L O N 



If x o, y 1 ; and if x 1, ^ a. 



If the abscissas increase in arithmetic progression, the ordinates in- 

 crease in geometric. 



The subtangent is a constant quantity, and = modulus of the system 

 of logarithms, whoso base a. 



Area between any two ordinates y and b in (y b), where m is the 

 modulus or subtangent. 



Content -^ (yt 62). 



Arc = ^/( m* -f #2) ^( m 2 4. 52) 



b (^( 

 + m log. - 



y(^/(m* + &) w 



Surface ~- T ( ?/ ^(w/2 4- ?/ 8 ) 6 ^ (wa 4. &g) 



LOGARITHMIC Spiral See Spiral 

 LONGITUDE Geographical (Woodhouse, Fince.J 



\sl Method, by a chronometer. 



Suppose a chronometer to be adjusted to mean solar time at Green- 

 wich, then if its motion were equable, and of the proper rate, we should 

 always know, whatever the place, the time at Greenwich. Compute .*. 

 the apparent, and by means of the equation of time, the mean time, at the 

 place of observation. The difference between this latter time, and that 

 shewn by the chronometer, would be the longitude, east or west of 

 Greenwich. 



2d Method, by an eclipse of the moon or of Jupiter's satellites. 



Having the times calculated when the eclipse begins and ends at 

 Greenwich, observe the times when it begins and ends at any other 

 place ; the difference of these times, converted into degrees, gives the 

 difference of longitudes. 



3d. Method, by the moon's distance from the sun or a fixed star. 

 The steps by which we find the longitude by this method are these : 

 From the observed altitudes of the moon and the sun or a fixed star, 



and their observed distance, compute the moon's true distance from the 



sun or star. 

 171 



