Later, on a bus travelling to Glasgow, we managed to connect to the Tel- Me online service to check on train times. Again we were triumphant, and there was not an external wire in sight.
The laptop office has been dreamt of for many years, but it was only when digital (GSM) mobile phone networks arrived that it became a practical possibility. Computers and telephones combined could create a seamless digital pipe, and the expanding mobile network could send data whizzing round the world. When a necklace of mobile network satellites is eventually in place, it will be possible to send messages from the middle of the Gobi desert to the North Pole - or, of course, from the pub to your boss.
In fact, it took more than the advent of GSM phones to make the laptop office a reality. The mobile network companies also had to market "data cards", the digital equivalent of a modem, before we could send e-mail, surf the Net and exchange faxes without wires. But in the past year or so they have been doing just that and the market is starting to take off.
One of the most attractive aspects of wire-free communications is their simplicity. Once the system is set up, it should be simply a question of choosing the word processor's "print" command, entering the fax number and pressing "send". E-mail is just as straightforward because most of the familiar packages will work with cellular links.
This is a great help to anyone who is frequently on the move. Fax bureaux are fine but expensive, and for those using just a laptop there is one serious obstacle: to send the fax, it has to be printed out, which means carrying yet another (heavy) piece of hardware.
Even the fax modem does not resolve the traveller's problem, because it can often prove impossible to find a suitable socket for the cable.
The mobile phone and data card solve all these problems and more. No socket? No problem. Stuck in a traffic jam? Surf the Web. Train broken down at Crewe? Catch up on e-mail from the office. Lost in the Cairngorms? Fax for directions home (do not try this one, it really annoys the mountain rescue teams).
Digital mobile networks offer speeds of 9,600 baud (slower than most new modems but the same speed as a standard fax machine). This is fine for e-mail and reasonable for the World Wide Web, especially with the graphics turned off. It is a bit slow for file transfer, but this is being addressed. Manufacturers are working on protocols to allow higher speeds, perhaps faster than those available on a normal phone line.
The lines are clear and reliable, in most cases, and it is now possible to send and receive faxes. It is also possible to store faxes in a mailbox when the phone is off, or busy on another call. And users can send text messages from their PCs to colleagues who only have phones, using GSM's short messaging system.
Disadvantages? There are a few. Tim Sheppard, managing director of Lerryn, says people buy ready-to-go packages from companies such as his because configuration can be a nightmare: you have to know the right modem "initialisation" strings for several different services and, he says, you can easily come a cropper.
A more serious deterrent is cost, especially of the hardware: a GSM digital data card is pounds 450, and you must add another pounds 200 or so for the mobile phone (the models advertised in the high street for pounds 30 do not have data interfaces). Users of older laptops will also need a PC card (PCMCIA) adaptor, which adds a further pounds 150 or so. And mobile calls are expensive compared with fixed phone charges.
The "go anywhere" tag does need to be approached with caution. Mobile phones use radio signals to communicate with the fixed public telephone network, and these are subject to interference from geographical features or even from the weather. Some parts of the country - for example, northern Scotland or the Pennines - have no digital coverage at all. GSM phones do work abroad, but not all countries have a data network.
Mobile phones also work less well in vehicles. Coverage can be improved significantly with a "car kit" (extended aerial, signal booster and hands- free adaptor), although these are expensive. There is no such option for the train.
More seriously, coverage inside buildings varies enormously. This is a particular problem for large buildings with few windows, including most hotels. We were freezing in the grounds of Gleneagles simply because our system did not work inside the hotel.
The alternative to heading outside - finding a socket and conventional modem, or hanging the phone by its data cord from an open window - might have been warmer but would have been much less practical.