The message
from The Natural Philosopher contains these words:

Both ridge and purlins only serve to stop the rafters moving sideways.
(Euler buckling etc,). They have very little structural effect beyond
that. The rafters transfer all the loads to a downwards and outwards
force at the eaves level: That's where you need serous material.

Sorry TNP but I don't buy that argument. Purlins are often very
substantial pieces of timber and with a heavy roof they need to be. Very
few roofs have a pitch greater than 45 degrees so if the load is
resolved into rightangle components only half or less is being
transmitted directly down the rafter.

If all that was needed to be done was to stabilise the rafters a dinky
bit of 4" x 2" (likely the same section as the rafters) nailed flat
against the rafters would do.

I am quite sure that if I nailed a few bits of 4 x 2 across my rafters
and then cut out the purlins most of the 20 or 30 tons of stone on my 30
degree roof would promptly join me inside the house. Rafters are only 4"
x 3" (or 4 x 2 where they have been replaced) but the clear span is
never more than about 4 feet (which is perhaps half what you might
expect for a lightweight slate roof).

--
Roger Chapman