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In the lab the ice core was cut into rods just over three feet long that were stood on a heating pad and melted from the bottom. Grooves in the pad directed water from the central and purest part of the core to instruments known as mass spectrometers that continuously measured the quantity of lead down to one hundredth of a picogram, which is one trillionth of a gram. When the ice core was set to melt at the rate of two inches per minute, Dr. McConnell’s team found they could take 12 measurements per year throughout the Roman era.

The dates of these ice years were verified by synchronizing them with other chronologies, such as those derived from tree rings and volcanic eruptions.

The continuous record of lead pollution is not as good as having figures for Roman gross domestic product, which no one knows, but it does seem to reflect the general economic health of the Roman state.

The results, published in Monday’s issue of the Proceedings of the National Academy of Sciences, show a fluctuating line whose peaks and troughs correspond to salient events in Roman history. Lead emissions rose in periods of peace and prosperity, such as the Pax Romana, which ran from 27 BC to 180 A.D. and dropped during the civil wars that preceded the Pax and the rise to power of the emperor Augustus. There were also dramatic drops that coincided with the Antonine plague of 165-180 A.D., thought to have been small pox, and the Cyprian plague, cause uncertain, of 250-270 A.D.

Lead was widely used in the Roman economy for making water pipes and sheathing the hulls of boats. Its production was also a proxy for a central economic activity, the use of silver in the Romans’ standard silver coin, the denarius. Silver occurs in lead ores, and the process of separating the silver from lead at high temperatures was a major source of airborne lead. In the early Roman Empire the denarius was 100 percent silver. But under the emperor Nero, starting in 64 A.D., the proportion of silver was reduced to 80 percent and the state made a tidy profit by recycling the all-silver denarii into debased ones.