I'd come across Iridology before, but Sclerology is new to me.

Sclerology is the study of the red lines in the white of the eyes and how they relate to stress-patterns in a person's health. Once you learn to interpret these lines, you will hold the key to understanding how the body is struggling or adapting to maintain balance; and thus know how to apply natural therapies to prevent problems from occurring or help the body correct problems already occurring.
Balance of what?

http://www.sclerology-institute.org/

Still, it is encouraging to see that I could become a sclerologist for about £400 - plus shipping, of course.

You can become a Sclerologist!

Become certified as a Sclerologist with the ISI Art & Science of Sclerology home–study Certification Course and, with this special internet offer, save $200!

DISCOUNT. With this Internet offer, this US$799. Certification Course can be yours for US$599. plus shipping.
AND! the course is accepted as a credit in a Degree Programme from (among others),
The University of Natural Medicine, Santa Fe, New Mexico.

Super.