Many thanks to all who responded to this request, all but one being that you
looked at what other libraries were doing an priced accordingly.  My
particular thanks to Howard Nicholson at the University of Bath for the
suggested formula from which I have then developed my own.  I'm not
suggesting this is the definitive answer, but it might be useful.

Library and Information Research News spotted this item and asked me to turn
it into a short communication for them which I have done so, as you can see
drafted below.

Any further thoughts or ideas on this are very welcome.

Adam

Learning and Information Research News Short Communications 
Charging For External Users
1       Name & organisation of investigator(s):
J. Adam Edwards, Head of Learning and Information Services, Central School
of Speech and Drama
2       Library sectors covered by research (e.g. academic, public, special
libraries):
Academic
3       Reasons for carrying out the survey:
Central School of Speech and Drama runs the International Centre for Voice
(ICV).  The ICV wish to offer library borrowing as part of the full
membership fee. CSSD library is happy to agree,  as it will receive extra
books funded by the ICV.  ICV looked at competitor organisations and feel
that a fee of around £40.00 would be viable. This is less than our current
Alumni rate for external membership, so, in order not to give an unfair
advantage to the graduates from our MA Voice Studies course who would
qualify to join ICV, we proposed reducing our fee to match. Like most of the
responses to this survey, our current fee had been derived by looking at
what other libraries charged. Our Deputy Principal asked for calculations to
show what the Library costs are as evidence to show the auditors.  The
School is quite happy for the price to be a loss leader if this can be
justified.
4       How the research was carried out (including lists to which any
survey was posted):
Email were sent to both lis-sconul and lis-link asking for formulae used
elsewhere.  
5       Questions asked:
Has anyone worked out a costing for external membership rather than looking
at other libraries charges and coming up with a similar figure?
6       Number of responses:
Several from libraries who simply match what other nearby libraries do.  One
formula from the University of Bath.
7       Results & conclusions (100-500 words):
University of Bath responded to my email as follows:

We find that on average external usage rates track full-time on-site
undergraduate student usage rates at around 25%. We know that our current
funding is about £350 per FTE u/g student, so use this as a very crude
yardstick in considering the level of external fees. Of course, there are
enormous differences according to level of study and subject, but some of
these are likely to be subsumed within your fixed costs to provide a service
for your own users. But I would give you a completely different figure if
you asked me to quote for a per capita ticket for a drug company's
researchers using this Library, obviously.
The real consideration is are you charging to encourage or deter take up?
The level of fee should be set accordingly.
Howard Nicholson

This idea prompted me to look at the numbers of different borrowers we have
and the borrowing use of the library.  Given that we need a simple measure
of library use and given that the use is likely to involve staff time in
helping an unfamiliar users, my formula is:

(Library budget inc staff and materials / Number of issues) x Mean issues
per external user

For CSSD this is £111,704 / 44071 = £2.53 per issue x (119/5) = 23.8  

This gives a membership fee of £60.21 per annum.

Clearly basing the calculation purely on issues is very simplistic, but at
least gives a basic model.  Other suggestions are welcomed.
8       How the results affected the practice in your library: (100-250
words)
We changed the External Membership rates to

                £40.00 inc VAT for Alumni and ICV members and 
                £100.00 inc VAT for other externals 
9       Is a full report available?  (Please give details)
No



        > J. Adam Edwards
        > Head of Learning and Information Services
        > And Convenor - UK Libraries Plus
        > Central School of Speech and Drama
        > Embassy Theatre
        > Eton Ave
        > LONDON
        > NW3 3HY
        > 
        > Tel:                          020 7559 3995
        > Fax:                  020 7722 4132
        > Email:                        [log in to unmask]
<mailto:[log in to unmask]>  
        > Internet:                     http://www.cssd.ac.uk
<http://www.cssd.ac.uk>   
        > UK Libraries Plus:            http://www.uklibrariesplus.ac.uk
<http://www.uklibrariesplus.ac.uk> 
        >  
        > Central School of Speech and Drama provides government funded
further and > higher education courses in acting, art, arts management,
circus, costume, > design, directing, drama and education, drama and
movement therapy,
        > dramaturgy, lighting, media education with English, musical
theatre, > performance, prop-making, puppetry, scenic art, scenic
construction, > scenography, set design, sound, stage management, technical
theatre, voice and writing.
        > The Central School of Speech and Drama, a company limited by
guarantee in > England no 203645. > Registered as a charity no 312564.
Registered office: Embassy Theatre, Eton > Ave, London, NW3 3HY.
        >