Merge the layers and hit Alt/Opt + Cmd/Ctrl + F to access the last filter. Choose the Rectangular to Polar option, which gives you a squashed sphere. To remedy this, select Image > Image Size, uncheck Constrain Proportions and check Resample Image make its height the same as its width. Next, magnify the sphere using the Pinch filter, using a negative percentage to shift pixels away from the centre (I used -86 per cent).
You can now drag and drop the ball into your working document, at the transparent canvas area you created in Step 08. Position it between the hand and finger layers; use your Alpha channel again to help position it. Don’t worry about the sphere being slightly oversized – use an inverted Alpha channel selection to trim the overlap. In the real world, objects viewed through a solid glass sphere appear upside down – replicate this by simply rotating the sphere 180 degrees.
Polar coordinates work best with images with non-specific details, so use a different technique to distort the buildings. Target the buildings layer and draw a square selection, this time making it approximately 20 per cent larger than you did in Step 06. Float a new layer, rotate 180 degrees and select Edit > Transform > Warp. Use a custom warp to bend the buildings into shape. I also ran the Pinch and Spherize filters.