Glen Zook, K9STH, posted this to the Heathkit mailing list:

Many amateurs already know that "73" is from what is known as the "Phillips Code", a series of numeric messages conceived for the purpose of cutting down transmission time on the old land telegraph systems when sending text that is basically the same.

In the April 1935 issue of QST on page 60 there is a short article on the origin of 73. This article was a summation of another article that appeared in the "December Bulletin from the Navy Department Office of the Chief of Naval Operations". That would be December of 1934.

The quotation from the Navy is as follows: "It appears from a research of telegraph histories that in 1859 the telegraph people held a convention, and one of its features was a discussion as to the saving of 'line time'. A committee was appointed to devise a code to reduce standard expressions to symbols or figures. This committee worked out a figure code, from figure 1 to 92. Most of these figure symbols became obsolescent, but a few remain to this date, such as 4, which means "Where shall I go ahead?'. Figure 9 means 'wire', the wire chief being on the wire and that everyone should close their keys. Symbol 13 means 'I don't understand'; 22 is 'love and a kiss'; 30 means 'good night' or 'the end'. The symbol most often used now is 73, which means 'my compliments' and 92 is for the word 'deliver.' The other figures in between the forgoing have fallen into almost complete disuse."

One of the chief telegraphers of the Navy Department of Communications, a J. L. Bishop, quoted from memory the signals that were in effect in 1905:

1 Wait a minute
4 Where shall I start in message?
5 Have you anything for me?
9 Attention or clear the wire
13 I do not understand
22 Love and kisses
25 Busy on another circuit
30 Finished, the end-used mainly by press telegraphers
73 My compliments, or Best Regards
92 Deliver
Now days, 22 has become 88 (love and kisses). I don't know when this came about. 30 is still used in the newspaper and magazine business to indicate the end of a feature, story, or column. And, of course, 73 is still used by amateur radio operators to mean "best regards".

Making any of these numbers plural (73s, 88s, etc.) is incorrect since they are already plural. 73s would mean best regardses and 88s would mean love and kisseses. Those make no sense.

Anyway, the subject of where 73 came from comes up periodically and this article reinforces the "Phillips Code" origin.

Jim, N2EY, adds:

Some other related stuff:

Phillips Code "19" and "31" refer to train orders. They were so well known that the terms "19 order" and "31 order" were still in RR use in the 1970s, long after the telegraph was gone.

The abbreviation "es" for "and" derives from the Morse character "&". The prosign "SK" with the letters run together derives from the Morse "30".

The numeric code is a small part of the abbreviations outlined in the Phillips Code (developed by telegrapher Walter P. Phillips). Here are the numbers as referenced:

WIRE Preference over everything except 95
1 Wait a moment
2 Important Business
3 What time is it?
4 Where shall I go ahead?
5 Have you business for me?
6 I am ready
7 Are you ready?
8 Close your key; circuit is busy
9 Close your key for priorit business (Wire chief, dispatcher, etc)
10 Keep this circuit closed
12 Do you understand?
13 I understand
14 What is the weather?
15 For you and other to copy
17 Lightning here
18 What is the trouble?
19 Form 19 train order
21 Stop for a meal
22 Wire test
23 All copy
24 Repeat this back
25 Busy on another wire
26 Put on ground wire
27 Priority, very important
28 Do you get my writing?
29 Private, deliver in sealed envelope
30 No more (end)
31 Form 31 train order
32 I understand that I am to ...
33 Car report (Also, answer is paid for)
34 Message for all officers
35 You may use my signal to answer this
37 Diversion (Also, inform all interested)
39 Important, with priority on thru wire (Also, sleep-car report)
44 Answer promptly by wire
73 Best regards
88 Love and kisses
91 Superintendant's signal
92 Deliver promptly
93 Vice President and General Manager's signals
95 President's signal
134 Who is at the key?