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Proceedings of the Koyal Society of Edinburgh. [Sess. 
pendulum oscillations, etc., can be largely eliminated by taking the mean 
of the three results. As a matter of fact, in each of the cases illustrated 
by the graphs, one of the three registers had failed to work ; yet the 
graphs are almost entirely free from visible irregularities. 
§ 3. Each record consists of a linear series of needle-pricks in the 
paper. These can be readily seen if viewed under oblique illumination. 
The clock record is needed only to test the regularity of the motion of 
the paper, and so to supply a time scale. 
The punctures are spaced close together when the motion of the 
oscillator is rapid ; they are wide apart when the range is near its. 
maximum value. The position of the maximum is very easily found. 
In general it is attained at some instant between the recording of the 
two successive points which are most widely separated on the paper. 
But it might happen to be attained at some instant between the 
recording of two near points which have much larger intervals immedi- 
ately outside them. In either case, when a number of multiples of 10° 
are included in the range, it may be assumed that the maximum was 
reached at a point on the record midway between the pair of points 
referred to; for the times of in and out oscillation over a given small 
range in the neighbourhood of the maximum cannot differ greatly. 
Hence we get the time of a complete semi-oscillation. 
