Ii4 tWisTlG At iOV OF CERTAIN THEOREftf^ 



1 . fin (p^ 



and tan (p* inftead of — - — ; we have then. 



col ^*' coi (p^ 



<* m -^ (ly -- D) fee <P», 



a '=mD'-^^ (D' — D) tan ^», and 

 fkampV of tfhe i'9'. i^Q may apply thefe formulas to the computation of-, 



compreflion de- (I 



duced from the Szc, from the degrees of the meridian and perpendicular, mea- 



jcrpcndicukr.' f^^ed in thQ fouth of England. We find, in one example, 



(Phil. Tranj: 1795, p. 537), that D~ 60851 fathoms, D' — 



©1182,. the latitude, or ?> being — 30^ 41^ From this — zr 



D'— D 331 1 



which 



2D'cor»cp ■" 2x61 182 X (cof 50"* 41/)* "^ 148.4 

 is nearly the fame refult with that deduced fn tlfie paflage juft 

 referred to. Indeed the folution of this problem, contained iil 

 the Trigonometrical Siirveif, is quite unexceptionable ; and the 

 theorems here offered are not given as containing a more 

 accurate folution, but one that is in fome refpedls more fimplej 

 Whether the The al>bve compreflion, if qy© remarks already made be well 



rnagnitudc of founded, is much too great, being mor6 than double of what 

 prcve an irrcgu- was obtain^ from comparing the whole arch of the meridian 

 lit figure. meafurei in Frai)cevvith the whole of that meafured in Peru. 



At' the fame tune, it is right to obfeirve, that all the other eom- 

 parifons of the degrees of the meridian, with tliofe of the 

 curve perpendicular to ifc, ifiade frotii the obfervations in the 

 fouth of England, agree nearly in giving the fame oblatenefs 

 to the terreftrial spheroid. For this circumflancci it is cer- 

 tainly not eajy to account; the unparalleled accuracy with 

 ivbich^Ke' S^noie of the m^afurement has been condudled, 

 makes it in the higlie^ degree improbable that it arifes from 

 any *-tror ; and eve» if errors were to be admitted, it is not 

 iikely that they fliOuld all fall on the fame fide. The authors 

 of the TrigdinomeiTical Survey feem willing, therefore, to give 

 Mp the elliptic figure of the earth, (Ibid. p. 527); but before 

 we abandon that very natural and fimple hypodiefis, it may 

 perhaps be wortli vvhile to attend to the following confi- 

 dtrations, 



20 



