It is generally accepted among teachers that there are certain forms of arrangement in arithmetic with which pupils are more comfortable and more sure. Addition, for example, is usually considered to be more rapid and more accurate when the addenda are placed beneath each other as in vertical tots than when they are placed side by side as in across tots.

When considering the advantages and disadvantages of the different methods used in long multiplication of money I decided to commence with an investigation into the various forms of setting out short multiplication of money. The surprising results obtained led me to extend the work to other items of the arithmetic syllabus. Each item of the whole investigation is recorded in the chronological order with which it was dealt.