Whats the gradiant from east finchley to highgate then?

I'm sure Mark Brader will be along to correct me in a minute ;-)

Chortle.

but from memory it's something like 1 in 50 or 1 in 60. The issue
with that one is that it goes on for so long and has a reasonably sharp
horizontal curve near the bottom, making runaway trains a potential
problem. IIRC this was the first place on LU (or perhaps the world)
that signalling to detect and stop speeding trains was introduced.

After explaining the renaming of the original Highgate tube station to
its present name Archway, RTTC says:

# At Archway the running tunnels had continued for a short
# distance beyond the sttaion to provide to dead-end sidings.
# The northbound siding was extended to form the northbound running
# tunnel to East Finchley, and the southbound was retained as a
# nine-car reversing siding between the two running roads, with
# the new southound running tunnel joining the old from the east
# side, just north of the station. Since this tunnel came in with
# a 990ft radius curve at the foot of a long 1 in 50 descent from
# Highgate, speed-control signalling was installed to ensure that
# southbound trains kept within the 30mph limit. Two successive
# signals would clear only if the train passed through the two
# timing sections at less than 40 and 30mph respectively. If a
# train had exceeded these limits, and was held at the signal
# as a result, the signal would clear automatically after it had
# been brought to a standstill. During the 1960s, speed-control
# signalling was also installed to reduce the speed of southbound
# trains entering Highgate station, where heavy braking caused
# noxious fumes.
#...
# From Highgate, the line continued beneath the LNER in 12ft
# iron-segment tunnels, at first rising at 1 in 61 and then at 1
# in 100. Near the tunnel mouths there were short stretches of
# 1 in 50 northbound and 1 in 40 southbound.

So this source doesn't say anything specific to answer the question,
except to mention a "short stretch" at 1 in 40, and the need for
"heavy braking" on arrival at Highgate. But John's 1 in 50-60 sounds
reasonable enough, even if he did confuse the two installations of
speed-control signaling.
--
Mark Brader | "We may take pride in observing that there is
Toronto | not a single film showing in London today which
| deals with one of the burning issues of the day."
| -- Lord Tyrell, British film censors' chief, 1937

My text in this article is in the public domain.