104 
six mean points, such that the sum ol the shortest distances 
of the several points of any one group from the curve is zero. 
The mean points were obtained by means of the arrange- 
ment shown in Fig. 1. 
The wooden rod AA has a steel point CC fixed at one 
end, and a graduated scale of tenths of an inch at the other; 
the axis of the steel point is kept vertical and the scale 
horizontal while the rod is being rotated, by the strip of 
wood TTP, the end P sliding on the table. The centre C 
being placed at some fixed point, the curve-paper is then 
adjusted on the table, so that some particular division on 
the scale (found by trial) describes a circle through a group 
of points, and also through two adjacent groups, one on each 
side, which circle if drawn would pass not far from the mean 
points of the three groups we are proceeding to determine. 
The distance from each point of the middle group to the 
centre C is then read off on the scale to the ToVoth of an 
an inch, with the aid of a lens, and a second scale divided 
into Troths of an inch ; and a point plotted near the centre 
of gravity of the middle group at a distance from C equal 
to the mean of these readings. 
This process is repeated for each of the four middle 
groups, the mean points of an end group being determined 
with the paper and centre C in the same positions as for 
the second group from that end. 
A nearer approximation to the true position of the mean 
points may then be found, by making use of those already 
obtained, to find more correctly the radius of the circle 
through the three groups, and repeating the process of 
measuring and plotting. 
In one case an isolated point occurs ; this is taken as one 
group, and the curve drawn through it. 
