Narrative of the surveying voyages of his majesty's ships Adventure and Beagle (vol.2- Appendix): between the years 1826 and 1836 : describing their examination of the southern shores of South America, and the Beagles's circumnavigation of the globe

320 APPENDIX. that any one had suddenly varied from its rate, its result was omitted in the determination. The method of interpolating for the alteration of the rates which I have adopted, is one that was successfully employed by Captain Flinders in his survey of New Holland ; and one that I have been for many years in the habit of using with most satisfactory results. In cases where chronometers alter their rates suddenly, the rule cannot be applied ; but, in general, the alterations are caused by changes of temperature ; and as these changes are "gradual, so the rates alter in the same progressive manner. The correction has, therefore, been obtained by an arithmetical progression ; in which the first term, the number of terms, and the common difference, are given to find the sum of the terms. The difference between the two rates divided by the number of days that have intervened, called the daily variation of rate, is the first term F ; as well as the common difference D : the interval between the determination of the errors of the watches, in mean time, of the place left and arrived at, is the number of terms N : and the sum of the terms is the correction required, S. The formula, when reduced to its simplest form, is F (N-fl) ^=S. The places which I was instructed to visit for the purpose of mea- suring their respective meridional differences were Madeira, Santa Cruz in the island of Teneriffe, the north-east end of San Antonio, and Port Praya in the island of St. Jago, in the North Atlantic ; and the island of Trinidada, Rio de Janeiro, and Monte Video, in the South Atlantic Ocean. After the chronometers had been carefuUy rated at the Observa- tory, they were embarked on board H.M.S. Adventure, on the 23rd April, 1826 ; but as the ship was detained at Deptford and North- fleet until the 4th May, an opportunity was offered of ascertaining what change had been produced by the alteration of the place ; and it turned out to be by no means inconsiderable. Five of the watches had accelerated, and the remaining four had retarded rates. It would be difficult to assign any other reason for this change than the effect of the ship's local attraction. With this newly found rate we sailed for Plymouth ; and, after five days' passage, arrived in the Sound ; and, on the 9th May, ob- tained a set of corresponding altitudes upon the Breakwater, upon a stone marked ^ ; which, by the Ordnance map, is 0' 31 "-5 in longi-