The attempts to utilize the pneumatic micrometer as a magnifying device for measurement of surface roughness have been made by some researchers. But there are some other problems in that field yet left untouched. Here we studied about the response phenomenon of the manometer reading due to a "step" or "sinusoidal" displacement at the delivery orifice to find the dynamic character of pneumatic micrometer.
From the results obtained, the fundamental conditions of measurements were determined and a tracer method surface tester with a pneumatic micrometer was constructed.
The magnification of this instrument can be set for any desired value by adjusting the length of water-column or the ratio of orifice and it was not difficult to get vertical magnification of 50, 000 times, but considering the radius of curvature of the extreme point of tracing needle or the measuring pressure the magnification was determined 4, 000 times in vertical and 88 times in longitudinal. These values are sufficient for the measurement of surface roughness from 1S to 4S.
The profile curves gained in this way show very actual feeling (as to be seen in the figure) and repeating character and accuracy are never worse than those of "Nippon Kogaku Surface Tester".

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About the spring retained in the watch barrel, it is clear that between the form of the spring out of the barrel and that of its torque curve there are some relations, but they are not yet given mathematical form. I have led a mathematical equation, neglecting the effect of the friction and the end condition, which shows the torque according to the winding angle of the barrel when the form of spring is given. s is the length from the inside end to a certain point along the spring. ψ'_max and F' are the curvatures at the point either when the spring is quite wound up or out of barrel and free respectively, Then the ideal form is
ψ'_max-F'=2p/t,
where p is the proportional limit of the material represented by strain in percentage.
I show as examples three curves in Fig. 5. only changing the form of the spring. A is that of the ideal spring. B and C springs are so deformed from A spring that the curvature of the spring in each point may be decreased proportionally to the length of the spring from the inside and outside end to that point respectively. B is unsatisfactory in flatness of torque curve. The torque curve in C is expected to become irregular when friction is large, and both B. and C are smaller than A in torque when p is the same.

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[in Japanese]

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