These formulae are now available by choosing help>algorithms from the analyze bar menu.
Formerly one could access these on-line by going to here. You also now need to register with SPSS technical support to access these algorithms (just click on the link) at the above website. You will be e-mailed a login password and username. Go back to the website and login. Then click Statistics Documentation twice firstly in the left hand menu and then in the main window. Then click algorithms. The algorithms manual will then load (this may take a minute or so). Once the manual has loaded it may be browsed, printed or downloaded. The manual contains details of algorithms underlying all the SPSS procedures. From SPSS version 16 in the help menu there is an algorithms option which also contains all the formulae used in statistical procedures in SPSS.