now measuring on the ContinenL 



187 



arcs ; with the corresponding length of a degree of the parallel, 

 as separately deduced from each of the arcs : — 



In order to obtain from these results the most probable 

 value of the degree of the parallel, MM. Brousseaudand Nicollet 

 have followed a method recommended by Lieutenant- Colonel 

 Puissant, of the Corps of Ingenieurs-geographes, in a memoir on 

 the determination of the figure of the earth, inserted in the eighth 

 volume of the Memorial Topographique et Militaire. This 

 method consists in making as many equations of condition as 

 there are partial arcs, of the form : — 

 ^__r__ e_ 



rr "" 240 " 240 

 wherein b is the arc in metres, T the observed celestial ampli- 

 tude in seconds of time, e the probable error of that deter- 

 mination, and X the most probable value of the degree ; and 

 these equations being treated by the method of least squares, 

 the value of a; is obtained*. 



By this process the most probable value of the degree of 

 the parallel deduced from the six preceding results is 77865,75 

 differing 3.15 met. from 77862,60, the value deduced from 

 1010996,176, the total arc in metres divided by 59', 56", 948, 

 the sum of the several celestial amplitudes ; and 1,71 met. from 

 77864,04 m^t., the value obtained by taking an arithmetical 



♦ Or substituting for a?, /S + a*, in which a value is taken for /S, diflpering 

 not more than a few units from the most probable vahie of the degree, 

 and X a quantity so small that its square may be neglected ; the equa- 

 tions of condition may then be made of the following more convenient 

 form : — 



240. b. 240. b. 



from whence the value of x being ascertained, and added to that as- 

 sumed for /S, tlie most probable mean value of the degi-ee is obtained. 



