less, for changes in the spring, permits a more free movement 

 of the balance; while, parting the rim of a balance having 

 equal thicknesses of brass and steel in its structure, at a dis- 

 tance of one-sixth of its circumference from the arm, he 

 assumes the middle of the longer portions, and the free ends of 

 the shorter, as places where weight requires no compensation, 

 the longer portions carrying on their free ends only a moderate 

 weight for the compensation needed. 



2d. The work performed by the balance near its center of 

 motion is a source of error that has been generally neglected. 

 It is a settled principle of dynamics, that "if a body revolving 

 on an. axis strike an immovable obstacle at the center of percus- 

 sion, the point of suspension will not be affected by it ;" while 

 "if the blow be struck in any other point, a part of its motion 

 will be employed in endeavoring to continue the motion." Thus 

 if we take into the hand at one end a club of uniform thickness, 

 and by a motion from the wrist as a center strike an obstacle at 

 a distance of one-third its length from the other end, the hand 

 feels no effect from the blow ; but if it be struck by any other 

 point, the hand will receive a part of the blow, — greater as it is 

 further from the point named. Now the "center" or line of per- 

 cussion of a balance is in or near the rim, and the resistance to 

 its motion, by means of the spring and escapement, is near its 

 center ; and "the force thus lost, as to the movement of the 

 spring and escapement, is transmitted to the pivots of the bal- 

 ance as useless friction. The errors arising "from the relative 

 positions and directions of these forces and that of gravitation, 

 and the changes therein from change of position or latitude, 

 from the density of the air and the space in which the balance 

 moves, varying friction from the oil, lurches on shipboard or 

 jolts in the pocket, and from the different rates of expansion of 

 metals as they affect the friction of the balance or pivots or the 

 working of the escapement — these furnish a problem to aacertato 

 or compensate their average effects, sufficiently complicated to 

 account for the little progress that has been made in perfectiBg 

 the chronometer. For however small may be their effects on a 

 single movement of the balance, when it is multiplied by four- 

 teen to eighteen thousand for every hour, or three or four hun- 

 dred thousand in twenty four hours, they become so readily 

 appreciable as to deserve attention and amelioration. 



Now if we can remove from the balance pivots this intermit- 

 tent and useless friction, leaving only its own greatly reduced 

 and uniform amount, unchanged by change of position or 

 temperature, a balance of greater momentum could be substitu- 

 ted, which, in a proportionate degree would lessen the effect of 

 the remaining sources of error, and this, it is believed, can be 

 accomplished by simple and practicable mechanism. 



