We have developed a GPS solar watch for women, Cal.3X. Cal.3X has been downsized by developing a secondary battery and a planar antenna. In the development of the planar antenna, we tried to achieve both downsizing and reception performance of the antenna. Also, the usability of the GPS solar watch has been simplified to realize a simple design. As a result, we have realized a GPS solar watch that is easy for women to use.

  Among the adjustment of the balance-spring system of mechanical watches, the balancing of balance wheel is easy to understand and well done in the world. But as far as the adjustment of hairspring, it is difficult to understand it’s theory, except only the centering of hairspring position is done as the general custom.

  Suppose if the inner end starts from the just center of balance pivot, if the outer end reaches at infinite far distant point, and also if the material of hairspring has no problem as the elasticity quality, then the hairspring has the complete isochronism. The restoring force of hair spring is completely proportional to the rotation angle of the balance wheel.

  But if the hairspring starts at the collet inside and goes to the limited distant placed outside end as usual, then these two ends arise the not-proportional force to the angle of vibration. For these situations, the mathematical equation of vibration must have the precise correspondence to any case they will be. Here the several mathematical steps are proposed so as to have a precise solution for any case. This is the main purpose of this lecture. In last paragraph is shown the result of the case of free outer end of hairspring.