If ab is the numerical value of the product of two factors a and b, and if h is added to a (for the purpose of bringing the product up to an assigned value P, or for any other reason), then bh must be added to ab. If, now, k be added to b (for the same or any purpose), the product must be increased by k (a + h) where (a + h) is the new value of the factor previously a. These facts are so elementary that they merit quoting only on account of the curious neglect of their systematic alternate use by the arithmetician.