Goniometric Trollems. 139 



justment of the instrument before each observation ; and no 

 angles should be measured when the wind is high, and the 

 stand or scaffolding not very firm *. 



Legendre has proved, in a work lately published by him, 

 entitled " Nouvelle Mcthode pou7- la Determination des Or- 

 lites des Cometes," that in order to diminish as much as pos- 

 sible the influence of errors committed in measuring arcs, 

 or in any series of observations whatever, we must render 

 the sum of the squares of these errors a minimum. He has 

 also proved, in another work, that the difference between 

 spheric and spheroidic angles does not amount to so much 

 as the -^^-g\.\\ part of a second in the greatest of the French 

 triangles. The consideration of the spheroid may therefore 

 with safety be neglected, and the earth may be taken as a 

 perfect sphere in all such geodesic operations as are usually 

 carried on. 



The real places of the stations cannot be assigned by only 

 knowing their distances ; it it necessary, besides, that we 

 should know the latitude and longitude of one place, and 

 the angle made by one of the sides of the triangle with the 

 meridian of this place : we may then refer the other two 

 places to the meridian find equator, or determine their lati- 

 tudes and longitudes. 



In taking a scries of triangles for any purpose, such as 

 determining an arc of the meridian, it is necessary to mea- 

 sure either one or two bases of verification, in order to as- 

 certain whether the results obtained from the calculation are 

 correct at the end of the operations. 



* It frequently Ixappens that exhalations, and other causes, will make the 

 object move about in the field of view of the telescope : when this is the case, 

 the observation had better alwaysbe deferred till the object appears steady. 



XIX. On 



