A sufficient condition is given for the formal differential operator -ry(t)=(p(t)y'(t))'+q(t)y(t) defined on the interval [a, b), b O and q(t) are real-valued functions locally Lebesgue integrable on [a, b). The operator Tr is said to be of limit-circle type at b if every solution f(t) of the differential equation 7-y(t)=O satisfies the condition rb (2) 1 fb(t, dt O on I,, and 003 (3) ,p3/2q1"2 J -l(s) ds) =d x n==1 then the operator r defined by equation (1) is of limit-point type at b. PROOF. For each n= 1, 2, * *, let the interval In have endpoints an and bn, where a,