The Quincunx, mystically considered

Huge fan, I am, of reading old gardening books.

While looking for some good pictures of roses for the current Días de los Muertos art project, I ran across this odd word - Quincunx. Odd and old, not to mention hard to pronounce.

Wikipedia has an entry for it. Merriam Webster has a definition. Visually it is the five spot on a domino - four dots on the corner and one in the middle.  The origin is thus: "Latin quincunc-, quincunx, literally, five twelfths, from quinque five + uncia twelfth part". According to MW, first known use was 1485. Now I'm still thinking how does 5/12 relate to planting.

Both the California Nursery and Fancher Creek Nursery talked about orchard planting and the Quincunx. Roeding's Fruit Growers Guide (1919) probably helped disseminate the information.

"The Ladies' Companion to the Flower-Garden; 
Being an alphabetical arrangement 
of all the ornamental plants usually grown 
in gardens and shrubberies with full directions for their culture"  
by Jane Loudon, p. 269

Here's the full entry for Quincunx from "The ladies' companion to the flower-garden", 1858. From the pattern, you can see the 5 spots and the pattern is repeated. In this picture, the 4 trees are not in a square.

The mystery unfolds. Many very old books to very current books talk about Quincunx in planting. I will post them below. The meaning may have shifted over time. There is some difference in opinion whether the quincunx has its four dots in the shape of a rectangle or a square.

This cookie was baked by someone who
did not know about quincunx.
Because the flat edge was not exposed to the heat,
the sugars did not caramelize
as much as the exposed sides.
It was still a really good cookie.

But I have finally "gotten" why someone decided we needed this word. We've all used a Quincunx system when we are trying to fit those last few cookie balls on the baking pan. We skootch the rows around and offset the rows, so there's enough cookie space. If we don't, we get some big co-joined odd-shaped cookies.

Those of you who just ate the last two raw cookie dough balls, I understand completely.

The trick is that the quincunx is based on the (if one believes the oldest work, equilateral) triangle which along with the diamond and hexagon are pretty amazing shapes, much more interesting sometimes than the square. Just ask a bee what shape is best for packing the most stuff in a space. Check out wikipedia's hexagon article.

And the handy thing about laying out the orchard in the quincunx system is that when you stand in the middle of the orchard you have three directions of rows.

Fancher Creek Catalog. Not sure which! Which pattern is this? So many rows.

"What is more beautiful than the quincunx, that, from whatever direction you regard it, presents straight lines?" (Garden of Cyrus)

Is the quincunx based on equilateral triangle? Or a square with a point in the center? Here's the frontpiece from The Garden of Cyrus (Sir Thomas Browne, 1658), from Wikipedia. This looks like it is an equilateral triangle based diamond.

Quid quincunce speciosius, qui, in quamcumque partem spectaveris, rectus est (What is more beautiful than the quincunx which however you view it, presents straight lines?)

"...the quincunxial lozenge, or net work plantation of the Ancients, artificially, naturally, mystically, considered" (The Works of Samuel Johnson, 1825)

Other interesting old books on the quincunx

Books listed in order of my discovery, not necessarily on logical order at all:

• Notes on Nets; or, The Quincunx Practically Considered to Which are added Miscellaneous Memoranda, 1837.  See wonderful picture of mer-people below. Is a Quincunx the best way to get the smallest holes in a net with the least amount of string?
• The Elements of Forestry, Franklin Benjamin Hough, 1882. Discusses using "Quincunx Order" (p. 47) to get more trees in same space and to be able to cultivate in three directions.  See picture below.
• Prof. Tait on Listing's Topologie in Philosophical Magazine, 1884.
• The Orange: Its Culture in California, 1885. Chapter X, The Quincunx System. Chapter XI, The Septuple System. There does seem to be some disagreement as to whether the quincunx is based on equilateral or not. Here the Septuple system is like the honeycomb, with six sides and a dot in the middle. The trees in the Septuple system are equidistant. 'Quincunx Defined. - Webster defines the word quincunx as follows: "An arrangement or disposition of things by fives in a square, one being placed in the middle of the square; especially an arrangement as of trees, in squares, consisting of five trees, one at each corner and a fifth in the middle, this order being repeated indefinitely so as to form a regular group, with rows or ranks running in various directions.' My eyes were spinning from that definition. A picture is worth a thousands words! Need picture!
• The Horticulturist, and Journal of Rural Art and Rural Taste, 1854. Some good pictures in the "Foreign Notices" section.
• The American Agriculturist, Volume 42, 1883. "Laying out the Quincunx" "It is a more pleasing arrangement and allows of about one-seventh more trees on a given area. An acre set in squares twelve feet apart takes 302 trees; planted quincunx it holds 349; put fifteen feet each way in squares it holds 193 trees; set quincunx it takes 223."
• The "California Fruits and How to Grown Them", p. 126
• Dissertation Upon Phalaris, 1777. "The Divisions of the AITPA; ________ a coin of Five ounces Brass, or of Silver equivalent to them, is mentioned by Epicharmus, in that fragment produced above; ... The Latins called it Quincunx. And perhaps, as the Latins had the Septunx too; so the Sicilians might have ______ though we have now no Author that mentions it."
• According to Wikipedia, the quincunx was one of the bronze coins of the Romans, introduced 280 BC which is much earlier than 1485 mentioned by MW.  A quincunx was a fractional (5/12) coin of an as and sometimes denoted by 5 dots.
• A New Universal Gazetteer, Or, Geographical Dictionary: Containing a Description of the Various Countries, Provinces, Cities, Towns Seas, Lakes, Rivers, Mountains, Capes, &c. in the Known World : with an Appendix, Containing an Account of the Monies, Weights, and Measures of Various Countries with Tables Illustrating the Population, Commerce, and Resources of the United States : Accompanied with an Atlas. See the table below with Roman measures.
• The Works of Samuel Johnson, 1825. "To this treatise on Urn-burial was added The Garden of Cyrus or the quincunxial lozenge, or net work plantation of the Ancients, artificially, naturally, mystically, considered. This discourse he begins with the Sacred Garden, in which the first man was placed; and deduces the practice of horticulture from the earliest accounts of antiquity to the time of the Persian Cyrus, the first man whom we actually know to have planted a quincunx; which, however, our author is inclined to believe of longer date, and not only discovers it in the description of the hanging gardens of Babylon, but seems willing to believe, and to persuade his reader, that it was practised by the feeders on vegetables before the flood." See "Garden of Cyrus...." in Encyclopedia Britannica.
• The Garden of Cyrus from Wikipedia, written by Sir Thomas Browne, published in 1658.
• The Garden of Cyrus. "What is more beautiful than the quincunx, that, from whatever direction you regard it, presents straight lines?" University of Chicago.
• Fancher Creek catalog explaining Quincunx planting (1921)
• California Nursery catalog explaining Quincunx planting (1921) Oh, George!

What about the Quincunx today?

The quincunx has been discussed for quite a while. What do current day methods of planting suggest? The quincunx method is mentioned in a New Mexico publication (Designing a Pecan Orchard, New Mexico State University, 2000.). However, the equilateral triangle method is called the "Triangle" and quincunx method is more like the 5-spot face of the domino. 

"This design is seldom used in New Mexico. It is difficult to lay out and is not as well adapted to fillers or temporary trees because distances between trees will not be the optimum when every other row is removed."

Some current day bloggers on quincunx

• Quick Quincunx Quiz
• The Classical Quincunx in Early American Gardens
• Garden History Girl blog on Quincunx and check out Eric Ravilious and Paul Nash The Garden of Cyrus woodblock prints.

Some fun pictures from all of those references

I wouldn't want you to miss these!

Dedication in Notes on Nets.
Not the name of a musical group, but it should be,
the Worshipful Company of Fishmongers still exists in London,
being in existence for some 700 years.

The Elements of Forestry shows the various ways to plant.

From A New Universal Gazetteer
Quincunx is a Roman Square Measure