272 INVESTIGATION OF CERTAIN THEOREMS, 



Other aHvantage, which in the cafe of theBritifli furvey is un- 

 doubtedly very great, viz. that all the data arc furniflied from 

 one fyftem of trigonometrical operations; executed according 

 to the fame plan, with the fame inftruments, and by the fame 

 obfervers. 

 To determine 30. One other application of geometrical meafurements to 



die earth's difcover the figure of the earth yet remains to be confidered. 



ngure by com- . , . ■' 



paling an arc of This is the comparifon of an arch of the meridian with an arch 

 the rr.er. with of a parallel of latitude which croffes it. The meafure of a 

 {n fame lat. parallel of latitude can be executed readily, and is not confined 

 to a fmall arch, as in the cafe of a perpendicular to the meri- 

 dian. The plumb-line, while it is carried along the circum- 

 ference of a parallel to the equator, tends continually to the 

 fame point in the earth's axis, fo that there is no difficulty in 

 afcertaining the amplitude of the arch meafured, providing 

 there be no unufual difturbance of the dire6lion of gravity. 

 As an arch of a parallel to the equator, however, is not the 

 fliorteft line between two points on the furface of the fpheroid, 

 the meafurement along that furface will not give the length of 

 the arch truly. To obviate this difficulty, it is only necelTary to 

 follow the method fo properly introduced into the TrigonomC'^ 

 trical Survey, of reducing the meafures, both of lines and 

 angles, to the chords and to the planes of the redilineal tri* 

 angles contained by them. In this way, the chord of an arch 

 of a parallel of latitude ipay be determined, however great the 

 arch ; apd it is worthy of being remarked, that, whatever be 

 the defle61ions of the plumb-line at the intermediate ftations, 

 when the redu6lions are all properly made, the length of the 

 chord meafured will not be aflfe6led by them ; the amplitude 

 of the arch indeed may be aflfefled by fuch defle6tions, if they 

 happen at its extremities ; but the eflfe^ of this error will b© 

 rendered the lefs, the greater the arch that is meafured. We 

 may fuppofe, therefore, that the chord of a large arch of a 

 parallel of latitude is meafured, ar^d the amplitude of the arch 

 itfelf {it the faiTie time accurately ^fcertained. This laft may 

 ' be done, either by ipeafuring the convergency of the meridians, 



if it be in a high latitude, or by any other method of afcertain- 

 ing diflferences of longitude which admits of great accuracy. 

 The chord being thus given in fathoms, and the arch fubtended 

 by it being given in degrees and minutes, the radius of the 

 parallel itfelf becomes known, 



3 J. NoW;, 



