# Gravity goes downwards

By Marcus Wilson 06/08/2013

Yesterday afternoon I was engaged in a spot of DIY – putting up some shelves. Even for me, as someone who takes to DIY like a duck to mountaineering, it’s a fairly simple task, and I’m pleased to say that I got there without the ‘do’ in DIY turning into ‘destroy’. With the help of my trusty stud-finder (Karen – who has a knack of locating those invisible studs behind plasterboard walls just be tapping), I managed to locate two studs by drilling just three holes. The rest of the job took only four tools – a drill, a pencil, a screwdriver and the all-important spirit level.

I’ve always been fascinated by just how simple a tool the spirit level is. It does a fantastic job of getting things level (level enough for general domestic purposes, anyway), just by using a bubble of air in a liquid. The physical principle by which it works is hardly taxing – the bubble (the lack of fluid) rises to the highest point in its tube, as the liquid sinks down as low as possible to minimize its potential energy. A similarly simple method – the plumb line – gets things vertical – though a second tube turned by 90 degrees on the spirit level turned through 90 degrees can do the same task.

In fact, it is hard to imagine a complicated machine to find where ‘vertical’ is. If one assumes that ‘up’ is the opposite direction to the force of gravity, one simply has to measure the direction of the force of gravity, and hanging something on a string is the most obvious method to do it. Sure, one can get technical and enclose the thing in a pipe so that wind doesn’t get to it, and so forth, but the basic weight-on-a-string is simple and effective.

There are some hiccups to think about, however. One needs to be sure what one actually means by ‘vertical’ and ‘horizontal’. The force of gravity isn’t precisely towards the centre of the earth at all places on the earth’s surface. A weight on a string will be affected by the presence of nearby mountains, or large-scale variations in the geology underneath the surface. A quick estimate based on Newton’s law of gravitation and the size of mount Te Aroha, for example, suggests that houses in Te Aroha town might have their vertical distorted by a few thousands of a degree. Not a great deal but enough to be detectable with half-decent equipment.

But is the vertical really out? If the definition of a vertical is "the direction of the acceleration due to gravity" then, no, it isn’t. If one is putting up shelves in Te Aroha and wants them horizontal (so that a ball placed on the shelf stays on the shelf) one wants them at 90 degrees to the local force of gravity. If that means a few thousands of a degree different from what you’d get in Hamilton, then so be it. It just depends on your definition of ‘up’.

[And, of course, it is more than a few thousands of a degree different from Hamilton anyway – being 44km away on a sphere of 6400km radius, that’s about 0.4 of a degree due to location.]