52 n. PARTICULAR MOTIONS OF A POINT. 



tion 67), by an arithmetical approximate quadrature, cp was calculated 

 for a number of values of z, from which with the polar coordinates 

 tp ) r=~\/l / * z*, the horizontal projection Fig. 15 d was drawn. It 

 will be observed that it almost exactly coincides with the observed 

 curve Fig. 15 c. From the projection and the values of z the per- 

 spective Fig. 16 b was constructed, which in like manner nearly 

 coincides with the observed Fig. 16 a. The eye is below the shaded 

 square in the figure. Figures 15 d, 16 b were constructed by Mr. Joseph 

 G. Coffin. 



Fig. 16 a. 



2. If /3 is negative, the projection of the circle z = a is still 

 within that of z = ft, for since a + /3 > 0, the lower circle is farther 



Fig. 16 b. 



from the center than the upper. The projection of the path is also 

 tangent to the equator. 



The angle AOB in Fig. 15 a has the value 



69) *-f 



a 



cldz 



Inserting the value y = - ~T~ * 



