The surviving pattern published in Juan de Alcega’s ‘Libro de Geometria, Practica y Traca’(1589) represents almost everything we know about the farthingale. Most articles on recreating the Alcega farthingale focus on faithfully reproducing the pattern based on fabric widths. Honestly, though, calling this a “pattern” is a bit of an overstatement: the book was more intended as a series of cutting diagrams to help tailors avoid waste. The problem is, Alcega included some rather sharp commentary on on what he considered the proper size for the bottom hoop of the farthingale, but no real information on the size of the intended wearer. Complicating things further, modern bodies aren’t build quite like the popular model of the 16th century. So what’s a costumer to do? How about some trigonometry!
Trust me, this won’t hurt. Well, it won’t hurt me, at any rate. Then again, I wandered away from the tv in the middle of an “important” football game to start a trigonometric analysis of Janet Arnold’s reproductions of the Alcega farthingale… My idea of pain might differ from yours. (“But honey, football makes me feel stupid -can I go play trig instead?”) Why trigonometry? Glad you asked. See, trig is the study of angles. And when you’re trying to make a support skirt to correctly recreate a period silhouette, angles are everything. If the skirt is too wide, you look more like you’re fleeing Union troops than the Spanish Armada. And if it’s too narrow, well, it looks like you forgot something (and it’s hard to walk!). By doing a little math, we can figure a good approximation of the angle of the original skirt. Great! But that’s only half the battle, because the skirt needs to be proportional to the wearer. But the terms “too wide” and “too narrow” are entirely relative to the wearer – put a willowy girl in the hoops that look right on me, and she’ll look all antebellum. Put a larger lady in the same, and the look a little confined. Different hoops for different hips, I guess.
I’m going to use Janet Arnold’s work with the Alcega farthingale as a jumping off point here because a) she was a far better researcher than I will ever be, b) most people firmly believe in her work, and c) I’m lazy. That said, you can find Arnold’s work on the Alcega farthingale in Patterns of Fashion (p7) or in Queen Elizabeth’s Wardrobe Unlock’d (p196).
While Alcega himself gives no indication of where or how boning should be used on the farthingale, Arnold worked her reconstructions with 6 hoops, beginning 13″ down the skirt and placed into 1.5″ tucks spaced 6″ apart. (Got all that? Great!) She states that this creates a skirt that will correctly fit a woman of approximately 5’2″. Generously, she also gives us the size of the hoops in her reproduction. We don’t know the waist or hip sizes of the wearer, nor indeed her waist to ground measurement. (“About 5 foot 2” is a little vague for my tastes as a pattern maker. I’m picky like that.) So we’re actually going to analyze the size of the hoops, rather than the overall size of the skirt.I’ll be the first to admit that I’m making a massive assumption here, and that is that the Alcega farthingale was intended to make the skirts appear to fall smoothly and at a consistent angle from the waist/upper hip. Looking at Spanish portraits of the later 16th century, I feel fairly confident making this assumption…
So, let’s take a look at what we’re working with:
We are specifically interested in the hoops, and how they relate to each other. Now, I’m a visual learner, and I really like to color code things:
It kinda looks like one of those toys for babies with all the brightly colored plastic donuts that go onto a plastic spindle, right? They’re supposed to teach the kid how to stack things in order of size or something. (That’s not a bad analogy for how a hoop skirt works, really…) Now, these circles are stacked one over the other, and they share a common center point (concentric, as it were). That’s because they’re all suspended from the same skirt, and some pretty amazing contortions would have to happen to knock things out of line. If you looked at them from the top down, you’d have this:
Make the rainbows stop! It’s getting too happy in here! Ahem. Now, seriously, you can think of the hoops as a series of circles, each one a little larger than the one above it, all stacked right on top of each other. And that specific definition is really important, because it means that the distance from the center of any circle out to the edge (radius) is the radius of the circle directly above it plus an extra bit. And that’s absolutely fantastic, because that gives us…. <drum roll, please>
Triangles. That’s exciting (no, really, it is!), because the goal of all trigonometry is to get to triangles. We even know some stuff about these triangles: the slanty side is 5.5″ long, because that’s how far apart Arnold put her hoops. The bottom is the radius of hoop less the radius of the hoop directly above. The tall bit… Well, we have no idea yet. And ultimately, we don’t care. Actually, we don’t care too much about the length of any of the sides – what we really want to know is the angle of the slanty side. Let’s take a quick review of our basic right triangle:
There’s a 90 degree corner at the bottom left, traditionally marked with a little square. Across from that is the angle we want to find. The slanty bit has been renamed Hypotenuse, and the remaining sides cleverly called Opposite and Adjacent. (These are named relative to the angle we’re trying to find, by the way. Only poor ol’ Hypotenuse gets stuck with her name.) Now, the super-cool thing about trig is that it is the study of how the lengths of the sides of a triangle relate to the angles of a right triangle. If I know the lengths of two legs, I can use trig to find the missing angles. The Hypotenuse is a gimme: it’s 5.5″. I can figure out the length of the Adjacent side with a little circular jiggery-pokery: its the radius of the current circle (hoop), minus the radius of the hoop directly above.
Let’s start with our smallest circle, representing out topmost hoop. If you jump back to that last picture of the skirt, you’ll notice that there is no triangle above the top hoop. There isn’t enough information for us to figure that one out, because we don’t know the waist/hip side of the original wearer. But this circle’s radius is crucial, because it’s going to provide the base measurement we need to figure out the rest of the hoops. Arnold lists the size of this hoop (circumference) as 58″. Ooooh, that’s circumference, and we need radius – time to divide by 6.28! (Because circumference = 2 X pi X radius, or 2 X 3.14 X radius, or 6.28 X radius.) The radius of the uppermost hoop is 9.231″. Great. The second hoop is listed at 68″. Divide that by 6.28, and we get a radius of 10.823″. Fab! Now we have the radius of a hoop (10.823″) and the radius of the hoop directly above it (9.231″), so we can subtract them and know the length of the Adjacent side of the first triangle. It’s 1.592″, incidentally.
Ok. What exactly do we do with that knowledge, missa? Funny you should ask…. Trig is the ratio of two sides of a right triangle, which quite magically tells us the measurement of the an angle. In this case, we know Adjacent and Hypotenuse, and all the cool kids in Triglandia know that Adjacent-over-Hypotenuse is the definition of a Cosine. (This is important primarily because there’s a button for it on your calculator. This button will be of approximately no help.) If we divide Adjacent (1.592) by Hypotenuse (5.5), we get a very small number – .289, to be precise. What we do with that number is important – we’re going to look it up in a Trig Table, which is a time honored tradition. A cosine of .289 corresponds to an angle between 73 and 74 degrees. (That cosine button on your calculator? Yeah, it takes an angle measurement and hands you back the same decimal you got by the Adjacent-over-Hypotenuse trick. For us, it’s only useful for narrowing things down a bit – a little plug-n-chug tells me that the exact angle is 73.18 degrees.)
We could call it done right there, but why stop at one? (I’m labeling the angles with the letters I’ve used on the skirt pictures. H is red, I is orange, J is yellow, etc…)
Calculations for the Arnold Farthingale with Tucks
|Angle||Hoop Radius||Difference from Preceding Hoop (Adjacent)||Cosine (Adjacent/Hypotenuse)||Degrees|
Now, I’ve personally always wondered one thing about Arnold’s take on the Alcega farthingale. Arnold chose to put her hoops in 1.5″ tucks. Why tucks? They’re hard to sew in a cone shaped skirt – I’ve tried, and it’s a mess because the bottom part of the tuck is larger than the top. I’ve seen examples of support skirts from the 19th century that use tucks to hold ropes, but the earliest support skirts in Norah Waugh’s Corsets and Crinolines show applied bands to hold bents. Also, the earliest examples of support skirts in art show contrasting bands of fabric holding the bents. So, it’s easier to make the skirt with applied bands to hold the hoops and at the very least, it is not any less appropriate to the period. But does it make a difference in the overall silhouette? I redid the math, this time using a Hypotenuse measurement of 7″ (the original 5.5″ plus the 1.5″ of the tuck). Here’s the chart:
Calculations for the Alcega farthingale, using Arnold’s hoop measurements and no tucks
|Angle||Hoop Radius||Difference from Preceding Hoop (Adjacent)||Cosine (Adjacent/Hypotenuse)||Degrees|
So, again, visual learner over here…. The numbers don’t mean a lot to me, so I grabbed my handy-dandy protractor (because, surprisingly, I couldn’t find a simple little program to do this) and draw up the angles on a 1/8″=1″ scale:
The Arnold version, with tucks, is on the left. It has more of a flare than the untucked version, on the right. I did a little more math, to calculate the overall angle of each skirt. (Radius of bottom hoop minus radius of top hoop for Adjacent, and the sum of all Hypotenuse sides to compute the cosine, etc.) The Arnold/tucked version has an overall angle of 70 degrees, while the untucked version has an overall angle of 75.5 degrees. All in all, unless you’re reallyreallyreally tall, it’s not a huge difference. I like compromise, and this is far from an exact science no matter how much math I throw at it, so I’d say about 73 degrees is a pretty great angle.
Ok, we’re almost done. In fact, the rest you can do on a calculator – no charts involved. The title of this post says something about recreating the Alcega farthingale for modern bodies – that means keeping that 73 degree angle, but starting with your own waist measurement. This time, since we have the angle and some trig background, we’ve got a simple formula: the cosine of 73 degrees multiplied by the length of the skirt. Add to this the radius of your waist, then multiply the lot by 6.28. Or, 6.28((cos(73) X skirt_length) + starting_radius) .
I’ll leave you to do that up as a nice little bit of math-therapy. What? You don’t find math therapeutic? How odd. Well, gosh golly gee darn…. Next you’re going to tell me you don’t believe in knitting therapy, spreadsheet therapy, filing therapy, or .. Ok, tell me we can at least agree on martini-therapy. Please? Great news: I’ve done up a sheet with all the maths for waist sizes between 20 and 64″, in 5″ increments, for waist to ground measurements up to, er, 57.4″. If you’re much thinner or taller than that, I’ve no sympathy.
The downloadable file has been moved over here.