As a result of the studies on the way of proportioning the architectural orders in James Gibbs's "Rules for Drawing the Several Parts of Architecture" (London, 1732), the present author has already pointed out the relationship between Gibbs's proposed method of dividing a part into equal units and his propotional system of order. Gibbs mainly discussed the methodology of his divisions, but scarcely referred to the problem of proportion in his book. Therefore, his system of proportion has not so far been examined to its minutest details. Gibbs says in "To the Reader" of his book, "And having tried one Order with success, I proceeded to another, till at length I was satisfied it would'answer my intention in all'. This sentence, of course, implies the efficacy of his method, and it appears to suggest that he established his propotional system of orders by making use of his dividing method, although he did not explain the process clearly. The present paper inquires into the composition of the whole proportional system of Gibbs's five orders and consists of the following four sections : #1 Gibbs's description of the division of the Tuscan order #2 Analysis of the proportional system on the basis of the division ratio #3 Relationship arisen from the division of essential parts #4 Relations of the proportional systems in Gibbs's five orders From his description about proportiong of the Tuscan order, Gibbs starts with dividing the given length into several equal units and allotting some of them into components of an order. His method can be understood through the dividing number (the number into which a part is divided in its height and projection) and the division ratio (the ratio of one component to another). Thus, the dimension of each component is not determined by modules, but is expressed by the division ratio. In this dividing process, at first the whole height of an order is divided into three "principal parts," such as pedestal, column and entablature (shown by capital letters in Figure 1), and secondly each principal part is subdivided into the "essential parts,'.' such as architrave, frieze, and cornice (shown by asterisks in Figure 1), and finally the "members," fillet, cima recta and cima reversa, (shown by small letters in Figure 1) are allotted in the essential part. The division ratios derived from his divisions of the five orders are shown in Table 1. There are differences in the usage of the division ratios between the Tuscan and Doric orders, and the Ionic, Corinthian, and Composite orders, when the principal and the essential parts are proportioned. In the case of the division of members, an individual ratio is applied to a specific combination of members regardless of the type of the order, or determined in relation to the essential part and the type of the order. Therefore, the division ratios of members have freer and more various relations with orders than those of the principal and the essential parts, as the Ionic order has relation not only to the Corinthian and Composite orders, but also to the Tuscan and Doric orders, and does not belong to both. As a result of the comparisons of the procedure of division, the division ratios and the composition of the essential part between different orders, the present author found four types of relationship in proportioning the essential parts, such as follows : i) The essential parts of an order are composed by combining portions of the corresponding essential parts of other orders. ii) The essential parts of an order are made by adding some members to portions of the corresponding essetial parts of other orders. iii) The essential parts of an order are made by changing the division of the corresponding essential parts of other orders, though the members themseves are hardly altered. iv) ii) and iii ) are partially

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