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 |

M | 9.231 | — | — | — |

L | 10.823 | 1.592 | .289 | 73.18 |

K | 12.414 | 1.592 | .289 | 73.18 |

J | 14.006 | 1.592 | .289 | 73.18 |

I | 15.915 | 1.909 | .347 | 69.7 |

H | 18.621 | 2.706 | .492 | 60.5 |

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 |

M | 9.231 | — | — | — |

L | 10.823 | 1.592 | .227 | 76.86 |

K | 12.414 | 1.592 | .227 | 76.86 |

J | 14.006 | 1.592 | .227 | 76.86 |

I | 15.915 | 1.909 | .273 | 74.25 |

H | 18.621 | 2.706 | .387 | 67.25 |

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.

Hi,

This is great! I’m a fellow costumer for both theatre and historical garments. On your old site you mention something about publishing a pamphlet on math for costumers. Is that still in the works? Just wondering. Beautiful work!

I’ve seen pictures on other sites of the hoops not actually meeting each other in the back. I am going to use a 6mm round reed for my Alcega farthingale and have got everything done except the back seam. I was curious, can you just sew the hoops to the edges or is it recommended you splice the ends to overlap and strap them together as Janet Arnold shows in Patterns of Fashion 1550-1650.

I’m at work and don’t have the book with me, so I can’t reference the page, but I remember looking at something that showed how to cut a diagonal splice on both ends to match them up and then bind them together with yarn. I just remember looking at with my best friend and having this HUGE Obnoxious epiphany over the whole thing. I couldn’t for the life of me figure out how I was going to connect the ends.

I also have a small drill bit I could use to make a whole with to tie them together first, then bind them. Does that make sense?

Monique

Erm…. Well, ok, technically, you *can* just sew up the back seam, and that will hold all of the bents in place and it will form a support skirt.

The trouble is, it will be a teardrop shape, rather than a circle. You’ll see an angle at the center back where the seam is. This is because rigid hoops work a lot like bubbles — bubbles are round because the air inside exerts equal force on all parts of the soap-film-concoction that makes up the outside of the bubble. Rigid hoops stay round because the spring-like compression of the inside of the hoop material is applied equally to the outer edge of the hoop material all around. All the casing/body of the support skirt really add to the equation is vertical stability of the hoops. I mean, without the skirt, they all sort of fall to the floor. But the skirt itself doesn’t give shape to the bents – that’s a function of the material used.

If you cut the bents and make any sort of blunt, abrupt join (ie, put then in channels then sew the seam shut or join them with a flat cut edge to a flat cut edge) you’re going to disturb the balance of the compression that keeps them round. It’s sort of like when you have two bubbles together – they each get a flat side. In this case, the area of the bent farthest away from the join will have the most spring and inside-to-outside compression ratio on the physical material. In normal english, it’s going to make a good curve. As you get farther towards the cut end/blunt join, though, you’ve got a disruption in the inside compression – the absolute end effectively has none. As you get closer to the end, the lessening of the compression ratio shows physically as a lessening of the curvature of the bent.

That’s where that funky diagonal splice comes in – by creating that long join and binding it thoroughly, you’re essentially creating a system where the hoop is a full circle with no distinct end, and the inside-outside compression ration on the boning material is consistent all the way around.

Now, it it looks like a total pain in the patoutie, you can borrow a trick from the later 1600s and 1700s, and use a thicker bent (cane, bamboo, etc) that you literally soak, wet form, and dry to shape. Since the shape of the bent becomes permanent, you’re no longer relying on compression and your joins can be as easy as you please. Shaping the material, on the other hand, presents it’s own series of challenges.

Since you’re using a 6mm reed, which isn’t terribly large, you could work with bundles of them that you bind together. So long as the ends aren’t all in the same spot, and you’ve got them pretty tightly bound together, you should have a good shot at getting the kind of evenly distributed compression with no obvious areas of non-compression in the material that you’re going for. (I say should because I’ve not actually tried it….) Running a single, contiguous piece of bent through the same channel several times round will also work, but it’s a rather beastly process with something as draggy as reed – some tricks work best with plastic, and even then, they’re not fun.

With boning that relatively thin, you should also be able to lapp the bents by half a foot or so and bind them tightly (really, really tightly – much as I’m dead against it, this might be an excellent time to bust out the electrical tape), which should get you basically the same idea.

Hope that helps…..

Wow! You are one smart chick! I appreciate the input and it did help.

I have tried the 9mm reed but wasn’t able to get it to work. I found the technique Janet Arnold described (p. 7) and was searching for more of the 9mm reed, but was unable to find it anywhere :( Even the original distributed no longer carries it. The disappointing part was that my original shipment came in sections and some were not big enough for one full circle.

BUT… with the 6mm you are absolutely right, I can double up on them. I already soaked them and shaped them. After giving up on the 9mm reed, I had previously attempted using the hard PVC pipe which comes in a rounded bundle and using brass connectors (per the Renaissance Tailor Web site), but found the PVC I purchased very unflexible. Since the PVC is hollow, I soaked the 6mm round reed then threaded them into the hollow PVC piping, and tied the excess around the frame so the reed would dry in that shape. I am hoping to post the construction as my next dress diary.

I appreciate your input. I have to finish this soon so I can start on the gored kirtle I have planned. So much easier done with a proper farthingale to measure it over (especially for the non-math inclined novice sewer.)

Sincerely, Monique

Not so smart — I’ve just made that mistake before and had to sort out why it didn’t work! (I hate making farthingales. And, by hate, I mean loathe. I’ve tried every shortcut I could get my hands on to make them less of a fuss.)

I’ve used the clear poly-vinyl/jumbo aquarium tubing with the brass connectors, and it worked like a charm for me. There’s two kinds – one clear and bendy while the other is opaque and less flexible. Poly-vinyls are thermoplastics, though, so it can be persuaded with the judicious use of an iron, a heat gun, or even a bathtub full of really hot water. Heck, you could stake it out in the back of your car during the summer if you’re trying to be eco-friendly about it. Beware the fumes and the potential for melting, though. (Trivia: whalebone can also be heat-shaped and set. It’s bizarre composition makes it, essentially, a thermoplastic sans the new-fangled plastic. Leather, too. Any animal-based substance with enough collagen can be heat set, because the collagen itself liquifies under heat and becomes plastic-like when it solidifies. There’s chemistry involved, make no mistake, and chemistry is not so much something my brain gets on well with. Differences in the collagen and other compounds make for different outcomes. Whalebone, as I recall, can be reset. Once leather plasticizes, you’re pretty much stuck with the shape you’ve got and it becomes nearly impervious. Explains the idea of boiled leather armor, huh?)

Truthfully, though, I really prefer corded petticoats. They won’t hold the same diameters as a rigidly bented farthingale, but you can fold them. I love a support skirt that can be folded and put away in a drawer!

Thank you for all the articles, they have been very informative. I have used your articles to aid my research several times through the years. One favor, though… please change “diameter” in the above discussion to circumference. I spent all night trying to understand why we had to use trigonometry to figure the radius when we supposedly had the diameter measurement… which didn’t make sense either because 58″ diameter would be one huge hoop for the top hoop. I finally pulled my copies of Janet Arnold’s work trying to make sense of it, only to realize that I really DID know the math and it was the terminology that had me messed up. Thanks again for all the work you do.

Hi, Sandra,

Thanks for the proof reading, and good catch. (I swear, I really do know how to use my words *most* of the time…. And I actually do reread and proof the heavier posts. It’s just that I know what I meant….) Sorry for the confusion. It’s been corrected. I got on quite a roll of wrong for a couple sentences there. :(