I have a person who was discharged from the British Army "discharged under para 1805 (iii) (4)".
Anyone know what that means, or where I can find the text of that regulation (preferably online)?
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There is a list of discharge reasons under the 1912 regulations here which includes links to images of the actual text.
Assuming that paragraph (iii) in the 1805 regulations was basically the same then the reason would be "Not being likely to become an efficient soldier".
It looks like the British Library have a large number of editions of King's Regulations of various dates if you want to try and find the exact detail of the regulation.
There's a dreadful ocr'd copy of a Manual of Military Law 1907 at http://archive.org/details/manualofmilitary00greauoft which may help. I haven't searched for other relevant books.