[ 4 ° 4 ] 
Problem IV. 
7. To find at every infiant the variation of the place 
of the pole of the earth . 
The earth has two motions of rotation, the one 
about the axe of the equator, which is likewife the 
earth’s axis ; and the other about the axe C of the 
circle of the fun’s declination ; this motion is caufed 
by the fun’s adtion on the redundant matter about the 
equator. 
The point E,fig. 1. n° 2. which is the interfection 
of the circumference E ^ E ' 9fE of the equator and 
the circle P E P‘ E' P of the fun’s declination, will 
therefore have at every inftant two motions, whofe 
directions are perpendicular to each other. 
The former of thefe two motions, which is the 
diurnal motion, is uniform ; and if we call it m, the 
fpace run through in an inftant, dtf\s m dt\ the mo- 
tion being always equal to the fpace divided by the 
time, or the fpace equal to the produdt of the time. 
Alfo let E e be that fpace. 
The fecond motion of the point E which is per- 
formed in the circumference E P E' P' E of the circle 
of the fun’s declination, and arifes from the adtion of 
the fun, is continually accelerated, from the continual 
application of the fun’s adtion ; and if we call the 
initial motion at the firft term of the inftant, d t> 
or the increment of the motion, the motion at the end 
of the inftant dt, is jx. d t j and the fpace gone thro’ 
uniformly by the motion during the inftant d t y is 
ltd t x d or d P. Let E e be that fpace. 
The 
