Here's a step-by-step that I wrote up a few weeks ago.

The number of steps will initially make it seem more complicated than it actually is, but don't hesitate to ask questions if something isn't quite clear.
Your instructions are clear and this will align the reticle with the muzzle. But does this ensure that the scope tube is also aligned with the bore? If the bore is angled slightly differently from the scope tube, won't shots at various distances shift left-right of the vertical reticle? Is there a way to check and fix any bore-scope tube misalignment without shooting?
 
Your instructions are clear and this will align the reticle with the muzzle. But does this ensure that the scope tube is also aligned with the bore? If the bore is angled slightly differently from the scope tube, won't shots at various distances shift left-right of the vertical reticle?
No, but the scope tube does not need to be precisely aligned with the bore. The erector tube does, since it is the thing we are looking through to aim.

In other words, if we didn't have a floating erector tube inside the scope body, and the ability to manipulate it via the turrets, we would need to be concerned with precisely aligning the scope tube with the bore.
 
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