On the figure of ths EARTH. 313 



two right lines hlo (Fig. i.) and HLO reprefent two 

 tangents to the fame meridian ; and let fl and SL re- 

 prefent two rays, parallel to each other, and to the 

 common diameter of the meridian of the place and the 

 equator; the angles y/ /6 and SLH will be the altitude 

 of the fun at / and L as taken with Hadley's odant. 

 Draw zlm and ZLM perpendicular to the refpedtive 

 tangents through / and L and meeting each other in M, 

 then will the angles y/z and SLZ be the latitudes of / 

 and L. Hence it appears that the latitude of a place is 

 meafured by the angle formed by the common dia- 

 meter of the meridian and equator, and a perpendicular 

 to the horizon of the place ; for the lines fl and SL are 

 parallel to the common diameter ol the equator and me- 

 ridian (by conftruftion). Produce SL to T. The angle 

 ST/ is equal to the angle/"/;?, and confequently to the 

 latitude of / and the angle TLM (equal to SLZ) is equal 

 to the latitude of L. The angle ST / is equal to the 

 angles TLM and LMT taken together and confequent- 

 ly the angle LMT is equal to the dlfTerence between the 

 two angles bT / and TLM, equal to the difference be- 

 tween the latitudes of the two places. That is, the dif- 

 ference of latitude between two places on the fame meri- 

 dian, is meafured by the angle formed by the perpendi- 

 culars to the two horizons.* 



By all the obfervations made at Greenwich and elfe- 

 where, the altitudes of the heavenly bodies as obferved 

 with the mural and plummet quadrants agree with thofe 

 taken with the refledting or Hadley's odlant.f Now let 

 ABDE be an ellipfis (Fig. 2.) and HLO a tangent, ZLT 

 a perpendicular to that tangent fVj a ray of light (the 

 fun being in the equator and on the meridian) yLZ is 



the 



* In this demonftration nothing, which has been before demonftrated, 

 is, on that account alone, omitted. 



f This part of the demonftration is necefTarily experimental, not mathe- 

 matical. 



