WW's elegant presentation of doctrine of limits is best basis for elementary treatise but not for extensive work, because it involves imaginary functions. Charles Babbage is making progress in theory of functional equations.

Invites WW and [Thomas] Leybourn to join JH for dinner while Charles Babbage is visiting JH at Slough.

Let Josef Fraunhofer make WW's whole transit instrument, and mural circle as well. Attests to Fraunhofer's artistry. Germans will soon leave no stars to discover. Wishes someone would import G. F. Reichenbach's meridian circle and use it on F. W. Bessel's plan. Suggests WW order clocks from [Robert] Molyneux or [William] Hardy.

Edinburgh Institution's decision to order instruments from Josef Fraunhofer should send message to 'dilatory and ... abominably expensive' English artists. Axis of Fraunhofer's 8-foot transit instrument is too long. Compares those of Cambridge, Greenwich, Paris, and James South. [Robert] Woodhouse's paper in 1825 R.S.P.T. eliminated JH's hope that Cambridge would devote time to general catalogue.

Gratified by WW's volume. Recalls JH's catenary theorems. Writes function to complete theory of exponential transcendents. WW's applications have greater practical bearing than JH's early efforts, which JH now finds difficult to decipher. Sorry that WW declared Mr. Gilbert's tables defective.