620 



TRANS. ST. LOUIS ACAD. SCIENCE. 



The force at any point on the tangent line resolved along that 

 line will be 



F' 



m T 



^r'^ 4- T^^) 



(0 



where T is the distance of the point from the point of tangency. 



The value of JF' may be laid off at right angles to the plane m^ 

 O, T, and will be represented by a curve like F' in Fig. z. The 

 properties of the field are symmetrical around the radial line r/ 

 so that tangent lines through the point O, at right angles to each 

 other, would have the same values of F" at similar positions. 



The force along the radial line would vary according to the 

 equation 



F — 



ni 



(2) 



and may be represented by the curve F in Fig, 3. 



l i ii i H i l i ;!ii T 



Laplace's equation 

 dF 



dr f '•='•' ^ [dT \ 



.^o^ 1 dT \ T=o- 



means simply that the algebraic sum of the slopes of the three 

 curves at the point O is zero. 



If instead of resolving the force along the tangent line, it be re- 

 solved along any line cutting the tangent line in O and making 



