Cyanotype formulas can be divided into essentially two types: the original formula from 1842 made with ferric ammonium citrate (FAC) and potassium ferricyanide (PF), and the new formula invented by Mike Ware in 1994 wherein FAC is replaced with ferric ammonium oxalate (FAO). Although both formulas result in a print composed of Prussian blue, they require somewhat different practices.
I chose to standardize nomenclature when writing about the formulas. FAC cyanotype versus FAO cyanotype is inelegant. Old cyanotype versus new cyanotype connotes something that has passed its usefulness and implies replacement of a better sort. To call the original formula “traditional” implies there was a tradition and considering the hundreds of ways to mix FAC and PF in the literature there is hardly a traditional formula. I asked Mike Ware his preference, and he referred to his FAO formula as “new.” Sam Wang cinched it for me by differentiating the two with the terms “classic” and “new,” conveniently CC and NC, and that seemed right, because classic implies old in a good way.
Download and read the MSDS sheets at ScienceLab.com before using all chemicals. Exercise caution in the handling of all photographic chemicals. Use of any such chemicals constitutes some risk, and some are poisonous. The workplace should be well ventilated. Chemicals should be mixed only in the manner described. Avoid contact between the chemicals and eyes, skin, clothing, and furniture. Do not eat or drink while using chemicals. Keep them away from pets and children. Wear protective eye wear and gloves if necessary. In short, be mindful of all safety procedures for yourself and others.
It is surprising that there are so many classic cyanotype formulas, given there are only two ingredients, ferric ammonium citrate (FAC, the more light-sensitive part of the compound), and potassium ferricyanide (PF, also light-sensitive but not to the same degree as FAC1). It is precisely this immense flexibility that makes cyanotype so user-friendly. You could probably throw a handful of the two chemicals together in some water and get an acceptable print. For those who do not want to spend a lot of time reading about cyanotype and just want to make a print, the following classic cyanotype formula works well. Following this formula, we will discuss my favorite formula as well as others, and the finer details of chemistry, formula ratios, and added ingredients for those who want a more in-depth discussion of the process.
For repeatable and exact results, it is best to measure everything out with a gram scale. However, the tablespoon and teaspoon measurements are close enough to the suggested gram amounts if you don’t own a gram scale. As long as you are consistent with the way you measure, you can achieve consistent results.
Although the often-repeated formula in contemporary literature is a 20%/8% solution, this solution of 20%/10% is closer to the optimum ratio to be as fast as possible without the potential for the shadows bleeding into the highlights which problem will be discussed further on.2
Solution A 20% ferric ammonium citrate 20 g ferric ammonium citrate (5 tablespoons) 100 ml distilled water
Mixing Solution A:
1. Measure out 20 g of ferric ammonium citrate and add it to 75 ml distilled water and stir until dissolved.
2. Add water to make 100 ml total volume.
3. Store in a brown eyedropper bottle and label the bottle “Solution A.”
Solution B 10% potassium ferricyanide 10 g potassium ferricyanide (2 teaspoons) 100 ml distilled water
Mixing Solution B:
1. Measure out 10 g of potassium ferricyanide and add it to 75 ml distilled water and stir until dissolved.
2. Add water to make 100 ml total volume.
3. Store in a brown eyedropper bottle and label the bottle “Solution B.”
At time of use:
1. Shake both solutions before using to make sure the chemistry is evenly dispersed.
2. Mix equal proportions of Solution A and Solution B. 2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption. [Note: there are 5 ml in a teaspoon.]
My favorite classic cyanotype formula
With some papers—actually, more than a few—the typical 20/10 CC formula will produce gritty, grainy results wherein there is much wash off in the development baths and the final print has a scratchy appearance. This is greatly exacerbated if you live in a dry climate as I do, and in winter months when the humidity drops. My guess is those who live in humid climates rarely see this, and certainly if you are in the habit of humidifying your darkroom for other processes, you will probably not see this either.
When I first began testing papers for cyanotype I decided to level the playing field and use equal proportions of FAC and PF. I made my decision to do so based on the fact that there were so many varying proportions of these two ingredients in the literature. I decided to start with 10% solutions of both FAC and PF and then from there test increasing amounts of FAC.
I was surprised to find out that I preferred the more turquoise color of the 10/10, the washoff in the development baths was minimal, the exposure scale (ES) was long and smooth, rivaling the new cyanotype, and the exposure time was most often faster than that for 20/10! This is not what the literature says, including my previous books, I am embarrassed to say. It is thought the more Solution A, the faster the exposure, and, in fact, it is often suggested to double Solution A when coating, using a 2A:1B ratio to make exposure faster. I did not find this to be true with hundreds of step wedge prints.
What, therefore, is not to like about 10/10? The only drawback is that the Dmax, or how dark the darkest blue, is a modicum less, a difference not noticeable unless one were to put two prints side by side. For ease of use, I don’t mind this trade-off.
I am not proposing to reinvent the cyanotype wheel, but I do encourage you to give the 10/10 formula a try and see for yourself if you prefer it, especially in the winter months and in areas of low humidity.
For repeatable and exact results, it is best to measure everything out with a gram scale. However, the tablespoon and teaspoon measurements are close enough to the suggested gram amounts if you don’t own a gram scale. As long as you are consistent with the way you measure, you can achieve consistent results.
Solution A 10% ferric ammonium citrate 10 g ferric ammonium citrate (2 tablespoons) 100 ml distilled water
Mixing Solution A:
1. Measure out 10 g of ferric ammonium citrate and add it to 75 ml distilled water and stir until dissolved.
2. Add water to make 100 ml total volume.
3. Store in a brown eyedropper bottle and label the bottle “Solution A.”
Solution B 10% potassium ferricyanide 10 g potassium ferricyanide (2 teaspoons) 100 ml distilled water
Mixing Solution B:
1. Measure out 10 g of potassium ferricyanide and add it to 75 ml distilled water and stir until dissolved.
2. Add water to make 100 ml total volume.
3. Store in a brown eyedropper bottle and label the bottle “Solution B.”
At time of use:
1. Shake both solutions before using to make sure the chemistry is evenly dispersed.
2. Mix equal proportions of Solution A and Solution B. 2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption. [Note: there are 5 ml in a teaspoon.]
Bleeding is where the darkest blues or shadows of the image migrate into the highlight areas with a sort of blue, creeping stain. Alberto Novo, an Italian scientist, found in research through patents (specifically us Patent no. 2,350,991) that if the ratio of FAC:PF is no more than a 20–23% FAC to a 10% PF, bleeding is prevented, and the blue is deeper and the contrast better. This keeps the light sensitive iron in ferric ammonium citrate to no more than 2× the potassium ferricyanide (calculated with moles not grams).
Solution A
18 g green ferric ammonium citrate (15.1 g brown) 1 drop of 50% thymol solution (5 g thymol in 10 ml isopropyl or ethyl alcohol) 100 ml distilled water
Mixing Solution A:
1. Add the ferric ammonium citrate to 75 ml water and stir.
2. Add water to make 100 ml total volume.
3. Store in a 100 ml brown eyedropper bottle with a drop of thymol added to prevent mold and label the bottle “Solution A.”
Solution B
8 g potassium ferricyanide 100 ml distilled water
Mixing Solution B:
1. Add the potassium ferricyanide to 75 ml water and stir.
2. Add water to make 100 ml total volume.
3. Store in a 100 ml brown eyedropper bottle and label the bottle “Solution B.”
At time of use:
1. Shake both solutions before using to make sure the chemistry is evenly dispersed.
2. Mix equal proportions of Solution A and Solution B. 2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption. [Note: there are 5 ml in a teaspoon.]
There are two forms of ferric ammonium citrate, a brown (in historical literature sometimes referred to as “red”3) and a newer form that is chartreuse yellow-green. Before 1897 the commonly available kind was brown, which was slow to expose. Cyanotype is slow enough to expose as it is, so this was problematic. In 1897 green ferric ammonium citrate was introduced by Eduard Valenta. This new green form was said to make exposure eight times faster (a bit of a stretch, but the equivalent of three stops exposure)4 and it of course became the preferred ferric ammonium citrate. Green ferric ammonium citrate is the most commonly used kind today, though you can still find the brown scales.
This is the original Valenta formula from 1897 when he introduced the green form of ferric ammonium citrate for the first time, included here for historic interest.5 Note that Valenta’s ratio moves into a potential “bleeding range.”
Solution A
25 g green ferric ammonium citrate 100 ml distilled water
Mixing Solution A:
1. Add the ferric ammonium citrate to 75 ml water and stir.
2. Add water to make 100 ml total volume.
3. Store in a 100 ml brown eyedropper bottle and label the bottle “Solution A.”
Solution B
9 g potassium ferricyanide 100 ml distilled water
Mixing Solution B:
1. Add the potassium ferricyanide to 75 ml water and stir.
2. Add water to make 100 ml total volume.
3. Store in a 100 ml brown eyedropper bottle and label the bottle “Solution B.”
At time of use:
1. Shake both solutions before using to make sure the chemistry is evenly dispersed.
2. Mix equal proportions of Solution A and Solution B. 2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption. [Note: there are 5 ml in a teaspoon.]
In over one hundred formulas from 1844 on, the ratio of ferric ammonium citrate to potassium ferricyanide varied from 8/10 as much FAC to PF to one outlier formula that had almost sixteen times as much FAC to PF (and perhaps was recorded mistakenly). How can such a simple process that involves only two ingredients become so diverse? It is primarily this ratio of the two chemicals that accounts for the wide variety in formulas over 175 years. One author seemed to think the reason for this variety is that Prussian blue (ferric ferrocyanide) and Turnbull’s blue (ferrous ferricyanide) are different colors, and that “by varying the percentage of the two ferric salts forming the sensitizing solution, the color of the blue may be varied thereby. Hence the difference in the formulas given by different authors.”6
I compiled a chart of the various formulas as best as I could and include it here at the end of this chapter for historical interest. Complicating factors are that it is often not stated whether the brown or the green form of ferric ammonium citrate is used; before 1897 it was probably all the brown form but after that date, who knows? It was often not stated whether the chemistry is added to the recommended volume of water or up to the recommended volume, which would result in slightly different percentage solutions. Also, it is often assumed we know what measuring system is in use, but measurement systems vary—US, British, metric, avoirdupois, apothecary, grains, grams, or who knows what else.
When Herschel originated the process, he did not state any specific ratio of the two chemicals. It was only in his Memoranda where ratios are stated, and in the beginning the ratios went from more potassium ferricyanide than ferric ammonium citrate to more ferric ammonium citrate than potassium ferricyanide.7
What was said in the late 1890s is probably still true today: “Success is not so much dependent upon the proportions of the ingredients, for the process allows considerable latitude in this respect, and the formulae given for general use vary somewhat; nor does it require chemically pure material, that sold by druggists generally being of the requisite purity; but it does require carefulness in the preparation and use.”8
Suffice it to say that in over one hundred formulas from 1844 to present day, few have less ferric ammonium citrate than potassium ferricyanide, and since 1900 the amount of FAC in proportion to PF has increased, only partly because more green FAC is required to equal the brown variety. The give-and-take balance between the two chemicals can be summarized as follows:
More FAC
• Streaks more when coating
• Absorbs less readily into the paper (you can see minute specks on a freshly coated surface when viewed obliquely)
• Faster exposure speed (not in my practice!)
• More grain
• More bleeding
• More washoff
• More staining of the highlights
• More paper fogging
• More Dmax (darker darks)
• More reddish-blue
More PF
• Streaks less to none when coating
• Absorbs more readily into the paper
• Slower exposure speed (not in my practice!)
• Finer grain
• Less bleeding of darks into highlights
• Less washoff
• Less staining of the highlights
• Less paper fogging
• Less Dmax9
• More greenish blue
In 1883 Channing Whitaker tested cyanotype formulas from 2% ferric ammonium citrate: 20% potassium ferricyanide to 20% ferric ammonium citrate: 2% potassium ferricyanide. His conclusion was that having ferric ammonium citrate 1.5× the potassium ferricyanide was about the best, or 15 g ferric ammonium citrate and 10 g potassium ferricyanide in 100 ml water. Whitaker was using brown ferric ammonium citrate, not green, and in a single solution mix,10 so his ideal formula would equate to 18 g green ferric ammonium citrate to 10 g potassium ferricyanide.
There is probably no one holy grail formula, but there is a sweet spot where the formula has enough ferric ammonium citrate to make it as dark as possible, but not too much so graininess, scratchiness, washoff, and bleeding occur.
This formula is the one that Whitaker settled upon as the best. If he was going to print coated paper right away, he would increase the ferric ammonium citrate, because he wasn’t as worried that the increase in FAC would fog.11 Note that this formula is fairly close to Novo’s recommendation of 18/8, with slightly more potassium ferricyanide (which I find makes a less grainy print). Note also this is a combined solution stored in one bottle, but you can always mix separate solutions. One last point: this is double the strength of a normal formula; a normal two-solution formula is a combined total of 200 ml water whereas this is a combined total of 100 ml water, so more chemistry will be delivered to the paper surface at time of coating.
15 g brown ferric ammonium citrate (18 g green) 10 g potassium ferricyanide 100 ml distilled water
1. Measure out 75 ml water.
2. Add the ferric ammonium citrate and stir.
3. Add the potassium ferricyanide and stir.
4. Add water up to 100 ml.
5. Store as a single solution mix in a 100 ml brown eyedropper bottle.
At time of use:
2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption. [Note: there are 5 ml in a teaspoon.]
Combining solutions and shelf life
In the modern literature on cyanotype, ferric ammonium citrate and potassium ferricyanide are kept in separate solutions A and B and mixed at time of use. Often books will parrot the information that once Solution A and B are mixed, the combined solution only lasts a day until it goes bad, turns blue, gets contaminated, slows down, veils the highlights of the print, and doesn’t work. This is part myth and part truth. Out of one hundred formulas spanning 175 years, close to one-third of the formulas called for the ferric ammonium citrate and the potassium ferricyanide to be combined in one solution. Two-thirds called for the two solutions to remain separate and be mixed together at time of use. The practice of mixing all the chemistry in one solution fell out of favor over the decades, but the fact that a combined solution existed in practice is proof that at the very least the combined solution does not expire in a day.
Separate or combined, the solutions are light sensitive and should be stored in brown or light-tight bottles. Best practice is to keep the solutions separate, but if combined, a solution will last, by some accounts, up to a year, even if it has turned blue.12 I used a seven-month old formula and it was blue but worked fine. My practice is to store separate solutions, but whatever I combine, I use up until it is gone, even if it takes days.
Classic cyanotype with oxalic acid
Oxalic acid added to a cyanotype formula was said to print faster and result in brighter highlights.13 The formula is often repeated in 250 ml amounts, probably because of the minute amounts of chemistry needing to be measured, but here it is translated to 100 ml amounts like the rest of the formulas in this book. It is merely the Valenta formula with added oxalic acid and ammonium dichromate.
Solution A
25 g ferric ammonium citrate
0.5 g oxalic acid
Distilled water to make 100 ml
Mixing Solution A:
1. Add the ferric ammonium citrate to 75 ml water and stir.
2. Add the oxalic acid and stir.
3. Add water to make 100 ml total volume.
4. Store in a 100 ml brown bottle and label the bottle “Solution A.”
Solution B
9 g potassium ferricyanide 0.5 g oxalic acid
0.2 g ammonium dichromate Distilled water to make 100 ml
Mixing Solution B:
1. Add the potassium ferricyanide to 75 ml water and stir.
2. Add the oxalic acid and stir.
3. Add the ammonium dichromate and stir.
4. Add water to make 100 ml total volume.
5. Store in a 100 ml brown bottle and label the bottle “Solution B.”
At time of use:
1. Shake both solutions before using to make sure the chemistry is evenly dispersed.
2. Mix equal proportions of Solution A and Solution B. 2 ml (about ½ teaspoon) of combined solution are enough for an 8″ × 10″, 4 ml (scant 1 teaspoon) for an 11″ × 14″, but mix a few ml extra to account for initial brush absorption.
It is said that the more chemistry on the paper, the darker blue in the resulting print14 and therefore some cyanotypists coat the paper twice to get deeper blues. I have never felt a need to double coat to get a deeper blue than is already provided by a single coat except on a few papers—almost always lightly sized or unsized printmaking papers—that are very absorbent and seem to require more solution to cover, in which case I use more solution when coating. In other words, although double coating is not necessary, it is a technique you may find fruitful to test.
Over time Solution A will grow mold. It’ll look like brown globs. If Solutions A and B are combined, mold doesn’t happen. If Solution A is separate, which it usually is, and mold appears, merely filter the solution through a coffee filter and return it to the bottle. It tends to grow less mold after the first filtering. Mold is not something I have ever worried about, but the smell can be offensive to a sensitive nose. There are some quick fixes:
• Add rubbing alcohol to the tune of 5% of the formula (e.g. add 5 ml for every 100 ml of Solution A)15
• Add a few drops of 15% thymol dissolved in methylated alcohol16
• I always have thymol in my dimroom but if you do not, use Listerine. Your Solution A will smell minty fresh
• Add a few drops of formalin per 100 ml if you happen to have this on hand, which nowadays most people don’t
• Add 1 gram of ammonium dichromate to the solution.17 This affects exposure and contrast, though, whereas the other methods don’t affect sensitizer performance.
Adding dichromate to the formula
Dichromate added to the classic cyanotype formula accomplishes three things: it prevents mold growth in Solution A as stated above, it helps sensitized paper last longer, and it increases print contrast. The drawbacks are that exposure slows, you need another chemical in the dimroom, and you have to be cautious with dichromate because it is toxic.
Dichromate is not necessary. If mold is a bother there are other methods to prevent it. For increasing contrast with dichromate, you can choose a higher contrast curve. To keep coated paper good for a long time you can refrigerate it.
Dichromate does come in handy with low contrast film negatives. It also is good for preserving coated paper. You can add up to 1 g per liter of Solution A and coated paper will last 3–5 months.18 To add it to the coating solution only at time of use, mix a 1% solution (1 g in 100 ml) and at time of coating, add 1–6 drops to every 2 ml sensitizer which will increase contrast as much as one stop.19
• Potassium ferricyanide is soluble up to 33%20 whereas ferric ammonium citrate, which is hygroscopic, meaning it absorbs water from the atmosphere, is very soluble—1200 g per liter! Thus keeping the container tightly capped will prevent it turning into a lump of gooey green. It still works fine, but it’s harder to measure it accurately.
• Potassium ferricyanide when exposed to light when dry or in solution is decomposed to potassium ferrocyanide and can result in a blue precipitate when it is mixed with ferric ammonium citrate upon making your coating solution. This will result in stained highlights.21 Back in the day they used to rinse the crystals and dry between blotting paper22 or merely brush off the yellow crystals on top of the red crystals to get to the undecomposed potassium ferricyanide below.23 If all of a sudden your cyanotype exposure is proceeding at a snail’s pace when it used to proceed much faster, check your potassium ferricyanide.24
• Potassium ferricyanide should not be heated above 300°F or allowed to come in contact with any concentrated acid such as acetic acid in stop bath, because poisonous hydrogen cyanide gas can be produced!25
• In my research I came across a single solution classic cyanotype formula with added gum Arabic. You can get the same effect at time of coating by just adding 2 drops of gum Arabic per ml just before coating the paper, if desired.
• An addition of 5 g of potassium oxalate per 100 ml of sensitizer (5%) was used back in the day to increase speed, but the paper was said to not keep as long.26
Endnotes
1. Ware, Mike. Cyanomicon II, History, Science and Art of Cyanotype: photographic printing in Prussian blue. Buxton: self-published, 2016, pp. 52–57, 96. http://www.mikeware.co.uk/mikeware_downloads.html.
2. Ibid., pp. 91–92. Ware recommends mixing equal parts of a 20% brown ferric ammonium citrate with a 16% potassium ferricyanide, or a 26% green ferric ammonium citrate with a 12% potassium ferricyanide (w/v). The differences in formulas is because of the differing iron contents of the brown and green ferric ammonium citrate. His 26%/12% recommendation is equivalent to 20%/9.23%, which is slightly rounded up here to 10%.
3. Brown, George E. Ferric and Heliographic Processes: A Handbook for Photographers, Draughtsmen, and Sun Printers. New York: Tennant & Ward, 1900 [First edition 1900, reprinted 1905, this edition n.d.], p. 10.
4. Valenta, E. “The Use of Various Iron Salts in Printing Processes” in The Photographic Times, Vol. XXIX. New York: The Photographic Times Publishing Association, May 1897, pp. 237–238.
5. Valenta, pp. 237–238.
6. Duchochois, P. C. Photographic Reproduction Processes. New York: The Scovill & Adams Company, 1891, p. 34.
7. Ware, pp. 82–83.
8. Himes, Charles F. “Blue-Print Solution Will Keep” in The Photographic Times, Vol. XXIX. New York: The Photographic Times Publishing Association, May 1897, pp. 223–224.
9. James, Christopher. The Book of Alternative Photographic Processes. New York: Delmar Cengage, 2016, p. 173.
10. Whitaker, Channing. “Apparatus for Printing by the Blue Process” in The Photographic News, Vol. XXVII. London: Piper and Carter, December 7 1883, p. 359.
11. Ibid., p. 359.
12. Tennant, John A., ed. “The ‘Blue Print’ and its Variations” in The Photo-Miniature, Vol. 1, No. 10, January 1900, p. 489; Enfield, Jill. Jill Enfield’s Guide to Photographic Alternative Processes, Popular Historical and Contemporary Techniques. Burlington, Massachusetts: Focal Press, 2014, p. 67.
13. Langford, Michael. The Darkroom Handbook. New York: Alfred A. Knopf, 1992, p. 328.
14. James, p. 172.
15. Bolle, Oscar. “Prints in Turnbull’s Blue” in The Photographic Times, Vol. XXIX. New York: The Photographic Times Publishing Association, December 1897, pp. 579–580.
16. Seigel, Judy ed. The World Journal of Post-Factory Photography, Issue 5. New York: Post Factory Press, August 2000, p. 32.
17. Hirsch, Robert. Photographic Possibilities, 3rd ed. Boston: Focal Press, 2009, p. 199.
18. “Ferro-Prussiate Paper” in The Photographic News, The Journal for Amateur Photographers, Vol. XLI. London: Photographic News, January 15 1897, p. 48. The 3–5 month time frame is repeated in Hawkes, Lieut. H. P. Photography in a Nutshell, by “The Kernel.” London: Iliffe, Sons & Sturmey Ltd, 1898, p. 91. In Brown, p. 18, it is less, no more than 1 g of dichromate per liter of combined solution.
19. Crawford, William. Keepers of Light. New York: Morgan and Morgan, 1979, p. 166.
20. Ware., p. 90.
21. Tennant, p. 491.
22. Brown, pp. 118–119.
23. Tennant, p. 491.
24. Blacklow, Laura. New Dimensions in Photo Processes, 3rd ed. Boston: Focal Press, 2000, p. 102.
25. Hirsch, p. 199; Farber, Richard. Historic Photographic Processes, A Guide to Creating Handmade Photographic Images. New York: Allworth Press, 1998, p. 61.
26. Wall, E. J. “The Iron Salts I” in American Photography, Vol. XVI, November 1922, pp. 677–688.
Following is a chart of over one hundred formulas. To me, most interesting is how the ratio of ferric ammonium citrate rose in proportion to potassium ferricyanide through the years. It was closer to 1:1 to 1.3:1 in the early days and then quite obviously 2:1 today. Also of interest are the various additions to the formulas, noted in the right column of the chart. Third is noting how many of the formulas are used as a combined solution, denoted by “C.”
Abbreviations probably don’t need to be explained but are as follows: brn denotes brown FAC; grn denotes green FAC. FAO refers to ferric ammonium oxalate. G is grams, not to be confused with gr or grs which refer to grains. Pt refers to part or parts. S1:1 means separate solutions mixed in equal proportions at time of use. Am di and pot di are ammonium dichromate and potassium dichromate, am bromide and pot bromide likewise. Ltr, ml, and oz are liter, milliliter, and ounce as can be expected. Opt refers to an optional addition. To find the source for the formula, use the year and author and refer to the Bibliography.