Green’s Dictionary of Slang

conk n.1

also conc, conck, conque, konk
[? f. Lat. concha, a shell, and Gk kogcha, anything hollow]

1. [early 19C+] the nose; thus a nickname for one who has a large nose; thus conked adj., having a type of nose as specified.

2. [early–mid-19C] (UK Und.) an informer, a thief who betrays his accomplices [‘sniff things out’].

3. [early 19C–1900s] a policeman [‘sniff things out’].

4. [mid-19C+] the head; thus -conked, -headed; off one’s conk, crazy, eccentric.

5. [late 19C+] a punch, usu. on the nose.

6. [1940s] intelligence; thinking.

In compounds

conk-buster (n.) [bust v.1 (1); all three meanings imply the straining of one’s brain] [1930s–50s] (US black)

1. an intellectual.

2. an intellectual challenge, a difficult problem.

3. cheap liquor.

conkhouse (n.)

[20C+] (US black) the head.

conkpiece (n.)

[1930s-40s] (US black) the head.

In phrases

bust one’s conk (v.) [bust v.1 (1)] [1930s–40s] (US black)

1. to go mad.

2. to go to sleep.

3. to show one’s happiness in an emotional outburst.

4. to work very hard.