CASE OF A SINGLE MASS. 



121 



meridians, r n and r n+l the distance of two successive lines of force 

 from the axis, we may take 



whence 



This method of representation has the inconvenience, as we see, of 

 not representing a uniform field by equidistant lines of force. 



140. CASE OF A SINGLE MASS. A single mass m gives a system 

 of revolution about any axis passing through the acting mass. By 

 planes perpendicular to an axis Ax (Fig. 31), the sphere may be 

 divided into successive concentric zones of the same surface, and 

 corresponding to the same flow. 



The flow corresponding to the circular zone whose semi-angle 



Fig. 31. Fig. 32. 



at the summit is 0, is proportioned to the cap of semi-aperture 0, 

 that is to say, to the height PB or to i - cos 0. 



Let N be the order of the line of force AN, we shall have 



N i - cos 6 



471772 2 



whence 

 (7) 



COS 0=1- 



N 



To draw the lines of force, it is therefore sufficient to divide 

 the diameters BB' (Fig. 32) into 47170 parts, to draw the corresponding 

 verticals, and to join the points of intersection with the circumference 

 with the point A. 



