Per our recent discussion on Western Union services, I found some information about Western Union's public facsimile services.
Western Union ran several advertisments in the New York Times for its public "wirefax"/"telefax" service. I found ads for 1959-1962.
The maximum size of a document was 8.5" x 11", and the transmitted portion was roughly 1" shorter on all sides (7.5" x 10"). Transmission took five minutes.
The service was offered in New York City, Washington DC, Chicago, Los Angeles, and San Francisco. In the time span I checked no additional cities were added.
The material had to be taken to a Western Union office. WU would pick it up at an additional charge for their messenger. It would be delivered by Western Union messenger without charge to any place within the city limits of the destination city.
The first 4" vertically between NYC and Chicago cost $2.40 and 40 cents for each additional inch. plus Federal tax. The first 4" between NYC and San Francisco cost $4.00 and 65 cents for each additional inch plus Federal Tax.
So, a full page letter (with margins) to Chicago would cost about $3.60 per page, to San Francisco would cost about $5.95 per page, both plus Federal Tax (10%?), in 1960 dollars, plus the expense of delivery to the central WU office. By today's dollars that seems quite pricey.
An engineering drawing would probably be larger than regular office size and need to be cut up for transmission in multiple pages. Legal contracts are usually multiple pages. Thus, a typical business document would be very expensive to transmit. Given that high price I can't help but wonder if a business might be willing to wait a day or two for air mail and special delivery, at a fraction of the cost. Other alternatives might be a Night Letter telegram or a Telex/TWX message. The business world moved a bit slower in those days*.
I presume there was some sort of air express service by 1960, but I have no idea what they'd charge for a small package back then. I believe Railway Express Agency (REA) offered expedited shipping on the fast overnight trains between New York and Chicago (eg the Twentieth Century Limited), but again I don't know the charges.
Certain documents would not be faxed such as photographs, or legally prohibited, such as drug prescriptions, naturalization certificates, legal tender, etc. I could understand prohibiting legal tender, but drug prescriptions and naturalization certificates are the kind of documents a traveller might need transmitted in a rush.
--NYT, 12/3/1959, display ad.
*I am amazed that anyone can sit at their desk today and, at no charge, receive stock quotes, stock history, and current analysis from many newspaper websites; that information that once was only available in a stockbroker's office to regular customers. Stockbrokers used the Western Union "900 speed" ticker to keep up. The Bunker Ramo company had stock-lookup computer terminals in the mid 1960s.[public replies, please]