LATITUDES AND LONGITUDES. 



By knowing exactly the time of rotation of the earth, and 

 having ascertained that its diurnal motion is uniform, we can 

 determine by simple arithmetic what extent of its surface will 

 pass, in a given time, under any point of the firmament. Thus 

 if we say in round numbers that the whole circumference cor- 

 responds to twenty-four hours, it will follow that fifteen degrees 

 will move under the point z each hour, or one degree in four 

 minutes. 



If we suppose z to represent the place of the sun, then it will 

 be noon, or twelve o'clock, at the place which is immediately 

 under z ; that is, at p. If c be fifteen degrees west of p, then it 

 will arrive under z one hour after p ; consequently, when it is 

 noon at p it is eleven o'clock at a place fifteen degrees to the 

 west of p ; and, for the same reason, it is ten o'clock at a place 

 thirty degrees to the west of p, and so on. 



Again : if a be a place fifteen degrees to the east of p, a must 

 have been under z an hour before p reached it. It will be noon, 

 therefore, at <z, an hour before it is noon at p ; therefore, when it 

 is noon at p it is one o'clock at a. In the same manner, and for 

 like reasons, if b be a place thirty degrees east of p, b will pass 

 under z two hours before p ; and therefore when p passes under 

 2 it will be two o'clock at b. 



It will be apparent from these explanations, that in general, 

 the hour of the day at different places upon the earth, at the 

 same time, will depend upon their relative position east or west 

 of each other. If one place be east of another, the hour at that 

 place will be later with respect to noon than the hour at the 

 other ; and the extent to which it is later will depend on the 

 distance which one place is east of the other. In calculating 

 this difference of time from the difference of position east or 

 west, we may take fifteen degrees to correspond with an hour, as 

 already explained. 



But this distance of one place east or west of another, 

 expressed in degrees, is, in fact, the difference of their longitudes ; 

 and if one of the two places in question be that from which the 

 longitudes are measured, the determination of the longitude of 

 a place would resolve itself into the discovery of the hour of the 

 day in the place whose longitude we want to find, and also at the 

 place from which the longitudes are measured. 



Thus, for example, let us suppose that we ascertain the hour 

 of the day in New York, and find that it is two o'clock in the 

 afternoon, and that we have a means by which we can discover, 

 at the same time, what the hour of the day is at Greenwich, and 

 that by these means we know that it is 56 minutes past 6 o'clock. 

 We know, then, that the time is 4 hours 56 minutes earlier at 

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