To find the increase in temperature on the Fahrenheit scale, we use the relationship between the Celsius and Fahrenheit temperature scales. The formula to convert Celsius to Fahrenheit is:

$$F = \frac{9}{5}C + 32$$

However, since we are interested in the increase in temperature, we can ignore the "+ 32" part of the formula, because this constant does not affect the change in temperature, only the absolute temperatures. Thus, to find the increase in temperature on the Fahrenheit scale, we can use:

$$\Delta F = \frac{9}{5}\Delta C$$

Given that the increase in temperature is $$40^{\circ}C$$, we can substitute this value into the equation:

$$\Delta F = \frac{9}{5} \times 40^{\circ}C$$

$$\Delta F = 9 \times 8$$

$$\Delta F = 72^{\circ}F$$

Therefore, the increase in temperature on the Fahrenheit scale is $$72^{\circ}F$$. So, the correct answer is:

Option C $$72^{\circ} \mathrm{F}$$