Werner and Hauptmann triangulate Volkheimer's location

The search for Frank Volkheimer is a midnight field test in which Werner Pfennig and Dr. Hauptmann use triangulation to locate a hidden transmitter across a snow-covered landscape. Its decisive turn comes when a successful calculation brings Werner within sight of Volkheimer—and Dr. Hauptmann raises a pistol, making the exercise briefly seem like a real threat. The scene tests not only the equipment but Werner’s capacity to understand what its measurements mean when a person stands at their end.

The field test begins

At midnight, Dr. Hauptmann’s hounds run through frozen fields beside Schulpforta, their movement likened to quicksilver against the white. Dr. Hauptmann follows in a fur cap, taking short strides as though counting distance; Werner brings the pair of transceivers that he and his teacher have been testing for months. The setting is both a working landscape and an immense obstruction: from the chosen clearing Werner sees no tracks, only snow and forest.

Dr. Hauptmann explains the arrangement. Frank Volkheimer has gone ahead with a KX transmitter hidden in an ammunition box. He is to conceal himself and broadcast continuously until the searchers find him or the battery dies. Even Dr. Hauptmann does not know where he is. The search area covers ten square kilometers, and the task is to locate the signal—and, through it, their fellow cadet.

The exercise makes the transmitter’s invisibility central to its purpose. Volkheimer is somewhere among the trees, but the searchers cannot use footprints or a known destination to reach him. Dr. Hauptmann calls this the enjoyable part of the work; Werner, looking toward the expanse of snow-covered forest, asks whether the target is really out there. The difference between the teacher’s confidence and the scale of what Werner sees gives the test its initial tension.

Turning a signal into a position

Werner sets up the two transceivers two hundred meters apart, using a measuring tape to pace the distance. He uncoils their grounding wires, raises the aerials, and switches them on, working with fingers already numb from the cold. Dr. Hauptmann tells him to try eighty meters: teams in the field may not know which band to search, but for this first test they will make the problem easier.

With a headset over his ears, Werner tunes through static, raises the RF gain, and adjusts the filter until both receivers pick up Volkheimer’s transmitter pinging along. He reports that he has the signal. Dr. Hauptmann then insists that Werner do the calculation on the radio itself, since a field team may not have paper. Werner uses a grease pencil to sketch the equation on the transceiver’s metal casing, enters the figures, and works with a slide rule. Within two minutes, he has a vector and a distance: two and a half kilometers.

That result converts the signal from a sound in the headset into a direction and measurable range. Werner draws lines with a protractor and compass on the map, then follows the indicated route with Dr. Hauptmann and the hounds. As the first reading brings them closer, the calculation dictates the next movement through the woods; mathematics is not merely discussed but used to decide where the searchers go.

Closing in on Volkheimer

Farther up a third climb, Werner unfolds the map and checks his bearings with a compass. The trees remain silent and bright with snow, and there are no tracks except those made by the search party. Dr. Hauptmann signals him to be quiet. Werner triangulates again: the new reading places them less than half a kilometer from the earlier estimate. He packs the equipment and picks up his pace, carrying the cases as the dogs begin to respond to a scent.

The approach is described through the convergence of instruments, animals, and sight. The dogs freeze and twitch their noses; Dr. Hauptmann holds up a hand. Coming through a gap in the trees, Werner sees a man lying faceup in the snow, with the transmitter at his feet and its antenna rising into low branches. The concealed operator and the source of the signal are now physically present in the same scene. Werner’s reflection that he has found a way in and is solving the problem captures the exhilaration of a method becoming real just as the search becomes personal.

The human stakes of the calculation

Dr. Hauptmann keeps one hand raised and draws his pistol with the other. He warns Werner that, at this close distance, hesitation is not possible. Volkheimer lies with his left side toward them; Werner can see his breath rise and disperse. Dr. Hauptmann aims a Walther at him. For a startling moment, Werner believes his teacher is about to shoot the boy and that all the cadets are in grave danger.

The threat forces the search out of the safe register of technical practice. Werner recalls Jutta’s question about whether it is right to do something only because everyone else is doing it. As Dr. Hauptmann fires, however, he shoots into the sky, not at Volkheimer. Volkheimer leaps into a squat as the hounds charge, but they recognize him and bound around him in play; he throws them off as if they were housecats. The alarm Werner has felt gives way to relief, while Dr. Hauptmann laughs, his pistol still smoking.

The test ends in success and celebration: Dr. Hauptmann passes Werner his flask, Werner drinks, and his teacher identifies the exercise as an example of what they are doing with the triangles. Volkheimer approaches carrying the KX transmitter and rests a mittened hand on Werner’s cap. Quietly, beyond Dr. Hauptmann’s hearing, he says, "It’s only numbers." The remark leaves the scene’s central contrast unresolved. Triangulation has located a person with precision, but the successful solution has also made that person, for a moment, the target at the end of a line on a map.