refyBt&ng the Caufe of the Tides. 147 



circle, a greater or lefs portion of ground will be patted over 

 before the defired elevation is obferved ; and the measure- 

 ment of this ground uneqnivocallv decides whether this 

 degree is part of a larger or fmaller circle. In this cafe the 

 measurement is admitted, but the conclusion denied. St. 

 Pierre feenis to have fup poled, that the academicians di- 

 vided the polar arc into 47 parts, and then meafured one of 

 thefe parts : a thino; impracticable and ridiculous. The fact 

 is, that the polar arc, which, if the earth were a perfect 

 fphere, would contain 47 °, does not actually contain l'o 

 many, but perhaps about 46" of a larger circle; and if the 

 polar degrcs arc parts of a larger circle, as they certainly 

 are, it is demonftrably evident that, the real arc muft he 

 contained within the fphericai arc, and. confequcntly, that 

 the earth is flattened at the poles *. 



[To be continued.] 



* Let die circle A B C D, Fig. 4. reprefcm the earth as a fphere, and let 

 P represent the polar ftar, having no fenfible parallax. Draw the diameter 

 1>D, prolonging it to P; draw the traufverfe diameter C A, the tangent 

 A P, am! the line F P, parallel to A P ; ln(e£t the quadrant A D equally 

 at F ; draw the tangent K. L perpendicular to the radius G F, and with 

 the radius B F d.fcnbe the circle E O M N, and let the fegment II E F 

 re;ireient the earth flattened at the pole; draw the tangent S K. to the 

 circle EOMN, perpendicular to the radius B F. An obferver at A will 

 perceive the polar ftar P in the horuon ; an obferver at D or E will per- 

 ceive it in the zenith, or at an elevation of 90 . If the earth be a fphere, 

 , the tangent K L will be the horizoji to an obferver at F, and the angle of 

 elevation P F K is, by conftruftion, 45 ; but if the earth is not a fphere, 

 but flattened towards the pole, as iu'the fegmetit H E F, the tangent S R 

 will be the horizon to an obferver at F, ai.d of couife the ang'e P F S will 

 be the angle of elevation. Now, the angle I 7 . G F is bv coniUudtion 45 , 

 confequcntly, the <FGB 1 5 5 , and the angles GRF and G F B each 

 42° 3c'. Draw the dotted line EF- Now the triar J.e BEF is an ifofceles 

 triangle, and the angle G B F being found =- zz° 30', it follows that the 

 an?Ls B E F and B FE are each 78" 45', and the < S F B being a right 

 angle, the < SFE is 90° — 78° 45' = 11 15'. At E draw the tangent 

 T V, and, for the fame n afori, the < VEF=u c 15'; and conftquently 

 the < E.vF = 157? jo', and tiv; < V .r F = iz° 30'. Now the < FZS 

 is a right angle, therefore the angle P F S = iHo° — 90" — 2; 30', or 

 67° 30'. The difference, therefore, between the elevation at E and at F 

 will be 9 <° — 67,30= iz°. 30', but the difference between the elevation 

 at F and D will he 43°; whence it is evident that a larger mcafuiement 

 .of ground will be included in a degree in proportion as HEF is the (eg. 

 pent ( f ;. largci . . ircJe. 



U? VIII. Je- 



