It is well known to those who have studied the theory of chances. that where the magnitude of a risk may be divided into an indefinite number of parts, it is possible, by this multiplication of smaller parts, to confine the probability of the occurrence of any given excess or deficiency in the result, above or below its mean value, within any given limits; and it is of great practical importance to ascertain both how far the subdivision ought to be carried with regard to insurances, and what are the inconveniences to be apprehended from the admission of occasional deviations from the general rule.