PHYSICAL ASTRONOMY. 311 



scribe in i an indefinitely small portion of time, be 

 q> ; and if the angle described in the same time by 

 the diurnal revolution be v, the axis of that revo- 

 lution will be changed by an angle of which the 



. 

 tangent is 



The substitution of the tangent for the ratio of the 

 two sines mentioned in the proposition, is made, 

 because the angle which the axis'of the diurnal re- 

 volution makes with the intersection of the equa- 

 tor and ecliptic, is a right angle. 



316. If the force which produces the motion 

 <p, were, like that which produces the motion v, 

 a force that acts only once, and leaves its effect 

 to continue without diminution or increase, the 

 change thus made in the position of the Earth's 

 axis would be permanent, and no farther varia- 

 tion would take place ; but the force that pro- 

 duces <p being one that acts continually, with 

 more or less intensity, the quantity <p is con- 

 stantly renewed, and the position of the Earth's 

 axis is subject to continual change. 



The relation between the momentary precession and 

 <p, the momentary change in the position of the 

 axis, will be made plain by a diagram. 



Let 



