In Black and White by Phi
In a ‘Playfair’ code-square, letters of key word or phrase, in which no letter recurs, precede the rest of the alphabet in order: I does duty for I and J. To encode a word, split it into pairs of letters thus: PE RV ER SI TY. If letters of a pair occur in same rank in square, use letters to right of each (for last letter of rank use first letter); if in same column use letters below each bottom letter of column use top letter): otherwise treat them as limits of diagonals of a rectangle and use limits of opposite diagonals (PE = HD, not DH, which = EP). Result: HD EW RM PC OT; then join into one word HDEWRMPCOT.
The Playfair code is governed by a common 2-word 13-letter phrase (not in Chambers) with three components A, B and C. There are three unclued variations on each of A and B. The four words entered in Playfair code are clued by wordplay only and share a common definition associated with C, and indeed the phrase as a whole. 22 down is an uncommon proper noun, verifiable through Wikipedia.
ACROSS
1 Have a ride after college (6)
5 One joking about hairpiece gives a signal (6)
10 A court case in America ignoring large European country (7)
12 Singular recall of offhand state (5)
13 New start in America, say, backing on leaving African republic (5)
14 Mother welcoming Queen – with this? (4)
15 Variation on A (6)
17 Thematic figure has a link in music (5)
19 Calm and rational before replacing one (6)
20 Racing initially to home key? (7, 2 words)
23 One past villain of the Elizabethan stage (4)
24 Independent rule: solution for Middle East state (4)
27 Friend of Charlie’s seen around court with medicinal substance (7)
29 Metal especially good as a muscle relaxant (6)
31 Rain at Loch Ness? A blow when touring Loch (5)
34 Variation on A (6)
36 Fuddled, having polished off whiskey? Mac’s having a nap (4)
37 French level in game in middle of week (5)
38 Learned man seen with a lot of experienced gents? (5)
39 Ambassador receiving little space for logical responses (7)
40 Glassblowing aid beginning to moderate a fluid motion one suppressed (6)
41 Queen is surrounded by endless money (6)
DOWN
1 Those agreeing to enter street spoke once (6)
2 Most of check up is enthusiastic (4)
3 Rubber or corded material used in church (5)
4 American unit almost entirely seen as typographical error (7)
5 Variation on B (5)
6 Radical invoking constitutional change, one supported by a remarkable King (6)
7 Subversive change of government applied to Ireland (8)
8 Broadcast excellent collection of operas (6)
9 Variation on B (4)
11 Group eyes switching ends (4)
16 Ingeniously constructed below, height being excluded (4)
18 School getting to heart of adolescent development (8)
21 King demoting foremost nobleman (4)
22 Australian anthropologist having obligation to go round rocky land (7)
25 Regret abandoning energy drink for salad plant (6)
26 Old sheriff continually upset about one after end of rustling (6)
28 Hearts in sacks upset Sultan (6)
30 Variation on A (5)
31 Put decoration on for one, bringing medal round (5)
32 Experts putting down Conservative character from former days (4)
33 Variation on B (4)
35 Covering up a weaver bird (4)
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