# Hydrometer

Hydrometer from Practical Physics
Schematic drawing of a hydrometer. The lower the density of the fluid, the deeper the weighted float B will sink; the depth can be read off the scale A.

A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water.

A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall container, often a graduated cylinder, and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a scale inside the stem, so that the specific gravity can be read directly. A variety of scales exist, and are used depending on the context.

Hydrometers may be calibrated for different uses, such as a lactometer for measuring the density (creaminess) of milk, a saccharometer for measuring the density of sugar in a liquid, or an alcoholometer for measuring higher levels of alcohol in spirits.

## Principle

Operation of the hydrometer is based on Archimedes' principle that a solid suspended in a fluid will be buoyed up by a force equal to the weight of the fluid displaced by the submerged part of the suspended solid. Thus, the lower the density of the substance, the farther the hydrometer will sink. (See also Relative density and hydrometers.)

## History

An early description of a hydrometer appears in a letter from Synesius of Cyrene to the Greek scholar Hypatia of Alexandria. In Synesius' fifteenth letter, he requests Hypatia to make a hydrometer for him. Hypatia is given credit for inventing the hydrometer (or hydroscope) sometime in the late 4th century or early 5th century.[1]

The Round Tower of Copenhagen website has the following data about Ole Romer's hydrometer : The hydrometer Rømer's hydrostatic measurements by Erling Poulsen

From Accademia del Cimento, Florence. App. 1660.The hydrometer (also called an aerometer) is an instrument which today is mostly used by home-brewers but which previously was an apparatus often used to determine the density of fluids. There are two main types of the instrument; the best known is the type in which the neck is supplied with a scale, so one can determine the density of a fluid, or other things which depend on it, ex. the alcoholic strength, by how low the weight sinks into it. However, on the other type there is one mark on the neck (where the instrument sinks when placed in pure water) and a pan on top of the hydrometer; when one has to measure a density, the weight is lowered down into the fluid and a number of leads are placed on the pan until the weight has sunk down to the mark, which means that during all the measurements one displaces the same volume, and by using Archimedes' principle one comes to the conclusion that the relative density (water is fixed to 1) becomes p=1+m/mo, where m is the weight of the leads on the scale and mo is the weight of the empty instrument. In many places, Fahrenheit gets the credit for having invented this type of hydrometer. He describes the instrument as new in his article Aræometri novi description & usus (The description and usage of a new hydrometer), but after Ole Rømer (Roemer)'s notebook was retrieved in the beginning of the last century, the credit must be assigned to him (today, a further development of the instrument is known as Nicholson's Hydrometer); Fahrenheit has probably seen Rømer's hydrometer during his visit in 1708, just as he during his visit also learned a lot about the production of thermometers.

```The most serious problem connected to the calibration of the first type is that the top upper part where the scale is located has to have exactly the same diameter all over which is difficult to ensure. The least bit of imprecision will cause the instrument to give extremely erroneous results (unless one does not want big problems with the graduation of the units of the scale). The advantage connected to the Rømer instrument is the fact that it displaces the same amount of fluid and that imprecision therefore does not matter.
If then, on top of it all, it is possible to make an instrument, which precisely weighs 100 or 1000 times as much as one's standard leads, these could be used and the conversion to relative density would merely consist of counting the leads. The fact that it is exactly what Rømer is trying to do is shown below, although he does not succeed. The instrument does not sink low enough, but the problem is solved at the cost of the easy conversion.
```

The oldest stories about an apparatus of this kind derive from around the year 400 (Hypatia in Alexandria), but they have apparently been forgotten. The next time an apparatus is mentioned is in Samuel Peppy's journal on December 9, 1668, where Boyle is displaying one: and did give me a glass bubble, to try the strength of liquors with. Robert Boyle himself refers to his apparatus in “New Essay instrument”, in which his article is really about how one easily determines if a gold coin is a fake. But he has the idea for the apparatus from a hydrometer which he had presented earlier; both the description of the apparatus and the present depiction show that it is the type which sinks more or less in the fluid depending on its density. He writes, among other things: ….But afterwards considering this little Instrument somewhat more attentively, I thought the application of it might easily be as 'twere inverted, and that, whereas 'twas employed but to discover the differing Gravities of several Liquors, by its various degrees of Immersion of them… Rømer was already occupied with hydrometers during his stay in Paris, which is shown in a letter from John Locke to Nicolas Toinard (sent in 1679), in which it says: Therefore, the Rømer hydrometer, which they have had made for me, has all the properties, which can make a thing highly treasured.

Rømer's brine measurement

```The paragraph about the concentration of brine focuses on how one can measure how many lod of salt per pot of water there is in a brine given. Rømer assigns an instrument (a hydrometer with a pan) to measure the concentration of salt, along with a table so one, from a measured value, can determine this. There are three tables in this paragraph, only one of the two first has been measured, but which one?
The first table indicates how much a brine weighs in comparison to the weight of the same amount of water, if the weight is set to 1000. it could have been measured by weighing out 1000 ort of water (barely a pot) in a flask and placing a mark on it thus when a brine with a known concentration (lod of salt per pot) was mixed it could be filled to the mark and the added weight could be directly measured with the accuracy of 1/16 ort (his smallest leads). The numerical values are in compliance with the modern measurements.
The second table indicates how much extra-weight one has to place on the hydrometer when it is sunk into different brines in order for it to sink to a mark on it. The numbers are given with the accuracy of 0.01 unit weight, and when one takes into account that the unit for the overweight is approximately 0.06 g (0.01x0.206x29 9/16 g (see later)) the accuracy of the numerical indications is impossible to obtain through a direct measurement, and a different explanation to the table has to be found.
Thus, we have to conclude that Rømer has only measured the values in the first table because he could; the second table is an aid table which has been calculated and which leads to the last table, which is the one that is supposed to be used in practice.
After having made the first table, he notices that the relative density of a brine does not increase linearly with the amount of salt; there are a couple of measurements on the basis of this strange relationship, as well as an attempt to explain it. Rømer imagines that the salt penetrates into the pores of the water.
```

The hydrometer

From AdversariaHere comes a description of the instrument, which consists of a small container, possibly glass, in which something heavy is placed at the bottom (lead or mercury?). The weight is 26 15/16 As; it is strange how sixteenths are used since his lightest ort lead weighed 1/16 ort = 0.3 As. On top of the container, a small pan is placed (made of brass or lead?, it could be that plumbea means equipped with a seal, since it would be appropriate), which brings the collected weight to 29 9/16 As; the leads he has to use on the scale to make the apparatus sink into a brine has the unit of 1/100 of this weight. Apparently, the unit for his overweight does not fit his regular leads.

```The weight of the apparatus is more comprehensible if it is converted into ort (here, his first measured value is used, 1 pound = 2425.12 As.). The result is that 26 15/16 As. = 5 11/16 ort (the difference is below 0.01 %). Now the pan is added and the total weight becomes 29 9/16 As. = 6 ¼ ort = 100/16 ort (the difference is approximately 0.14 %). The unit of overweight thus becomes his smallest leads of 1/16 ort.
```

p = 112.35 x (d-1000)/1000

```In this way table two is worked out (p is stated with two decimals).
Empirically, he now found a connection between p and the number of lod salt per pot of water c. Rømer explains the connection by using words and logarithms:
```

Log p = log 1.38 + (1-1/20-1/300) x log c

```Through interpolation and calculations, he was now able to find the last table in the paragraph, in which there for integral values of p (1/16 ort) is indicated how many lod and qvints of salt there are per pot of water in the given brine. Next to the table, we find some “secret” writing, which indicates that he wanted to keep the construction of the hydrometer a secret, which might also be the reason why he stated the weight in As. Thus, after having thought out and constructed the hydrometer, Rømer has measured the relative weight of a number of brines in relation to water. On this basis, he works out a table, so the apparatus can be used for future measurements of the quality of brines.
```

Other measurements and a conclusion

This is where the paragraph on brines ends with the description of some other experiments, during which he notices, among other things, that a sugar solution in water can be diluted to half the concentration, which corresponds to half of the overweight, contrary to what he discovered during the tests with salt water. And Rømer concludes: Thus it is proven that if a pot of salt or sea water is diluted with a pot of fresh water, it does not add up to a mixture of two pots.

```Apparently, the fact that 1+1 does not always equal 2 has puzzled him.
```

The measurement of alloys

```An example of how Rømer arranged an instruction in a technique so even unlettered people could measure important sizes can be read in the notes. It is a description of how one, in a simple way, can find the composition of alloys and other mixtures.
The theory behind this paragraph is as follows: let there be given c parts by weight of a mixture, which consists of the substances A and B; in the mixture, is a parts of A and c-a parts of B. When the mixture is sunk into water, qc parts is lost in weight; c parts of A and B loses qa and qb parts respectively in water. From this, the relative density of the alloy, of A and B, is determined (in relation to water), which leads to:
```

a/(c-a) = (qb-qc)/(qc-qa) or a/c = (qb-qc)/qb-qa). If A is gold, one is interested in the number of weight units A per 24 weight units of the alloy, and it becomes as follows:

The carat weight = 24 x (qb-qc)/(qb-qa)

In regards to the use of the method, an example is given: 855 parts by weight of gold-copper. The alloy loses 55 parts by weight in the water; 855/19 (the density of gold in relation to water) = 45; 855/9 (the density of copper in relation to water) = 95; from this the carat weight = 24 x (95-55)/(95-45) = 19 1/5 carats.

```To make the method even easier to use, since division, at that time, was found to be extremely difficult for regular people, a table was set up in which the density is set at 19.16, 10.45, and 8.96 for gold, silver, and copper, respectively; the weight quantity of the alloy is set at 100000. From one simple measurement of the weight loss in the water, as well as knowledge of what metals are included, the carat weight can be determined; another table has also been given, so the quality (measured in sixteenths) can be determined in a silver-copper alloy. Then, a big table is given, which can be used if the mixed metal is an alloy of silver and copper, although one has to know the relation between the two; he mentions how this can be estimated from the colour.
In a completely different paragraph in the notes, Rømer takes the matter up again, in which he gives a graphic method for the determination, so the work of measuring is minimized further. The method can also be used if one part of the mixture is lighter than water; there is an example in which lead is mixed with wax and wood.
```

References

```Alic, M. (1986). Hypatia's Heritage: A History of Women in Science from Antiquity to the Nineteenth Century. London: Women's Press Ltd.
The internet: http://www.pepys.info/1668/1668dec.html
```

“Philosophical Transactions”, June, 1675 “Philosophical Transactions”, 1724, vol. 33.

```Thyra Eibe and Kirstine Meyer 1910: Ole Rømers Adversaria. København. The original is at the Royal Library, Copenhagen.
Red. Claus Thykier 1989: “Ti Rømer Facetter”, ISBN 87-983081-1-4, Albertslund.
Per Friedrichsen and Christian Gorm Tortzen 2000: Ole Rømer. København.
Andreas Nissen 1944: Ole Rømer. Et Mindeskrift. Fr. Bagges Kgl. Hofbogtrykkeri, København
Per Friedrichsen and Christian Gorm Tortzen 2004: Ole Rømer-videnskabsmand og samfundstjener. København
```

The instrument in question is a cylindrical tube, which has the shape of a flute and is about the same size. It has notches in a perpendicular line, by means of which we are able to test the weight of the waters. A cone forms a lid at one of the extremities, closely fitted to the tube. The cone and the tube have one base only. This is called the baryllium. Whenever you place the tube in water, it remains erect. You can then count the notches at your ease, and in this way ascertain the weight of the water.[2]

According to the Encyclopedia of the History of Arabic Science, it was used by Abū Rayhān al-Bīrūnī in the 11th century and described by Al-Khazini in the 12th century.[3]

It later appeared again in the work of Jacques Alexandre César Charles in the 18th century.

## Ranges

A NASA personnel measures the brine density

In low-density liquids such as kerosene, gasoline, and alcohol, the hydrometer will sink deeper, and in high-density liquids such as brine, milk, and acids it will not sink so far. In fact, it is usual to have two separate instruments, one for heavy liquids, on which the mark 1.000 for water is near the top of the stem, and one for light liquids, on which the mark 1.000 is near the bottom. In many industries a set of hydrometers is used — covering specific gravity ranges of 1.0–0.95, 0.95–0.9 etc. — to provide more precise measurements.

## Scales

Modern hydrometers usually measure specific gravity but different scales were (and sometimes still are) used in certain industries. Examples include:

## Specialized hydrometers

Specialized hydrometers are frequently named for their use: a lactometer, for example, is a hydrometer designed especially for use with dairy products.

### Lactometer

Lactometer is used to check purity of milk. The specific gravity of milk does not give a conclusive indication of its composition since milk contains a variety of substances that are either heavier or lighter than water. Additional tests for fat content are necessary to determine overall composition. The instrument is graduated into a hundred parts. Milk is poured in and allowed to stand until the cream has formed, then the depth of the cream deposit in degrees determines the quality of the milk. The device works on the principle of Archimede's principle that a solid suspended in a fluid will be buoyed up by a force equal to the weight of the fluid displaced. If the milk sample is pure, then the lactometer floats on it and if it is adulterated or impure, then the lactometer sinks.[citation needed]

### Alcohol meter

A alcoholometer testing beer immediately after brewing, before fermentation.

An alcoholmeter is a hydrometer which is used for determining the alcoholic strength of liquids. It is also known as a proof and Tralles hydrometer (named after Johann Georg Tralles, but commonly misspelled as traille and tralle). It only measures the density of the fluid. Certain assumptions are made to estimate the amount of alcohol present in the fluid. Alcoholometers have scales marked with volume percents of "potential alcohol", based on a pre-calculated specific gravity. A higher "potential alcohol" reading on this scale is caused by a greater specific gravity, assumed to be caused by the introduction of dissolved sugars. A reading is taken before and after fermentation and approximate alcohol content is determined by subtracting the post fermentation reading from the pre-fermentation reading.[5]

### Saccharometer

A saccharometer is a hydrometer used for determining the amount of sugar in a solution, invented by Thomas Thomson.[citation needed] It is used primarily by winemakers and brewers,[6] and it can also be used in making sorbets and ice-creams.[7] The first brewers' saccharometer was constructed by Benjamin Martin (with distillation in mind) and initially used for brewing by James Baverstock Sr in 1770.[8] Henry Thrale adopted its use and it was later popularized by John Richardson in 1784.[9]

It consists of a large weighted glass bulb with a thin stem rising from the top with calibrated markings. The sugar level can be determined by reading the value where the surface of the liquid crosses the scale. It works by the principle of buoyancy. A solution with a higher sugar content is denser, causing the bulb to float higher. Less sugar results in a lower density and a lower floating bulb.

### Thermohydrometer

A thermohydrometer is a hydrometer that has a thermometer enclosed in the float section. For measuring the density of petroleum products, like fuel oils, the specimen is usually heated in a temperature jacket with a thermometer placed behind it since density is dependent on temperature. Light oils are placed in cooling jackets, typically at 15 °C. Very light oils with many volatile components are measured in a variable volume container using a floating piston sampling device to minimize light end losses.

As a battery test it measures the temperature compensated specific gravity and electrolyte temperature.

### Urinometer

A urinometer is a medical hydrometer designed for urinalysis. As urine's specific gravity is dictated by its ratio of solutes (wastes) to water, a urinometer makes it possible to quickly assess a patient's overall level of hydration.

### Barkometer

A barkometer is calibrated to test the strength of tanning liquors used in tanning leather.[10]

### Battery hydrometer

The state of charge of a lead-acid battery can be estimated from the density of the sulfuric acid solution used as electrolyte. A hydrometer calibrated to read specific gravity relative to water at 60 degrees Fahrenheit is a standard tool for servicing automobile batteries. Tables are used to correct the reading to the standard temperature.

### Antifreeze tester

Another automotive use of hydrometers is testing the quality of the antifreeze solution used for engine cooling. The degree of freeze protection can be related to the density (and so concentration) of the antifreeze; different types of antifreeze have different relations between measured density and freezing point.

### Acidometer

Sometimes spelled acidimeter, an acidometer is a hydrometer used to measure the specific gravity of an acid.[11]

## Use in soil analysis

A hydrometer analysis is the process by which fine-grained soils, silts and clays, are graded. Hydrometer analysis is performed if the grain sizes are too small for sieve analysis. The basis for this test is Stoke's Law for falling spheres in a viscous fluid in which the terminal velocity of fall depends on the grain diameter and the densities of the grain in suspension and of the fluid. The grain diameter thus can be calculated from a knowledge of the distance and time of fall. The hydrometer also determines the specific gravity (or density) of the suspension, and this enables the percentage of particles of a certain equivalent particle diameter to be calculated.

## References

1. ^ Female Inventors - Hypatia of Alexandria http://www.inventions.org/culture/female/hypatia.html
2. ^ Taken from the two-volume set of Letters, Essays and Hymns of Synesius translated by A. Fitzgerald, published by Oxford University Press in 1926 and 1930. Available on-line at: http://www.webcitation.org/query?url=http://www.geocities.com/athens/acropolis/5164/synesius.html&date=2009-10-25+12:50:58
3. ^ Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 639, in Rashed, Roshdi; Morelon, Régis (1996), Encyclopedia of the History of Arabic Science, 1 & 3, Routledge, pp. 614–642, ISBN 0-415-12410-7
4. ^ http://chestofbooks.com/reference/Encyclopedia-Of-Practical-Receipts-And-Processes/Degrees-of-Baum-e.html
5. ^ The dictionary of beer and brewing - Google Books. Retrieved 2009-10-11.
6. ^ Country house brewing in England ... - Google Books. Retrieved 2009-10-11.
7. ^ Patisserie - Google Books. Retrieved 2009-10-11.
8. ^ The Brewing Industry in England... - Google Books. Retrieved 2012-03-16.
9. ^ Instruments of science: an ... - Google Books. Retrieved 2009-10-11.
10. ^ Charles Thomas Davis, The manufacture of leather: being a description of all of the processes for the tanning and tawing with bark, extracts, chrome and all modern tannages in general use. H. C. Baird & co., 1897. Retrieved 2009-10-11.
11. ^ "Acidometer". The Free Dictionary. Farlex. 2003. Retrieved 18 September 2010.