Would a horologist only work on small timepieces, like watches and mantel clocks? Or would horologists be called for big clocks such as Big Ben?

It’s the craft of timepieces. Big or small is not the point.

Big Ben is just as intricate a piece of machinery as a regular clock. Just the weight of a penny applied to its pendulum will slow the clock down. Bigger clocks seen by the public must be kept accurate—especially with a reputation like British Parliament

^^^^Mass does not affect the swing rate of a pendulum. You could add a five lb weigh to the pendulum of the Great Clock and it would not change the swing rate,

Big Ben is the striking bell of the Great Clock. And yes, it is worked on by horologists.

Some small weights, such as coins, have been added to the mechanism of Big Ben’s clock to make it more accurate. Certain of these coins have been there for a very long time. The driving force of a clock such as Big Ben is driven by weights. I believe the weight of the pendulum is important, but what is more important is the position of the weight on the pendulum itself. Like a cuckoo clock that you might have on your wall. Lowering the weight will slow the clock down while raising the weight will make it speed up. If a slight amount of extra weight is allied to the driving weight, it would speed the clock up while removing weight would slow it down. Adding a coin at this place (on the weight) would affect the long term accuracy of the clock. A very fine adjustment, this.

I agree with @kritiper and not @zenvelo in this case.

There is an exact science in how much weight added to a pendulum will slow a clock down, and by how much.

@Yellowdog There is a difference between the drive weight and the mass on a pendulum. @kritiper was speaking about the drive weight, the weights that hang from a clockwork mechanism to keep the clock ticking.

Pendulum swing rate is dependent only on the distance from the pivot point to the center of gravity of the weight, not on the mass.

LONDON (Reuters Life!) – A pile of old coins which have helped keep the clock mechanism of London’s Big Ben accurate for the last 150-years were replaced on Thursday by a new five pound ($8.29) coin to mark the 2012 Olympics.

The pre-decimal pennies are stacked on the pendulum of the clock and have acted as weights to help regulate it since 1859 when the clock tower was completed and the first strikes of its 13.7 ton bell, nicknamed “Big Ben,” were heard.

The center of the ,mass of the pendulum are where the pennies are applied.