FELLOWSHIP

, Company, or Partnership, is a rule in arithmetic, of great use in balancing accounts among merchants, and partners in trade, teaching how to assign to every one of them his due share of the gain or loss, in proportion to the stock he has contributed, and the time it has been employed, or according to any other conditions. Or, more generally, it is a method of dividing a given number, or quantity, into any number of parts, that shall have any assigned ratios to one another. And hence comes this general rule: Having added into one sum the several numbers that express the proportions of the parts, it will be, As that sum of the proportional numbers: Is to the given quantity that is to be divided:: So is each proportional number: To the corresponding share of the given quantity.

For Ex. Suppose it be required to divide the number 120 into three parts that shall be in proportion to each other as the numbers 1, 2, 3.—Here 120 is the quantity to be divided, and 6 is the sum of the numbers 1, 2, and 3, which express the proportions of the parts; therefore as

This rule is usually distinguished into two cases, one in which time is concerned, or in which the stocks of partners are continued for different times; and the other in which time is not considered; this latter being called Single Fellowship, and the former Double Fellowship. |

Single Fellowship, or Fellowship without Time, is the case in which the times of continuance of the shares of partners are not considered, because they are all the same; and in this case, the rule will be as above, viz, As the whole stock of the partners: Is to the whole gain or loss:: So is each one's particular stock: To his share of the gain or loss.

Ex. Two partners, A and B, form a joint stock, of which A contributed 75l, and B 45l; with which they gain 30l: how much of it must each one have?

Double Fellowship, or Fellowship with Time, is the case in which the times of the stocks continuing are considered, because they are not all the same.

In this case, the shares of the gain or loss must be proportional, both to the several shares of the stock, and to the times of their continuance, and therefore proportional to the products of the two. Hence this Rule: Multiply each particular share of the stock by the time of its continuance, and add all the products together into one sum; then say, As that sum of the products: Is to the whole gain or loss:: So is each several product: To the corresponding share of the gain or loss.

For Ex. A had in company 50l. for 4 months, and B 60l. for 5 months; and their gain was 24l: how must it be divided between them?