Dalgliesh or Dalgleish

[scotglas]

Never seen second spelling in relation to P D James' detective

[berny]

dalgliesh is the correct spelling but for this answer you have to alter the position of the e & i

[xcutter]

I checked my Chambers Biographical to make sure and it gives the spelling as Dalgleish.

[Fibonacci]

http://en.wikipedia.org/wiki/Adam_Dalgliesh