But there can be no doubt that if the apparatus above described were so constructed as to meet the actual conditions in time recording instruments, very valuable data could be thereby secured. This could be done by reducing the weight of the disk, so as to make the weight bear the proper relation to the size of the pivots. FOOTNOTES: [7] Thurston. Friction and Lost Work in Machinery. [8] Philosophical Transactions, 1877, Vol. CLXVII., p. 502. [9] The Horological Journal, Apr., 1881. Vol. XXIII., page 98. [10] The writer has italicised this phrase. CHAPTER IV. APPLICATION OF THE LAW OF FRICTION AND LUBRICATION IN HOROLOGY. ~45.~ The scope of this work will not permit the discussion of the proper size, shape and construction of each and every part of all the various kinds of time-keeping mechanisms which have been produced. However a number of _representative_ cases of friction and lubrication will be considered, and the laws applying to the same will be demonstrated. Practical methods of obtaining the best results will be shown and mistakes to be avoided will be pointed out. The knowledge of what we ought not to do is sometimes of vastly greater importance than it is usually considered to be. ~46. The Proportions of Pivots, Shoulders and Bearings~, where the bearings are not capped jewels, should be such that the coefficient (33) of the combined solid and fluid friction will be a minimum, and such that the lubricant will not be expelled at normal pressure, while the "fit" (37) must be good. 1. _The diameters of all pivots_ should be of the smallest size compatible (43,6) with the foregoing condition, and with the stresses which they are expected to sustain. 2. _The length of bearing surfaces_ is regulated by the pressures which may occur (43) between them, and by the nature of the materials of which they may be composed. 3. Given the diameter and the pressure, the length of the bearing surfaces can be so proportioned as to prevent abrasion and to present surfaces, between which the film of oil is interposed, of such magnitude that the lubricant will not be expelled at normal pressure. [Illustration: Fig. 13.] 4. In Fig. 13 the length of bearing surface of the pivot is equal to its diameter, but the proportion must be varied according to conditions. 5. The barrel arbor pivots are sometimes necessarily of large diameter, and the bearing surfaces can be made shorter in proportion, as the surfaces will then be great enough to give good results as well as to retain (48) the oil. 6. In the center pinion (49) where the diameter of the the pivots is made small for reasons explained (43, 6), the length of the bearing surfaces must be such that abrasion will not occur, and that the oil will not be expelled. 7. The rest of the train is subject to the same laws. The length of the bearing surfaces of the pivots remote from the motive force can be made shorter in proportion.