Hamlet is not the only character in Shakespeare’s play who offers us a soliloquy. Claudius, Hamlet’s uncle and the murderer of Hamlet’s father (Claudius’ own brother), also gives us a detailed insight into his thoughts, for the first time, in this private moment as he goes to pray in Act III Scene 3 of Shakespeare’s play. ‘O, my offence is rank, it smells to heaven’ definitively confirms Claudius’ guilt for the first time in Hamlet. For this reason, among several others, it’s worth stopping to analyse ‘O, my offence is rank’ in terms of its language and meaning. We’ll offer an analysis by summarising the soliloquy line-by-line, glossing any words that require it.
O, my offence is rank: it smells to heaven;
It hath the primal eldest curse upon’t,
A brother’s murder. Pray can I not,
Though inclination be as sharp as will:
My stronger guilt defeats my strong intent;
Claudius begins his soliloquy by describing his ‘offence’ – killing his brother, Old Hamlet – as ‘rank’, i.e. foul-smelling and offensive. His crime is the very first murder in the Bible: Cain’s murder of his brother Abel, from the book of Genesis, and the subsequent curse placed upon mankind. Claudius, now he is alone, tries to pray; it’s interesting that Shakespeare uses the soliloquy here as a kind of ‘prayer’ or confession to us, the audience, in the absence of Claudius’ ability to confess to God. Claudius wants to be able to pray, but his guilt is so great that he’s afraid even to address God, given the weight of his crime. As the editors of Hamlet (The Arden Shakespeare, Third Series)
And, like a man to double business bound,
I stand in pause where I shall first begin,
And both neglect. What if this cursed hand
Were thicker than itself with brother’s blood,
Is there not rain enough in the sweet heavens
To wash it white as snow?
Claudius’ problem is that he has two tasks to undertake, and the two are incompatible: he wants to beg forgiveness for his crime, but he isn’t truly sorry for it (he enjoys being King, and being married to Gertrude, his brother’s widow). So he finds himself at an impasse. His next lines – a rhetorical question – seems to be of a sort with Macbeth’s famous question (‘Will all great Neptune’s ocean wash this blood / Clean from my hand?’). But given the context of Claudius’ words, they invite a more nuanced analysis. Claudius is lamenting that his guilt 
may be too great to be forgiven; but he’s also giving himself a way out. (In other words, ‘Well, I’m not going to be forgiven for such a sin, so what’s the point in even pretending to be sorry? I’m clearly not.’) This ambivalence is possibly reflected in Claudius’ choice of hand-washing as a metaphor for his state of mind: it conveys both the idea of absolving oneself of guilt and washing one’s hands of something, i.e. abandoning it.
Whereto serves mercy
But to confront the visage of offence?
In other words, what is the point of mercy if it doesn’t confront guilt itself?
And what’s in prayer but this two-fold force,
To be forestalled ere we come to fall,
Or pardon’d being down?
That is, the purpose of prayer is either to prevent us from committing a sin before we do it, or to forgive us after we’ve already done it.
Then I’ll look up;
My fault is past. But, O, what form of prayer
Can serve my turn? ‘Forgive me my foul murder’?
Claudius knows that words are insufficient to beg forgiveness of the murder of his own brother.
That cannot be; since I am still possess’d
Of those effects for which I did the murder,
My crown, mine own ambition and my queen.
‘Well, God isn’t going to be convinced by my plea for forgiveness, when I haven’t given up all the worldly benefits I’ve accrued as a result of my crime: I’m king, I’m still ambitious to rule more lands, and I have Gertrude, who I still share a bed with, after all.’
May one be pardon’d and retain the offence?
Is it even possible for us to be forgiven for something while we hold on to the fruits of our crimes?
In the corrupted currents of this world
Offence’s gilded hand may shove by justice,
And oft ’tis seen the wicked prize itself
Buys out the law: but ’tis not so above;
In the world, which is corrupted, many criminals can use wealth (‘gilded hand’) to make sure they don’t suffer punishment for their crimes. But you can’t do this with God, who can’t be ‘bought’ like this.
There is no shuffling, there the action lies
In his true nature; and we ourselves compell’d,
Even to the teeth and forehead of our faults,
To give in evidence. What then? what rests?
No, before God we ourselves become our own worst witness, having to testify or give evidence against ourselves.
Try what repentance can: what can it not?
Yet what can it when one can not repent?
A neat couple of lines, which are chiastic in structure: you can try to repent, but if your heart’s not in it, God will know you’re not sincere, so what’s the point?
O wretched state! O bosom black as death!
O limed soul, that, struggling to be free,
Art more engaged! Help, angels! Make assay!
Bow, stubborn knees; and, heart with strings of steel,
Be soft as sinews of the newborn babe!
All may be well.
NB: ‘limed’ means ‘trapped’, like a bird trapped in birdlime (which was spread on the branches of trees). Claudius likens his immortal soul to a bird struggling on the sticky branch, and, knowing that it’s trapped, struggles all the harder to be free.
‘O, my offence is rank’ is an important moment in Shakespeare’s Hamlet not just because it confirms Claudius’ guilt – something we have probably long suspected, despite Hamlet’s fears over the veracity of the Ghost’s account. It is important because Hamlet offers a picture of Claudius’ state of mind, as someone ‘sorry not sorry’, repentant yet unable to repent. Claudius wants forgiveness because the weight of his sin is bearing down on him; but he is torn between spiritual absolution and worldly ambition and enjoyment. He doesn’t want to give up Gertrude and the crown, even if it means the continued plight of his soul.