The gist of the dialogue obtainable (sorry, there are too many pages to grant each and all of the hyperlinks) is that wands help to concentration the magic resident interior the witch or wizard, yet wandless magic continues to be achievable, relatively for terribly proficient people like Snape and Dumbledore. some examples ... Apparition Assuming one's Animagus sort (or Metamorphpagus) Accio (the Summoning attraction) Elves can do magic without using wands Lumos
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Verified answer
(1) pH = -log[H+]
[H+] = 10^(-pH)
do the math
(2) pH + pOH = 14
so
pOH =14 -pH
and
pOH = -log[OH-]
[OH-] = 10^(-pOH)
so now do the math on that one, too.
The gist of the dialogue obtainable (sorry, there are too many pages to grant each and all of the hyperlinks) is that wands help to concentration the magic resident interior the witch or wizard, yet wandless magic continues to be achievable, relatively for terribly proficient people like Snape and Dumbledore. some examples ... Apparition Assuming one's Animagus sort (or Metamorphpagus) Accio (the Summoning attraction) Elves can do magic without using wands Lumos