Miniaturists' Mathematics.  page 2 On measuring (If the idea of measuring makes you feel unhappy, go here for a section on Not measuring)

Frances Armstrong

Miniaturists' Mathematics.  page 2 On measuring (If the idea of measuring makes you feel unhappy, go here for a section on Not measuring)

My helper Max has a project under way, and to start off he needs to find the middle of a wall.  He has several rulers (and he is learning to call them "rules" as experts do).

This rule(r) is tiny by our standards, but a bit large for Max.

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Here is a bigger helper, Maggie, who, in the picture on the right, is trying to use that same little ruler.  We'll ask her to try the Real Thing, an architect's rule(r).  This is the one pictured below that is triangular in cross-section, and it's really confusing at first.

Maggie is trying to measure her doll (the one with her nose on the ruler, below).

Being quite small herself, she uses the part of the ruler nearest her, enlarged above. By luck or good judgement she has chosen correctly.  These architect rules have different scales on all three sides, and on each single side there are different scales that run upside down and/or backwards.  In the picture above left, you can see a "20" which seems out of place, and the upside down markings don't seem to match the ones at the top.

You can figure out for yourself what all these scales are.  Maggie and I will stick with the one I've enlarged above.  This is because it shows 1/12 scale: t he inch is divided into twelve parts. The twelfths are numbered backwards from 0 through 3 and 6 and 9 to an unnumbered 12.   In the picture below I've put the numbers in, in red.

So we can treat this little section of the architect's rule as if it were a small ruler on its own. We can use it for two scales: 1/12 and 1/144.  Here I'm going to make a digression and explain what is special about those two scales.

When we make a 1/12 scale model of something we take its measurements--height, width, etc.--and divide them by 12.  If we use a metric system, we might measure 96 millimetres and divide by 12 and make our model 8 mm long.  Using feet and inches, there is a kind of short cut.  If what we measure is 60 inches long, we can recognise that that is 5 feet, and then make our model 5 inches high.  This is of course the same thing as dividing those 60 inches by 12; we could forget about "feet" and work entirely in inches.

When we make a 1/144 scale model, we could similarly divide our inches by 144, but many of us find that using "feet" is easier. We take those 60 inches and call them 5 feet, and then we look at a ruler like the architect's rule and measure directly in twelfths.  Each of those red numbers above marks a miniature foot.

So there's no need to divide anything by 144, as long as you think in feet.  Compare the pink footprints with your own foot. and you'll have an instinctive notion of the scale 1:144. If you were wondering how big a 1/144 inch is, divide the footprint into 12 and you'll see that a single inch is practically invisible to humans.  In  the picture above. the smallest division is 3 inches: from a red line to a green line is 3 scale inches, and from the green line to the blue line is also 3 inches.

If you fell asleep during all that, it doesn't matter.  To make things in 1/144 scale you need to be either highly trained or highly playful.  This last picture should give a clue as to my own attitude.  That chair was very difficult to carve, and still is too clumsy to be well scaled, but  the dolls like it and I had fun.

Since dollhouse miniatures are usually concerned with people (real or imaginary) and their houses  and belongings, what matters is that a chair should fit the person sitting in it, not its measurements in inches or even in metres.  As I've said several times, a bed is about as long as a person is tall, a tabletop comes about half-way up a person, a chair seat is about a quarter of the way up.  A door is also about as tall as a person. Miniature stores and shows will understand if you pull Maggie out of your pocket and let her try out a chair, but if you work in 1/144 scale it will be more difficult to explain that you want to check the beads in a necklace as seats for a nearly-invisible doll.  So when you are feeling shy, take out your favourite toothpick and use it to size up possibilities.  Sand off the very sharp tip or tips, and then mark off a length of a bit less than half an inch (about 22 mm).  You can use the turned end if you have that kind of toothpick, improving the proportions if they aren't to your liking. You can make a whole pursefull of little measurers,  human or inanimate.  Attemtping to do this may actually be an education in itself: try to mark off how long a 1/144 teapoon would be, and you'll probably decide that it's not worth the making.  Or with the perversity typical of small-scale enthusiasts, you may just be more eager to take on the challenge.

Not measuring