They are both in either's powers: but.
This swift business .
I must uneasy make, lest too light winning.
Make the prize light. (I.2.453-5).
Miranda is very loving to her father and is very devoted to him. This is the most important relationship in this play as they are the reason for the shipwreck and were sent to the island. This act with Miranda and Prospero speaking together tells us all about the past and why they are there. Miranda treats him with respect as she speaks formally to him by calling him Sir (I.2.78) and "my dearest father" (I.2.1).
He has a very unusual relationship with Ariel, as he is very loving with him. .
Ariel: Do you love me master?.
Prospero: Dearly, my delicate Ariel. (IV.1.48-9).
He also tells Ariel off when Ariel goes against him and also orders Ariel around.
Thou liest, malignant thing! Hast thou forgot.
The foul witch Sycorax, who with age and envy.
Was grown into a hoop? has thou forgot her? (I.2 257-9).
Ariel is very respectful with Prospero and likes to do the work that Prospero orders him to do. Ariel is like Prospero's slave and is very determined to be free. This relationship is significant because if Ariel hadn't done Prospero's order and scare the people on the ship then there would not have been a storm. The ship would not have stopped at the island and Miranda would not have met Ferdinand. Also Prospero and Antonio would not have been re-united.
Prospero forgives Antonio, Alonso and Sebastian even after the thought that they usurped him for Prospero's laziness of his dukedom.
.
Yet with my nobler reason "gainst my fury .
Do I take part: the rarer action is .
In virtue than in vengeance: they being penitent,.
The sole drift of my purpose doth extend.
Not a frown further. (V.1.25-30).
Alonso feels bad about usurping Prospero and Miranda, under Antonio's orders, after Ariel speaks to him. Alonso is scared what Ariel will do to him and instantly wants to die after realising how evil he was towards them 12 years ago.
