Ammonium Hydroxide Name
The fictitious substance “ammonium hydroxide” $(\ce{NH4OH})$ was suggested in accordance with the Arrhenius theory. In 1882–1883, Svante Arrhenius had researched into the conductivity of electrolytes. His theory of electrolytic dissociation was discussed in his dissertation in 1884 and published in refined form in 1887. In 1903, the Nobel Prize in Chemistry was awarded to Svante Arrhenius “in recognition of the extraordinary services he has rendered to the advancement of chemistry by his electrolytic theory of dissociation”.

According to the Arrhenius definition, acids are compounds that dissociate and release hydrogen ions $(\ce{H+})$ into the solution:

$$\ce{HCl -&gt; H+ + Cl-}$$

Bases are defined as compounds that dissociate and release hydroxide ions $(\ce{OH-})$ into the solution:

$$\ce{NaOH -&gt; Na+ + OH-}$$

The need for a hydroxide group in bases according to the Arrhenius definition led to the proposal of $\ce{NH4OH}$ (i.e. “ammonium hydroxide”) as the formula for hydrated ammonia in water. (Note that this problem does not exist in the definition of bases according to the Brønsted–Lowry theory, which was proposed in 1923.)

However, ammonium hydroxide cannot be isolated; the fictitious solid compound does not exist. Nevertheless, the misleading traditional name “ammonium hydroxide” is still widely used for solutions of ammonia in water.

Actually, a solid compound (melting point: −79 °C) with the correct atomic composition (molecular formula) can be crystallized from aqueous solutions of ammonia. But even this compound is not ammonium hydroxide $(\ce{NH4OH})$. It actually is a real hydrate $(\ce{NH3.H2O})$ in which the molecules are linked by hydrogen bonding.