Precision of quasi-optical null-balanced bridge techniques for transmission and reflection coefficient measurements

The precision of quasioptical null-balanced bridge instruments for transmission and reflection coefficient measurements at millimeter and submillimeter wavelengths is analyzed. A Jones matrix analysis is used to describe the amount of power reaching the detector as a function of grid angle orientation, sample transmittance/reflectance and phase delay. An analysis is performed of the errors involved in determining the complex transmission and reflection coefficient after taking into account the quantization error in the grid angle and micrometer readings, the transmission or reflection coefficient of the sample, the noise equivalent power of the detector, the source power and the post-detection bandwidth. For a system fitted with a rotating grid with resolution of 0.017 rad and a micrometer quantization error of 1 μm, a 1 mW source, and a detector with a noise equivalent power 5×10−9 W Hz−1/2, the maximum errors at an amplitude transmission or reflection coefficient of 0.5 are below ±0.025.

The credit relationship between Henry III and merchants of Douai and Ypres, 1247-70

This article looks at an important but neglected aspect of medieval sovereign debt, namely ‘accounts payable’ owed by the Crown to merchants and employees. It focuses on the unusually well-documented relationship between Henry III, King of England between 1216 and 1272, and Flemish merchants from the towns of Douai and Ypres, who provided cloth on credit to the royal wardrobe. From the surviving royal documents, we reconstruct the credit advanced to the royal wardrobe by the merchants of Ypres and Douai for each year between 1247 and 1270, together with the king's repayment history. The interactions between the king and the merchants are then analysed. The insights from this analysis are applied to the historical data to explain the trading decisions made by the merchants during this period, as well as why the strategies of the Yprois sometimes differed from those of the Douaissiens.