Temperature of the Standard
Unfortunately, the world of specific gravity is not as simple as described above. Different fields have apparently chosen different standard temperatures. In addition to the 3.98 °C standard, others include 20 ° C (68 °F) and 60 °F (15.6 °C). A quick look through several laboratory supply catalogs shows many examples of hydrometers using each of these two, and a few odd ones thrown in for good measure (such as 102 °F for milk). Most authors writing about marine aquaria assume that people are using the 60 °F standard, but in reality many aquarists are not, and in some cases they don't even know what they are using. Some hobby hydrometers use other standards, with 77 °F being quite popular (used by Tropic Marin, for example).
The density of pure water at 20 °C is 0.998206 g/cm3, and at 60 °F it is 0.9990247 g/cm3. While these seem close to 1, and are often simply claimed to be 1.00 in many contexts, the difference can be substantial. For example, the specific gravity of natural seawater (S =35) is 1.0278 using the 3.98 °C standard, 1.0269 using the 60 °F standard, 1.0266 using the 20 °C standard, and 1.0264 using the 77 °F standard. [I calculated these based on tables of the density of seawater, different tables may present slightly different densities that might then result in slightly different specific gravities]. While these differences are small, they are real. They arise because the density of pure water and seawater change in slightly different ways with temperature. Seawater becomes less dense faster than pure water as the temperature rises. This effect may relate to the interactions between ions and between ions and water in seawater that are broken up as the temperature rises, but that's beyond the scope of this article.
Unfortunately, it has been my experience that many aquarists quoting a specific gravity measurement for their tanks do not know what standard is being used by their hydrometer. Most quality lab hydrometers will have the standard used written on them or their supporting documents. Some hobby hydrometers, however, make no mention of the standard used. Note that there is NO "correction" table that can convert readings at temperatures other than the standard temperature unless you know the standard temperature. If you don't know it, using such a table will not give accurate values, and may give a value farther from the truth than the uncorrected reading.
Temperature of the Sample
As if the confusion about the temperature of the standard were not enough, the temperature of the sample is also a variable. Many quality lab hydrometers also have the expected sample temperature indicated directly on them. This is referred to as the "reference" temperature. In a great many cases (though not all), the standard temperature and the reference temperature are the same: either 60 °F or 20 °C. This is often written as "60 °F/60 °F", though it is sometimes written simply as "Temperature of Standardization: 60 °F". If a hydrometer is used at the reference temperature, no special corrections are necessary (though the answer one gets will depend a bit on the standard temperature chosen by the manufacturer as described above).
Why does the temperature of the sample matter? There are two reasons. One is that the hydrometer itself may change its density as a function of temperature, and thus give incorrect readings at any temperature except that for which it is specifically designed (i.e., it floats higher or lower as its density changes). Unfortunately, unless you have a table for your specific hydrometer (which is rarely supplied), this effect cannot be corrected by a table because of the different materials of construction of hydrometers. Various types of glass and plastic are used for hydrometers, and each will have it own particular change in density as a function of temperature. It should be noted that this effect is substantially smaller for glass hydrometers than the second effect described below because the change in density of glass with temperature is 8-25 times smaller than the change in density of aqueous fluids.
The second reason that the sample temperature is important is that the sample itself will change its density as a function of temperature. For example, the density of seawater (S = 35) changes from 1.028 g/cm3 at 3.98 °C to 1.025 g/cm3 at 20 °C to 1.023 g/cm3 at a typical marine aquarium temperature of 80 °F. Since the density of the sample is changing with temperature, the measured specific gravity will also change, unless this is taken into account.
The impact of temperature on the density of the sample can be corrected in a table, assuming that one knows how the density of the sample would change with temperature (which is well known for seawater), and also that one knows the temperature of standardization of the hydrometer. For example, if you have a hydrometer calibrated for 60 °F/60 °F, then you will be correcting for the difference in density between the sample at 60 °F, and the temperature at which you measured it. If the actual sample were measured at 86 °F, then the correction is the ratio of the density of seawater at 86 °F (approximately 1.0217 g/cm3) divided by the density at 60 °F (approximately 1.0259 g/cm3), or 0.996. Thus a specific gravity reading, or more correctly, a hydrometer reading, of 1.023 would be corrected to an "actual" reading of 1.027.
Again, if you do not know the temperature of standardization, you are out of luck, and a correction using a table is as likely to cause bigger errors, as it is to correct any. Likewise, using a "correction" table that does not specify what it is intended to correct is equally risky.
