🚀 go-pugleaf

>Does anyone know where you can get the 'gadget' which is attached
>to a bicycle and then used to measure distances? 

Bike shops.   

>I know they are
>often used by race officials to lay out a certified course.
>What are they correctly called?

Bicycle computers.   Briefly, there are many models.   You only need
the most basic as I presume you're not interested in speed, max speed,
time elapsed or altitude of the bicycle.   They are only as accurate 
as the wheel circumference calibration you enter into the computer (read the
manual): you should measure wheel circumference whilst the bike is weighted
with the rider, at precisely the tyre pressure you intend using during
the measurement.   This is best achieved by painting some bright and viscous 
substance in a narrow line across the tyre and riding slowly down a smooth 
path.   Measure distance between the marks.

Certified courses are ***not** measured with bike computers, but with a
hand-pushed wheel with a solid tyre (to reduce pressure variation), bearing
a device similar to a bike computer.   The odometer on older models operates
mechanically rather than electronically.

Cheers,

Frith

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Frith Brown                           E-mail:  F.Brown@massey.ac.nz
Department of Plant Science Level 2   Phone:   +64 06 356 9099 ext. 8800
Massey University                     Fax:     +64 06 350 5614
Palmerston North                      
New Zealand                :-) Ride the bike, ride the bike, ride the bike ;-)
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