This work is the fruit of long experience in the domain of professional instruction in horological schools. We have endeavored to avoid speculations purely theoretical, as well as long descriptive explanations, which belong to books suited to the general public. If the solution of some problems cannot, in our estimation, be accomplished without the aid of higher mathematics, because of the precision required to attain the desired end, it must be noted that these questions can generally be put aside by those persons to whom the subtleties of mathematical analysis are unfamiliar. It is sufficient then to recognize the fact that the calculations have been made to verify the deductions and to make use of the conclusions which may be drawn from them.