Question: After what year was the "Z" number known as a physical characteristic of atoms?
About the article "Atomic number", section "Abstract".

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In chemistry and physics, the atomic number of a chemical element (also known as its proton number) is the number of protons found in the nucleus of an atom of that element, and therefore identical to the charge number of the nucleus.
It is conventionally represented by the symbol Z.
The atomic number uniquely identifies a chemical element.
In an uncharged atom, the atomic number is also equal to the number of electrons.
The atomic number, "Z", should not be confused with the mass number, "A", which is the number of nucleons, the total number of protons and neutrons in the nucleus of an atom.
The number of neutrons, "N", is known as the neutron number of the atom; thus, "A" = "Z" + "N" (these quantities are always whole numbers).
Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass,") is roughly (to within 1%) equal to the whole number "A".
Atoms with the same atomic number "Z" but different neutron numbers "N", and hence different atomic masses, are known as isotopes.
A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight.
Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.
The conventional symbol "Z" comes from the German word meaning number/numeral/figure, which, prior to the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights.
Only after 1915, with the suggestion and evidence that this "Z" number was also the nuclear charge and a physical characteristic of atoms, did the word (and its English equivalent "atomic number") come into common use in this context.
Moseley's law is an empirical law concerning the characteristic x-rays that are emitted by atoms.
The law was discovered and published by the English physicist Henry Moseley in 1913.
It is historically important in quantitatively justifying the conception of the nuclear model of the atom, with all, or nearly all, positive charges of the atom located in the nucleus, and associated on an integer basis with atomic number.
Until Moseley's work, "atomic number" was merely an element's place in the periodic table, and was not known to be associated with any measureable physical quantity.
Moseley was able to show that the frequencies of certain characteristic X-rays emitted from chemical elements are proportional to the square of a number which was close to the element's atomic number; a finding which supported van den Broek and Bohr's model of the atom in which the atomic number is the same as the number of positive charges in the nucleus of the atom. 
The atomic number of an element is equal to the number of protons in each atom, and defines the element.
For example, all carbon atoms contain 6 protons in their atomic nucleus; so the atomic number of carbon is 6.
Carbon atoms may have different numbers of neutrons; atoms of the same element having different numbers of neutrons are known as isotopes of the element.
The number of protons in the atomic nucleus also determines its electric charge, which in turn determines the number of electrons of the atom in its non-ionized state.
The electrons are placed into atomic orbitals that determine the atom's various chemical properties.
The number of neutrons in a nucleus usually has very little effect on an element's chemical properties (except in the case of hydrogen and deuterium).
Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may, for example, have 6 or 8 neutrons.
That is why the atomic number, rather than mass number or atomic weight, is considered the identifying characteristic of a chemical element.
The symbol for atomic number is "Z". 
A chemical element is a pure substance which is composed of a single type of atom, characterized by its particular number of protons in the nuclei of its atoms, known as the atomic number and represented by the symbol "Z".
The mass number is the sum of the number of protons and neutrons in a nucleus.
Although all the nuclei of all atoms belonging to one element will have the same atomic number, they may not necessarily have the same mass number; atoms of an element which have different mass numbers are known as isotopes.
For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, but atoms of carbon may have mass numbers of 12 or 13.
The standard presentation of the chemical elements is in the periodic table, which orders elements by atomic number.
The periodic table is arranged in groups, or columns, and periods, or rows.
The periodic table is useful in identifying periodic trends. 
Following conversations in 1913 with Niels Bohr, a fellow worker in Ernest Rutherford's Cavendish laboratory, Moseley had become interested in the Bohr model of the atom, in which the spectra of light emitted by atoms is proportional to the square of Z, the charge on their nucleus (which had just been discovered two years before).
Bohr's formula had worked well to give the previously known Rydberg formula for the hydrogen atom, but it was not known then if it would also give spectra for other elements with higher Z numbers, or even precisely what the Z numbers (in terms of charge) for heavier elements were.
In particular, only two years before Rutherford in 1911 had postulated that Z for gold atoms might be about half of its atomic weight, and only shortly afterward, Antonius van den Broek had made the bold suggestion that Z was not half of the atomic weight for elements, but instead was exactly equal to the element's atomic number, or place in the periodic table.
This position in the table was not known to have any physical significance up to that time, except as a way to order elements in a particular sequence so that their chemical properties would match up.
The ordering of atoms in the periodic table did tend to be according to atomic "weights", but there were a few famous "reversed" cases where the periodic table demanded that an element with a higher atomic weight (such as cobalt at weight 58.9) nevertheless be placed at a lower position (Z=27), before an element like nickel (with a lower atomic weight of 58.7), which the table demanded take the higher position at Z= 28.
Moseley inquired if Bohr thought that the electromagnetic emission spectra of cobalt and nickel would follow their ordering by weight, or by their periodic table position (atomic number, Z), and Bohr said it would certainly be by Z. Moseley's reply was "We shall see!
"Since the spectral emissions for high Z elements would be in the soft X-ray range (easily absorbed in air), Moseley was required to use vacuum tube techniques to measure them.
Using x-ray diffraction techniques in 1913-1914, Moseley found that the most intense short-wavelength line in the x-ray spectrum of a particular element was indeed related to the element's periodic table atomic number, Z.
This line was known as the K-alpha line.
Following Bohr's lead, Moseley found that this relationship could be expressed by a simple formula, later called "Moseley's Law".
formula_1 where: formula_2 is the frequency of the main or K x-ray emission line formula_3 and formula_4 are constants that depend on the type of line For example, the values for formula_3 and formula_4 are the same for all formula_7 lines (in Siegbahn notation), so the formula can be rewritten thus: formula_8 (Hz) Moseley himself chose to show this without formula_3 per se, which instead was given by Moseley as a pure constant number in the standard Rydberg style, as simply 3/4 (that is, 1- 1/4) of the fundamental Rydberg frequency (3.29*1015 Hz) for K-alpha lines, and (again) for L-alpha lines according to the Rydberg formula, where formula_3 must be 1/4 - 1/9 = 5/36 times the Rydberg frequency; this also was the way Moseley chose to write it.
Moseley's formula_4 was given as a general empiric constant to fit either K-alpha or L-alpha transition lines (the latter being weaker-intensity and lower frequency lines found in all X-ray element spectra, and in which case the additional numerical factor formula_4 to modify Z is much higher).
Moseley found the entire term was (Z - 7.4)2 for L-alpha transitions, and again his fit to data was good, but not as close as for K-alpha lines where the value of formula_4 was found to be 1.
Thus, Moseley's two given formulae for K-alpha and L-alpha lines, in his original semi-Rydberg style notion, (squaring both sides for clarity), are: formula_14 Hz formula_15 Hz