12 INVESTIGATION of certain THEOREMS 



ii. The fame thing that renders the companion of large 

 arches of the meridian ufeful for leffening the effect of errors 

 arifing from irregularities in the direction of gravity, makes it 

 ferve to diminish the effect of all the errors of the aftronomical 

 obfervations at the extremities of the arches, from whatever caufe 

 they arife. They are all diffufed over a greater interval, and 

 have an effect proportionally lefs in diminifhing the accuracy 

 of the lafl conclufion. 



12. The meafurement therefore of large arches of the meri- 

 dian, efpecially if performed in diftant countries, is likely to 

 furnifh the belt data for afcertaining the true figure of the 

 earth ; and on this account extenfive and accurate furveys, fuch 

 as that above mentioned, are no lefs interefting to fcience^ in 

 general, than conducive to national utility. The furvey of this 

 Ifland, when completed, will furnifh an arch of the meridian, 

 beginning at the fame parallel where that meafured in France 

 terminates, and nearly of the fame extent, fb that the length ot 

 an arch of more than i6°, or almoft a twentieth of the earth's 

 circumference, will become known. The different portions of 

 this arch compared with one another, or with the arch meafu- 

 red in Peru, will afford a variety of data for determining the 

 true figure of the earth. 



But furveys of the kind now referred to, afford like wife 

 other materials from which the folution of this great geographi- 

 cal problem may be deduced. Thefe are chiefly of two forts, 

 viz. the magnitude of arches, either of the curves perpendicular 

 to the meridian, or of the circles parallel to the equator. Exam- 

 ples of the firil of thefe have been given by General Ro\ and 

 Mr Dalby ; the obiervations which follow are directed toward 

 both. 



13. With refpect to the meafurement of arches perpendicu- 

 lar to the meridian, it may be obferved, that the directions of 



gravity 



