Starting with your cylinders around arbitrary minor axes, your work here is largely well done and I'm pleased to see a fair bit of improvement. Towards the beginning you weren't doing too badly, but the side edges tended not to necessarily fit together with the ellipses quite right, and you had a tendency to draw many of these with basically no convergence towards a vanishing point. This would be a mistake, as it would only occur when those side edges were aligned such that they run perpendicular to the viewers' angle of sight (the conditions under which a vanishing point "goes to infinity" in the manner discussed in Lesson 1). Since we're drawing cylinders that are rotated freely and randomly, the changes of that would be so low that we may as well always incorporate some amount of convergence, even if only very slight.

As you progressed through the set, you did push that foreshortening a lot more, incorporating much more variation, and in the process, also demonstrating that you appeared to understand - whether subconsciously or consciously - the manner in which the two "shifts" from one end's ellipse to the other operate in tandem. That is, the shift in scale where the far end is smaller overall than the closer end, and the shift in degree where the farther end is wider than the closer end.

These two 'shifts' both convey how much foreshortening is being applied to the cylinder here, telling the viewer whether the cylinder's length is equal to what we see on the page (in the case of shallower foreshortening), or whether more of its length exists in the 'unseen' dimension of depth (in the case of more dramatic foreshortening, like what we get when the cylinder is coming right at the viewer). It's critical that these two shifts operate together - if one is extreme, so too should the other, and if one is shallow, the other should match, so as to create a consistent impression.

So! If it was conscious, my explanation was redundant, but if it was subconscious, hopefully my explanation will have solidified it further.

Continuing onto your cylinders in boxes, your work here has come along quite well. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).

Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.

Through your correct, consistent, and conscientious use of the line extensions, you've definitely made a good bit of improvement with your estimations of the cylinders' proportions, and while there is certainly more room for continued growth, that's perfectly normal. I do however believe you're well equipped to weather the storms of the next lesson, and what you've developed here should serve you nicely.

I'll go ahead and mark this challenge as complete, so keep up the good work.