Abstract: In the internal combustion engines the intake and exhaust are accomplished by valve gear with cams. The profile of the cam is usually composed of circular arcs of different rad. The operating speed of internal combustion engine is rather high. In order to open and close the valve at certain definite instants with rather small interval and meanwhile to keep from too large an inertia force, it is best to arrange a uniform acceleration and retardation for the follows. According to this consideration, the profile of the disk cam with tip follower accomplishing straight line reciprocating motion, should be polar parabolas. But as there are difficulties in manufacturing such a profile, there appeared the circular are cams. When circular arcs are used in place of polar parabolas as the profile of a disk cam to obtain approximatedly a uniformly accelerated and retarded motion, such a modification to the preliminary design of the cam must be made as to make the arcs to be largest properly; otherwise, a serious impact will occur at the instant when the follower is in contact with the cam profile at the point of inflection of any two arcs, if the running speed of the machine is considerably high. In the book, a method for the above mentioned modification of the cam design has been given. By this method, although the radii of the arcs remaining unaltered after the modification is made, but the angles subtended by the arcs would not be kept unchanged. This result is objectionable in such cams as used in the valve gears of internal combustion engines where the cam angles are proportional to the times of opening and closing of the valves. In this case and in some other. similar eases, the angles subtended by the circular arcs as the profile of a cam are not allowed to be subjected to any change when they have been once determined. In this paper, a new method for the same purpose is suggested. After the design of the circular arc cam is modified in this way, the cam angles subtended by the arcs may be kept unaltered. This is preferable in practical uses. However, the results opposited to that of Peuetob will be observed; I.e. the radii of the arcs will be changed slightly after the modification of the design was made; but it is believed that this is not objectionable in practice.