112 Astronomical and Nautical Collections, 



not been done, the average result from the observations of each 

 limb should be taken, and the mean of these held as the true longi- 

 tude deduced from the whole observations. 



Upon these principles, M. Bouvard's calculations of the difference 

 of longitude between Greenwich and Paris will stand thus ; — 



From 31st August, 1800, to 6th August, 1803, when the obser- 

 vations both at Greenwich and Paris were made with the old transit 

 instruments, those at Greenwich being by Dr. Maskelyne, and his 

 assistants; 



Mean of observations of first limb . . 9' 24"'75 

 Mean of observations of second limb 9 20 -24 



Mean of both 9' 22"-50 



From 7th September, 1803, to 11th April, 1811, when the ob- 

 servations at Greenwich were made with the old transit instrument 

 by Dr. Maskelyne, and his assistants, and those at Paris with the 

 new transit instrument ; 



Mean of first limb 9' 25"-85 



Mean of second limb . 9 18 -07 



Mean of both . . . . 9' 21"-96 



From 14th May, 1811, to 2d June, 1816, when the observations 

 at Greenwich were made with the old transit instrument by Mr. 

 Pond, and his assistants, and those at Paris with the new transit 

 instrument ; 



Mean of first limb 9' 20"- 10 



Mean of second limb 9 20 -36 



Mean of both .... . . . . 9' 20"-23 



From 5th July, 1816, to 1st December, 1819, when the obser- 

 vations at Greenwich were made with the new transit instrument, 

 and those at Paris, as formerly ; 



Mean of first limb 9' 21'M3 



Mean of second limb 9 20 '50 



Mean of both . . 9' 20"'96 



The formula cf = a f ^ H- j may be expressed in ano- 

 ther manner, which will be found more convenient for calculation , 



