129 as before; and below this again is to be put down) the number which is obtained by adding the difference between the two. group-values, (already referred to, to the product of the least remainder in the odd position of order multiplied by the above optionally chosen multipher thereof, and then by dividing this resulting sum by the last divisor in the above division chain CHAPTER VI-MIXED PROBLEMS. Thus the creeper-like chain of figures required for the solution of this latter kind of problem is obtained. This chain is to be dealt with as before from below upwards, and the resulting number is to be divided as before by the first divisor in this last division chain. The remainder obtained in this operation is then to be) multiphed by the divisor (related to the larger group-value); and to the resulting product this larger group-value is to be added (Thns the value of the required multiplier of the given group number is obtained so as to satisfy the two specified distributions taken into consideration.) Examples in illustration thereof. 137. Ono hundred and seventy-seven (is the dividend-co- efficient of the unknown factor), 240 is the known quantity associated (with the product so as to added to or subtracted from it); the whole is divided by <01 (and leaves no remainder). What is the (unknown) factor here (with which the gizen dividend- coefficient is to be multiplied) ? 138. Thirty-five and other quantities, 16 in number, rising (thence successively in value) by 3, (are the given dividend-co- efficients). The given divisors are 32 (and others) as successively increased by 2. And 1 successively increased by 3 gives rise to the associated known (positive and negative) quantities. What are the values of the (unknown) factors (of the known dividend- coefficients), according as they are additively associated with positive or negative (known) numbers ? 17
