368 RELATIVE MOTION AND UNIVERSAL GRAVITATION. [CH. XIII. 



of the Sun in his path, relative to the frame of Earth and stars, 

 is much more nearly elliptic motion about a focus than uniform 

 circular motion, and in the second place from the fact that the 

 plane of the Sun's path is inclined to the equator. To define 

 the measurement of time by the average rotation of the Earth 

 relative to the Sun, we imagine a point to move (relatively to 

 the frame of Earth and stars) in the Sun's path, with a uniform 

 angular motion about the centre of the Earth (i.e. so that the 

 time .of describing any angle is a constant multiple of the time 

 in which the Earth turns through the same angle), and at such a 

 rate as always to coincide with the Sun at the nearer apse of 

 his path ; then we imagine a second point to move in the plane 

 of the Earth's equator with a uniform angular motion about 

 the centre of the Earth, and at such a rate as always to coincide 

 with the first point at the node corresponding to the Vernal 

 Equinox. This second point is called the Mean Sun. We may 

 determine a frame of reference by taking the centre of the 

 Earth as origin, the line joining the origin to the Mean Sun 

 as a line of reference, and the plane through this line and the 

 polar axis as a plane of reference. Relatively to this frame the 

 Earth rotates about its polar axis in an interval called a mean 

 solar day; this rotation can be used instead of the rotation 

 relative to* the stars as time measuring process, and time so 

 measured is mean solar time. The unit of time is the time in 

 which the Earth rotates relatively to this frame through an angle 

 equal to 1/86400 of four right angles, and this unit is the mean 

 solar second. 



*291. Change of the time measuring process. In the 



last Article we have explained how in a particular case it is 

 convenient to take as the measurement of time a multiple of 

 the time measured by some particular process, or, in other words, 

 to change the variable which expresses elapsed time by multi- 

 plying it by a constant number. In the same way we might 

 conceivably take as time measurer the value of any definite one- 

 valued function of the number expressing sidereal time, provided 

 the function always increases as the number expressing sidereal 

 time increases. In general such a procedure would introduce a 

 needless complication, but it is on the other hand conceivable 

 that it might produce a simplification. 



