Explain the line from Macbeth: "There's no art to find the mind's construction in the face."

When King Duncan speaks this line from act 1, scene 4 of Shakespeare's Macbeth, he has just been informed that the Thane of Cawdor has been executed. Malcolm tells the king that the men in charge of the execution have not returned from the task yet, but that he (Malcolm) talked to someone who saw Cawdor's execution. This messenger said that Cawdor admitted his crimes, deeply repented, and asked King Duncan's forgiveness. Then the messenger reported to Duncan that Cawdor died very well. At the end of Malcolm's speech, King Duncan responds:

There's no art to find the mind's construction in the face. He was a gentlemen on whom I built an absolute trust.

An art in this context means a creative skill. We use this word in several contexts. For example, there is an art and a science to teaching and practicing medicine. This word art also refers to magic arts, like mind reading or fortune-telling. What King Duncan means by this is that one cannot read another's mind by looking at his face. King Duncan had placed absolute trust in the Thane of Cawdor, therefore his betrayal took him completely by surprise. 

The description of the Thane of Cawdor's betrayal comes in act 1, scene 2 when Ross tells the king that the Norwegian flag is flying in Fife, and he saw the Norwegian king leading an immense army and being assisted by the Thane of Cawdor.

The irony of King Duncan's statement about not being able to read someone's mind based on their face is that he will be betrayed to an even greater degree by Macbeth, whom he is also unable to read and in whom he placed absolute trust.

Explain the line from Macbeth: "There's no art to find the mind's construction in the face."

In Act l, scene lV, King Duncan speaks these lines about the Thane of Cawdor, who has betrayed him. He has just discovered that Cawdor was executed after he confessed his treason and begged the king's forgiveness.

What Duncan means is that no one can determine what another is thinking by looking at his or her appearance or the expression on such a person's face. It is impossible, therefore, to judge whether the person bears you any ill will or not by reading his or her face. He acknowledges that the Thane of Cawdor deceived and misled him. He trusted the thane and believed that he was loyal. This fact is further supported by his earlier statement in Act l, scene ll, when he ordered that Cawdor be killed and Macbeth be given his title:

No more that thane of Cawdor shall deceive
Our bosom interest.

Lady Macbeth, from the outset, is intent on misleading others. She, for example, commands her husband to "appear the innocent flower but be the serpent underneath." She tells him that he must put on a face of conviviality and friendship when he meets Duncan and his entourage when he is, in fact, plotting his malice. Indeed, when she welcomes the king to their castle at Inverness in Act l, scene Vl, she puts on a show and warmly welcomes him:

All our service
In every point twice done and then done double
Were poor and single business to contend
Against those honours deep and broad wherewith
Your majesty loads our house.

Her exaggerated welcome hides her true intentions. She has already decided that Duncan should be murdered and that his visit will give her and her husband the ideal opportunity to enact their perfidy. Prior to this, she called on the powers of darkness to hide her malicious intent and empower her to commit evil. 

It is obvious that Lady Macbeth is sly and ruthless. She is intent on implicating others by creating the illusion that they are responsible for what she and Macbeth are about to do. She informs her husband that:

. . . what not put upon
His spongy officers, who shall bear the guilt
Of our great quell?

She intends getting Duncan's guards so drunk that they will be incapable of defending him during the assassination. They will not remember anything and will be easy to blame for a crime that she and her husband are about to commit. She and Macbeth will, after "learning about" Duncan's murder, put up such a show of grief that others will be convinced of their loyalty and love for their now-deceased liege and will, therefore, not suspect them of any wrongdoing.

In addition, she has convinced Macbeth that their task will not fail. He eventually succumbs to her will and agrees about putting on an act. He states, at the end of Act l:

False face must hide what the false heart doth know.

Lady Macbeth's conniving and plotting tie in well with the theme of appearance and reality. Her sole purpose is to illegitimately gain power. She will deceive and mislead to ensure that she and her husband achieve their goal. It is ironic that she is the first to eventually succumb to remorse. She is overwhelmed by guilt and becomes so overwrought that she commits suicide. 

Explain the line from Macbeth: "There's no art to find the mind's construction in the face."

The quote you reference is originally spoken by King Duncan in Act 1, Scene 4 of Shakespeare's Macbeth. In context, the quote references how the former Thane of Cawdor fooled Duncan and betrayed him. Basically, in this quote Duncan is acknowledging how difficult it is to know what's going on in someone else's mind based on their outward appearance. In other words, it's easy for someone to hide his or her real feelings in order to betray someone.

This quote could certainly apply to Lady Macbeth on multiple occasions, as she proves adept at hiding her true feelings for most of the play (until, of course, she's goes crazy and dies). The most obvious example of this is Act 2, Scene 3, at which point King Duncan's murder is discovered. At this point, we know Lady Macbeth had a role to play in the murder. That said, you wouldn't guess it from the way she pretends to be surprised, and then emotionally/physically weakened by the grisly "revelation." Indeed, Lady Macbeth carefully hides her guilty conscience by pretending she is too "weaK" to deal with the news of Duncan's murder. As such, at this point in the play Lady Macbeth's outward appearance certainly masks her "mind's construction."