This article calls attention to the following points: (1) A fundamental understanding of accounting for variation in gross profit is most readily imparted by the instructor, and assimilated by the student, if the factors involved are interpreted in terms of straight lines, areas, and their respective ratios; the resulting diagram would serve as a useful graphic accompaniment to any report containing a schedule of analysis of variation in gross profit; (2) Prior to the drawing up of the formal schedule(s) in customary "longhand" form, the use of "mathematical shorthand," as illustrated in the accompanying schedules as well as in the text of this article, appreciably increases the efficiency and effectiveness with which both oral and written discussion of the subject can be conducted; in the conventional analysis, at least two concepts, which still remain to be expressed satisfactorily in words, may be conveyed with ease and explicitness in terms of lines, areas, and symbols; (3) The conventional analysis and the various types of schedules resulting there from are subject to adverse criticism in respects other than the one very appropriately cited by Fullerton to the effect that part of the change in gross profit which is not due to the change in the physical volume of sales, is not due to the change in the gross profit rate, but to the change in the unit gross profit; (4) Although the scope of this article is restricted to the subject of gross profit variation, it should be observed that much of the following discussion has a direct bearing on the theory underlying standard cost accounting.

The purpose of this article is to call attention to certain fundamental relationships among those basic elements which constitute the distinguishing features of accounting problems involving the admission of a new partner by investment. These relationships are presented against the background of a simple illustrative problem of which the following is a preliminary statement. To explain the case a situation of a partnership firm is cited, in which a new partner is consented to admission by other partners at a pre-assumed equity ratio. The situation that rose due to the inclusion of another partner allows for the emergence of any one of three possible situations. The first presents a condition of no bonus, no goodwill. In other words the situation is termed as "par basis." The second situation entitles the company to a bonus or goodwill. The third situation entitles the new partner to a bonus or goodwill. This article analyzes each situation and compares their results. The investigation on which this article is based produced a number of expressions and corresponding definitions relating to the dollar values of bonus and goodwill.