LONGITUDE. 



them must be less than a degree upon the 

 equator, in the ratio of the co-sine of the 

 latitude to the radius. Hence, as the 

 radius is to the co-sine of any latitude ; 

 so is the minutes of difference of longi- 

 tude between two meridians, or their 

 difference in miles upon the equator, to 

 the distance of these two meridians on 

 the parallel of that latitude, in miles. 

 And, by this theorem, is the following- 

 table constructed. 



A TABLE, 



Shewing how many miles answer to a 

 Degree of Longitude, at every Degree 

 of Latitude. 



LONGITUDE, in navigation, the distance 

 of a ship or place, east or west, from an- 

 other, reckoned in degrees of the equa- 

 tor. As the discovery of a method to 

 find the longitude would render voyages 

 safe and expeditious, and also preserve 

 ships and the lives of men, the following 

 rewards have been offered by act of par- 

 liament, as an encouragement to any per- 

 son who shall discover a proper method 

 for finding it out : the author or authors 

 of any such method shall be entitled to 

 the sum of 10,0001. if it determines the 

 longitude to one degree of a great cir- 

 cle ; to 15,0001. 5 f it determines the same 

 to two-thirds of that distance; and to 



20,000^. if it determines the same to one- 

 half of the same distance ; and that half 

 of the reward shall be due and paid when 

 the commissioners of the navy, or the 

 major part of them, agree that any such 

 method extends to the security of ships 

 within 80 geographical miles of the 

 shores, which are places of the greatest 

 danger ; and the other half, when a ship, 

 by the appointment of the said commis- 

 sioners, or the major part of them, shall 

 thereby actually sail over the ocean, from 

 Great Britain to any such port in the West 

 Indies as those commissioners, or the ma- 

 jor part of them, shall choose for the ex- 

 periment, without losing their longitude 

 beyond the limits before-mentioned. The 

 French, Dutch, Spaniards, and other na- 

 tions, have likewise offered rewards for 

 the same purpose. 



Since, by the motion of the earth round 

 its axis, every point upon its surface de- 

 scribes the circumference of a circle, or 

 360, in twenty-four hours time, it is plain 

 it must describe 15 in one hour, because 

 3^ 15. Hence the difference of lon- 

 gitude may be converted into time, by al- 

 lowing one hour for every 15 degrees, 

 and proportionally for minutes ; also dif- 

 ference of time may be converted into 

 difference of longitude by allowing 15 

 for every hour, and proportionally for a 

 greater or less time. Consequently, by 

 knowing the one, we can easily find the 

 other. 



Whatever contrivance, therefore, shows 

 the hours of the day, at the same absolute 

 point of time, in two different places, 

 likewise serves to find the difference of 

 longitude between those places. Now, 

 since an eclipse of the moon proceeds 

 from nothing else but an interposition of 

 the earth between her and the sun, by 

 which means she is prevented from re- 

 flecting the light she would otherwise re- 

 ceive from the sun, the moment that any 

 part of her body begins to be deprived of 

 the solar rays, it is visible to all those peo- 

 ple who can see her at the same time ; 

 whence, if two or more different people, 

 at two or more different places, observe 

 the times when it first began or ended, 

 or note the time when any number of di- 

 gits was eclipsed, or when the shadow 

 begins to cover or quit any remarkable 



r, the difference of those times (if 

 e be any), when compared together, 

 will give the difference of longitude be- 

 tween the places of observation. 



The longitudes of places may also be 

 determined from the observations of so- 

 lar eclipses ; but these being encumber- 



