L E V 



a y x v 2 _. #x 

 a of James Bernouilli. 



or considered as a spiral 

 = a Vcos~2~0. 



LENGTHS ofctt.rve9.-See Rectification. 



LENS. See Refraction. 



LEVELLING. 



T\vo or more places are on a true level, when they are equally distant 

 from the centre of the earth ; and a line equally distant from that centre 

 in all its points, is called the line of true level. This line is nearly an 

 arc of a circle, and will evidently pass below the line of apparent level, 

 which, as determined by the instrument, will be a tangent or a parallel 

 to a tangent at the earth's surface at the point of observation. Hence 

 the depression of the true below the apparent level is always equal to the 

 excess of the secant of the arc of distance above the radius of the earth. 

 To find this depression, let L be the arc of distance in English miles, D 

 the depression in feet ; then 



TABLE shewing the height of the apparent above the true level for every 

 100 yards of distance on the one hand, and for every mile on the other. 



