On August 16, 1922, a fifteen-year-old girl was brought on a stretcher to Frederick Banting in Toronto. She weighed forty-five pounds after more than three years on a strictly controlled diet that had not stopped her decline. Banting, who had begun extracting insulin from animal pancreases at the University of Toronto the year before, started treatment immediately. Writing up her case in 1925, he noted that at that early stage the unit of insulin had not yet been worked out, so it was difficult to accurately estimate the dosage she received.

The danger ran in both directions. Too little insulin left the diabetes uncontrolled; too much drove blood sugar down into hypoglycaemia. Banting described that reaction arriving one and a half to six hours after an overdose: first an unaccountable anxiety and restlessness, often followed by heavy sweating, then a tremor in the limbs that the patient could still control at first. Yet the early doses were written down by volume. In February 1922 one of his patients was given five cubic centimetres of insulin, a quantity that said nothing on its own about how strong the extract in the syringe was.

The fix measured potency against something independently checkable: a rabbit's own blood sugar. One unit of insulin was defined as one-third of the dose needed to drop a fasted, two-kilogram rabbit's blood sugar from 0.118 percent to 0.045 percent within five hours, a reaction any laboratory equipped for the assay could reproduce. By 1925 the Toronto extract was tested on rabbits, diluted to a stated strength of 10, 20, 40 or 80 units per cubic centimetre, and tested again after filtering.

A rabbit's reaction in Toronto still had to mean the same thing in London. In 1923 American-made insulin, tested against a newly revised unit, was due on the British market at the same time as the first public offer of Britain's own home-made product. Doctors who already had a privately made supply had tested it against the original Toronto unit, worth about three of the new ones. The Medical Research Council adopted the revised unit, and P. J. Cammidge wrote to the British Medical Journal that the change would lead to endless confusion between doses on the English and Toronto bases. Henry Dale replied the next week from the council's Department of Biological Standards. The unit had been changed by the Toronto Committee and its American manufacturer, he wrote, not by the council, and the trouble of converting was small next to the need for one measure everywhere.

A unit of measurement is an agreement among the people measuring, and the agreement is what lets a number travel. Once insulin's unit meant the same measured potency whether the vial was made in Canada, the United States or Britain, a doctor anywhere could read a dose off a label and trust it without testing the batch.

The girl Banting had dosed before the unit existed was still his patient in June 1925. Her weight had climbed from forty-five pounds to a hundred and thirty-four; the insulin she needed to stay sugar-free had dropped by about a third, and she said she had never felt better in all her life. By then, the number on her vial was a measurement, not an estimate.