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Equation 5 · Part 6 · The Last Artefact: Redefining the Kilogram

Symbol h

N=8 Vsa3,ms=N m(28Si)=h N(m(28Si)h)N = \frac{8\,V_{\mathrm s}}{a^{3}}, \qquad m_{\mathrm s} = N\, m({}^{28}\mathrm{Si}) = h\,N \left( \frac{m({}^{28}\mathrm{Si})}{h} \right)
hh

What this part means

a constant of nature known to high accuracy, so with h fixed the sphere becomes a primary mass standard [ 4 ].

Its job in the formula

h is an input to the expression that computes the quantity on the left.

Where the article explains it

The ratio of the silicon-28 atomic mass to h is a constant of nature known to high accuracy, so with h fixed the sphere becomes a primary mass standard [ 4 ] .

The passage around this formula

…per cubic unit cell of lattice parameter a, the atom count follows from the macroscopic sphere volume, and the sphere mass follows from the count [ 4 ] : N=8 Vsa3,ms=N m(28Si)=h N(m(28Si)h)N = \frac{8\,V_{\mathrm s}}{a^{3}}, \qquad m_{\mathrm s} = N\, m({}^{28}\mathrm{Si}) = h\,N \left( \frac{m({}^{28}\mathrm{Si})}{h} \right). The ratio of the silicon-28 atomic mass to h is a constant of nature known to high accuracy, so with h fixed the sphere becomes a primary mass standard [ 4 ] . The mise en pratique notes that the second equality is not exact — the total binding energy of the crystal reduces the right-hand side by about two parts in 10¹⁰ — and that this is…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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