Unitates Stoneyanae

Georgius Stoney fuit primus qui intellexit onus electricum quantitates discretas tantum accipere posse; hoc ei suasit ut significationem universalem in minima unitate videret. Talis minima unitas (i.e. onus electricum electronis), una cum aliis tribus quantitatibus constantibus quas item is putavit universales (eae sunt celeritas lucis, constans gravitationis et constans Coulombiana), sivit eum systema creare, quod hodie in honorem eius appellatur.

Ad novum systema mensurae definiendum, Georgius Stoney has quantitates constantes elegit:

• c, celeritatem lucis in vacuo
• G, constantem gravitationis
• k_e, constantem Coulombianam
• e, onus electricum elementare (i.e. onus protonis vel electronis)

Nonnulli auctores posteriores, praesertim post reformationem unitatum primariarum systematis metrici^(en)(d) anni 2019, in locum constantis Coulombianae (k_e) aliquando 1/4πε₀ substituunt (ubi ε₀ est constans permittivitatis vacui^(en)).

Nomen	Dimensio	Aequatio	Mensura ad SI versa
Longitudo Stoneyana	longitudo (L)	${\displaystyle l_{\text{S}}={\sqrt {\frac {Gk_{e}e^{2}}{c^{4}}}}={\sqrt {\frac {Ge^{2}}{4\pi \epsilon _{0}c^{4}}}}={\sqrt {\frac {\alpha \hbar G}{c^{3}}}}}$	1.3807 × 10−36 m
Massa Stoneyana	massa (M)	${\displaystyle m_{\text{S}}={\sqrt {\frac {k_{e}e^{2}}{G}}}={\sqrt {\frac {e^{2}}{4\pi \epsilon _{0}G}}}={\sqrt {\frac {\alpha \hbar c}{G}}}}$	1.8592 × 10−9 kg
Tempus Stoneyanum	tempus (T)	${\displaystyle t_{\text{S}}={\sqrt {\frac {Gk_{e}e^{2}}{c^{6}}}}={\sqrt {\frac {Ge^{2}}{4\pi \epsilon _{0}c^{6}}}}={\sqrt {\frac {\alpha \hbar G}{c^{5}}}}}$	4.6054 × 10−45 s
Onus electricum Stoneyanum	onus electricum (Q)	${\displaystyle q_{\text{S}}={\sqrt {\frac {\alpha \hbar c}{k_{e}}}}={\sqrt {4\pi \epsilon _{0}\alpha \hbar c}}=e}$	1.6022 × 10−19 C

Constantes quae systema Stoneyanum definiunt, cum per ipsas unitates Stoneyanas exprimantur, partem numeralem habent unius:

${\displaystyle {\begin{aligned}c&=1\ l_{\text{S}}\cdot t_{\text{S}}^{-1}\\G&=1\ l_{\text{S}}^{3}\cdot t_{\text{S}}^{-2}\cdot m_{\text{S}}^{-1}\\k_{\text{e}}&=1\ l_{\text{S}}^{3}\cdot t_{\text{S}}^{-2}\cdot m_{\text{S}}\cdot q_{\text{S}}^{-2}\\e&=1\ q_{\text{S}}\end{aligned}}}$ 

Secundum ipsum systema pars numeralis constantis Planckianae minutae est

${\displaystyle \hbar ={\frac {1}{\alpha }}~l_{\text{S}}^{2}\cdot t_{\text{S}}^{-1}\cdot m_{\text{S}}\approx 137.036~l_{\text{S}}^{2}\cdot t_{\text{S}}^{-1}\cdot m_{\text{S}}^{~},}$ 

ubi α est constans structurae politae.

Proportio inter unitates Planckianae et unitates Stoneyanas est ${\displaystyle {\sqrt {{1}/{\alpha }}}\approx 11.7}$ . Idcirco: ${\displaystyle l_{\text{S}}={\sqrt {\alpha }}\,l_{\text{P}};}$  ${\displaystyle m_{\text{S}}={\sqrt {\alpha }}\,m_{\text{P}};}$  ${\displaystyle t_{\text{S}}={\sqrt {\alpha }}\,t_{\text{P}};}$  ${\displaystyle q_{\text{S}}={\sqrt {\alpha }}\,q_{\text{P}}.}$ 

Nonnulli auctores, unitates Planckianas imitantes, unitatem Stoneyanam temperaturae (T_S) systemati addunt, cui 1.2103 × 10³¹ K congruunt.

• Constans Coulombiana
• Constans gravitationis
• Systema internationale unitatum
• Unitates Planckianae