CURVATURE OF EQUIPOTENTIAL SURFACES 89 
(28) = cic 
where we have used (22), (23), and (24). The first of these is the differ- 
ence of (26a) and (26b) and the second is equivalent to (26c). 
We must express all our results concerning curvature in terms of 
U, and U,,, which are the quantities observed by the torsion balance. 
Equation (18) becomes 

yg techie aN Aw" BO 
(29) a —V/U x? aS AOE: 
g 
and equations (17) and (20); 
‘ + 2U uz, + Us 
(30) SUD Nae ae ey) COS, ON a een 
MIU? ae Mileage WUD? sei Alene 
and 
; ah Oe lati So a 
(31) (a= 12) SS aw a Uline ae LU 
g 
respectively. 
If, in (31), we use the positive sign, as is customary, then kz be- 
comes the curvature which is algebraically less in value than ki, and 
the value of \ corresponding to this least curvature is defined without 
ambiguity in sign: 

2U, 
(32) a ———_—— 
Yi? ae les 
and 
—= (U/ 
(33) cos 2\ = : 

VU? + 4U2,? 
This is the value of \ usually used in torsion balance work. Also the 
value of 

(34) R = | g(ki — he) |= VU se ley 
leads to 
—U 
(35) R= = 
cos 2A 
419 
