seeing with a bit less magnification.