Continues explicating P. S. Laplace's formula for determining Bernoulli's numbers. Concerned that JH sees HW claiming too much for HW's continued subtraction method.

Verified Leonhard Euler's values for Bernoulli's numbers up to B=25 by method previously outlined and to be stated fully in this letter. Mr. Hensley [of Trinity College] proposes to revise incorrect values given in Penny Cyclopaedia. Computing a Bernoulli number by P. S. Laplace's formula takes three days. HW's method of continued subtraction requires only 24 hours.

Proved accuracy of Leonhard Euler's values for Bernoulli's 27th number. Plans to test number 29. Will investigate Thomas Clausen's theorem, the generality of which JH appears to have disproved.

Demonstrates property of 'Coefficients of the terms of the Numerators of the Fractions which generate the odd powers of the Numbers of the Natural Series.' Claims this method can compute Bernoulli's numbers 37, 39, and 41.

[George Eden] Lord Auckland seeks meteorological 'reports.' CW will contribute instructions on atmospheric electricity, photometry, and optical meteorology. W. R. Birt will report on meteorological instruments and wind observations.

Lord Auckland [George Eden] asked JH to edit [Admiralty Manual] for officers on surveying and exploring expeditions. Charles Wheatstone will prepare instructions for meteorological observations. Asks WB to write instructions on detecting 'atmospheric waves and barometric fluctuations.'

All scientists named by GE, except [Adam] Sedgwick, will contribute to Admiralty Manual, but only one has a paper already prepared.

Lord Auckland [George Eden] has asked JH to edit Admiralty Manual and proposed that WH write section on botany. Would WH do this and when could WH complete it?

Is editing a manual for surveying and exploring expeditions. Asks WW to do section on tides.

Has now sent the letters and circulars to the various people in connection with the Admiralty Manual. Has not sent one to W. R. Birt, but will do so if JH thinks it advisable.

Has been reading as far as page 36 of the proofs with great pleasure. Regarding choice of words for a phrase. Richard Jones is uninfluenced as yet.

Congratulations on finishing his paper. Would he check over the proofs. Richard Jones is well, though not well enough to attend at the College chapel. J. E. D. Bethune and John Lefevre are staying with Jones. Bethune starts for India in February.

Francis Jeffrey (Lord Jeffrey) is the writer of Plaidoyer in the last number; intends it to be a judicial deliverance. Has sent JH's review of the translation of Kosmos to Lord Jeffrey and he praised it highly. Gives some of his comments.

JDH hopes to be at Aden tomorrow. On arrival at Alexandria 4 Dec Ld Dalhousie insisted he belong to his suite in future. Left Alexandria on Sunday for Cairo. Travelled with Captain Henderson & officers using Transit Offices steamer along the Makmoudea [Mahmoudieh] Canal, discusses the canals construction & death of many Egyptians. Describes landscape, mentions Tamarix, Dates, Acacias, Cyprus & Myrtle. Switched to a pleasure packet steamer placed at their disposal by Mehmet Ali [Muhammad Ali]. Describes luxurious fittings in the part for Lord & Lady Dalhousie. The rest of them: including the Prime minister of Egypt, messed on deck in little cabins with simple facilities. Describes the Nile as about as broad as the Thames at Kew, mentions reading Bruce's and Salt's travels in the past. River banks are cliffs of mud showing successive layers of deposited soil to which Egypt owes its scanty vegetation. Saw lonely Arabs, Dromedary, tents, & donkeys. Beyond river banks wide spread uninhabited sand deserts. Irrigation attempted here & there, houses rare & always built near trees. Numerous boats such as figured in Bruce's journey. Describes first glimpse of the Pyramids & Cairo. Few miles before the town are Mehmet Ali's country gardens and Palaces of Shoobra [Shubra]. Thinks the Leicester Square Panorama gives an admirable idea of Cairo's location. During Cairo stay visited Ali Pasha's Rhoda Gardens but on the whole disappointed & outlines the difficulties of an exotic garden in Egypt. Mr Traill received him very cordially & showed him the gardens which JDH briefly describes. Letter continues Aden 19 Dec. Describes Aden as wonderful, bleak & barren. Dr M[?] has gone to Bombay for good & is now at Scinde [Sindh]. The bulbs JDH would have are not above ground & everything but Capparis, & a few other things are burnt up. He has sent Lord Auckland's parcel of seed onto Bombay [Mumbai].

JDH describes his journey toward Ceylon [Sri Lanka] via Egypt, Suez, Red Sea & Aden. Writes of his time Cairo & the agriculture, vegetation & landscape of the region, the only trees are date palms, Acacia lebbek & Sycamore figs. Enumerates species seen on visit to Rhoda Gardens with Mr Traill, discusses problems of having this garden on an island in the Nile & recommends WJH read Traill's account in GARDENERS' CHRONICLE. Also writes observations of: visit to Fojal Forest with officers of the Sidon; the Pyramids; Cairo Pass tombs visited with the Governor General; fossil forest in the limestone desert; vegetation outside Cairo, mainly Capparideae, Zygophyylleae, Rutaceae & Hyoscyamus; dining with the with Consul General, a brother of Capt. Murray RN. Describes transit from Aleaxandria to Suez at the Pasha agents' expense. Ld & Lady D travelled by Barouche, vans transported Dr Bell, Jane, Courtenay, Capt. Henderson & various servants on roads the Arabs are bribed to maintain, Colocynth [Citrullus colocynthis] the only plant. Describes views of Red Sea & Sinai & the sterile landscape around Suez. At Suez met Col Heaney & son, Matilda Rigby & husband. Sailed down Red Sea in the 'Moozuffer' under Captain Ethersley. Sargassum prevalent at about latitude 20, describes islands passed. Boatswain killed. Saw conferovid plant described by Montagne in the ANNALES TRICHOSEMINA RYTHREENA. Passed Mocha & Strait of Babel Mandeb before arriving at Aden. Discusses wind phenomena & saltiness of Red Sea. Describes Aden volcano as resembling St Helena but even more barren than Green Mt in Ascension. Shore wooded with Acacias, Dates, and Mangroves. G.G. wants reports on tea districts of India. Assam did not enter into JDH's calculations. Also includes a printed black and white illustration entitled: ADEN "THE GIBRALTAR OF THE RED SEA".

JDH has been delighted with his trip hitherto. Describes visiting Cairo & wishes his cousin could see the pyramids as he did. Discusses belt of productive soil along the Nile & its small rate of soil deposition. Discusses location of the pyramids & the island on which the Nilometer is situated, & its influence on the corn market. Crossed the Nile on a boat similar to that figured in Bruce’s TRAVELS. Describes two sketches made during the crossing.. On both banks saw Egyptians, Ethiopians, Nubians, Abyssinians, Turks & a few Copts. Reached Ghizeh [Giza] & struck inland, carried by Arabs when it became very muddy. Arabs were scattering vegetable seeds. Reached the pyramids, thinks the Sphinx 'stupendous'. Bases of pyramids covered deeply with rubbish. Only had time to go over the Pyramid of Cheops properly. Describes the magnificent view from the summit. Made a few sketches of the grandest but certainly least attractive scene he has ever viewed. Collected lichens from pyramid summit. Went into pyramid interior & recalled every passage & chamber from childhood interest. Finds one grievous disappointment with the pyramids; their futility as simply mausolea. As a child he regarded them as being constructed for three purposes: as astronomical buildings; as places of worship; & as edifices to the genius of the Nile. He was glad to see Matilda Rigby so soon after she had dined with Lady Palgrave.