Mr. Grant, in the last issue of this Gazette , having made several references to “Arithmetical Types and Examples,” perhaps a few remarks in reply will not be altogether out of place. 1. Multiplication . The only difference between the two methods first given is in the position of the various digits of the multiplicand. We are told that the first rule (that “there are the same number of figures to the right of the decimal point in the first partial product as there are in the multiplicand,” and that therefore the first figure set down must be under the right-hand figure of the multiplicand) is mechanical; whereas the rule of “putting each first figure of a partial product underneath the figure to which that partial product is due” is sound and fundamental . It is not obvious to the writer that one is more mechanical than the other.