How to express in physics if some value depends on a variable? Dependence, or dependency? And what about the plural? [duplicate]

Question

In physics, people very often measure some values which depend on some variable, say the air temperature as a function of time. I think the verb depend is used correctly, since dictionaries define "dependent variables" and "independent variables". The resulting data (mostly shown in graphs) reflect something which mathematicians use to call a function (which would have a rigorous definition), but since the measurement involves often numerous parameters, physicists commonly call the result a dependence.

Is this correct? I have not found any dictionary definition of "dependence" which would express this relation between the imposed variable and the result.

The plural seems even more problematic. One may measure the air temperature and humidity in parallel. Is it then correct to say that the given graph contains these two dependences? Dictionaries say "dependence" is a mass noun, so there would be no plural. The plural can be found in Wiktionary, but without any explanation. Or should we use the word dependencies? For "dependencies" I can not find a suitable dictionary definition either.

Answer 1

This Science Direct article contains typical statements:

• Temperature dependence of the resistivity in a U3As4 single crystal was measured as shown in Figure 2 ....

• Temperature dependence of the elastic moduli Bij is another important anharmonic effect. This temperature dependence in quasiharmonic approximation results from ...

• The temperature dependence of viscosity of several melts is illustrated in Figure 7 ...'.

The non-count usage is certainly used in the first two examples above; I'd argue that the third example is indeterminate. The distributive singular is often used ([speaking to an adult male audience] "When you get home, tell your wife you love her").

The plural usage can also be found in academic articles, such as

• Temperature dependences of fluorescence lifetimes in Cr3+-doped insulating crystals.

[National Library of Medicine]

• Electron and gas temperature dependences of the dissociative recombination coefficient of molecular ions with electrons

{ie DRC = f(Te) and DRC = g(Tg)}

[Plasma Sources Science and Technology]

...................

In everyday English, dependence is often found in the noncount usage:

Another possible solution for minimising a person's dependence on family and friends outside the household is to recruit a relative to join the household.

[Cambridge English Corpus; Cambridge Dictionary] ('dependences' would be rare here)

and as CD says, 'dependency' is a spelling variant here.