Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

Let each capacitor have capacitance $$C$$.

When two equal capacitors are connected in series, the equivalent capacitance is $$C_s = \frac{C \times C}{C + C} = \frac{C}{2}$$.

When the same two capacitors are connected in parallel, the equivalent capacitance is $$C_p = C + C = 2C$$.

The ratio of the equivalent capacitances is $$\frac{C_s}{C_p} = \frac{C/2}{2C} = \frac{1}{4}$$.

So the ratio is $$1 : 4$$.

Hence, the correct answer is Option B.