168 Dr Pearson, On a series of lunar distances. [Oct. 21, 



the Local Time obtained from tlie Sun, or some other kiminary: 

 the results obtained from Luiiars taken on time thus established, 

 as compared with those taken on time certainly known, seem to 

 prove that no serious error can be fairly suspected on this account. 



It is stated in the paper referred to above that no very long 

 series of observations had led to a conviction that in certain cases 

 the error, if any, in the observed distance was almost always one of 

 defect, and in certain others one of excess; and that the deter- 

 mining cause of error was to be found in the relative positions of 

 the Sun or Star, and of the Moon towards the Meridian. The 

 problem, as far as is known to the author of this paper, has always 

 been made simply to depend on the relative altitudes of the two 

 luminaries : but the methods of solution hitherto used do not 

 seem to have given really satisfactory results. This may be as- 

 sumed on various grounds : in the first place, this method of ascer- 

 taining longitude at sea is now actually very much disused : it is 

 not given in the Berliner Jakrbuch, the recognized German nautical 

 Almanac : works on astronomy admit the difficulty of applying it 

 in practice: Captain Toynbee, F.R.A.S., in the Nautical Magazine 

 for Feb. 1850 (a paper of which there is an abstract in the Monthly 

 Notices of the R..A.S.), distinctly states that he had found by 

 experience that Lunars taken E. of the Moon always give a result 

 thirty or forty seconds different from those taken W., though his 

 mean result, he says, was always satisfactory; and until the early 

 part of this century all East Indian Longitudes were in error 

 about 7' 0" or 28® to the East ; a result which very fairly agrees 

 with the errors resulting from this series of observations. A method 

 of determining longitude, at once so useful and so scientific, so 

 simple and at the same time so nearly exact, ought not to be 

 abandoned because it has not as yet been brought to perfection. 



We will now proceed to give an outline of the results actually 

 obtained. 



Each one of the 200 distances now under discussion is either 

 a mean of three or two, or else depends on only one observation, 

 though there is no reason to think that the last are in any serious 

 degree less trustworthy than the others. The observed distance 

 and the Greenwich time being thus obtained for each example, 

 the altitudes have in all but a very few cases been computed, not 

 observed: and the distance then cleared by Borda's formula. An 

 example is here given of the method employed, in order to satisfy 

 those who may have given attention to the different ways in which 

 the problem itself has been solved. It should however be noted 

 that the following observation, and indeed all those for the year 

 1876, have been worked out by the aid of the Gonnaisance des 

 Terns, and to the meridian of Paris : it was thought that by work- 

 ing for one year on French for another on English authority, any 



