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- 



