VOL. LIV.] PHILOSOPHICAL TRANSACTIONS. idj 



before this time, to have been mistaken in the manner of converting the quan- 

 tities above mentioned into time, so I can find no reason to conclude so from 

 what has been cited above : on the contrary, from a full consideration of the 

 subject, I apprehend the method hitherto used by the mathematicians to be just, 

 and that the author has himself fallen into an equal mistake with that of which 

 he accuses them. But, in order to set this matter in a clearer light, it will be 

 first necessary to consider motion and time, relatively to each other ; for unless 

 this be done, it will be impossible to understand any thing precise from convert- 

 ing a certain number of minutes and seconds into mean solar time, or time of 

 the primum mobile. 



There are 3 different kinds of time used by astronomers, sidereal time, 

 apparent solar time, and mean solar time. The interval between the transit of 

 the first of Aries across the meridian one day, and its return to it the next day, 

 is called a sidereal day, which is divided into 24 equal parts or hours, and the 

 hours into minutes, &c. This time is shown by a clock regulated to agree with 

 the transit of the stars across the meridian. The interval between the transit of 

 the sun across the meridian one day, and his transit the next day, is called an 

 apparent solar day, which is divided into hours, minutes, &c. of apparent time. 

 The solar day, it is manifest, and its hours, minutes, &c. are of different 

 lengths, at different times of the year : on account of which inequality, a good 

 clock, which keeps equal time, cannot long agree with the sun's motion, which 

 is unequal. Therefore astronomers have devised an imaginary time, called mean 

 solar time ; which is what would be pointed out by the sun, if his motion in 

 right ascension from day to day was uniform, or, in other words, it is what 

 would be pointed out by a fictitious sun or planet supposed to move uniformly in 

 the equator, with a motion equal to the mean motion of the sun in longitude, 

 its distance from the first point of Aries (meaning hereby the mean equinox) being 

 always equal to the mean longitude of the sun : and as apparent noon is the in- 

 stant of the true sun's coming to the meridian, so mean noon is the instant at 

 which this fictitious planet would come to the meridian. The interval between 

 its coming to the meridian on any two successive days is a mean solar day, which 

 is divided into hours, minutes, &c. of mean solar time ; all which it is manifest 

 will preserve the same length at all times of the year. 



The equation of time, at the instant of apparent noon, or of the sun's 

 passing the meridian, being equal to the difference between mean time and 12 

 hours, is also equal to the interval between the mean Mid true sun's passing the 

 meridian expressed in mean solar time : to find which, we have the distance of 

 the mean sun from the meridian, at the instant of apparent noon, equal to the 

 difference between the sun's apparent and mean right ascension (both reckoned 

 cither from the mean or apparent equinox) which may be called the equation of 



