of determining Stream Lines and Equipotentials. 269 
sheet o£ tracing-paper, and drawing the diagonals of the 
chequers formed by the intersecting contours. 
VIII. Estimation of Errors. 
To one reading an account of this freehand method without 
having worked an example, it might seem as if there were no 
way of setting a limit to the errors of any particular graph. 
This, if it were true, would be a serious fault. But, happily, 
it is not so ; for it is commonly necessary to make several 
drawings and then select the best of them : so that by the 
time the draughtsman has reached a drawing which he can 
scarcely improve upon, he has before him deviations from it 
in divers directions. The difference, then, between the 
selected graph and the second best graphs is a measure of 
the errors of the latter and an outside limit to the errors of 
the former. The actual errors of the selected graph will be 
less than this limit, and may be estimated by comparing the 
errors in the shape of the individual chequers in the best and 
second best graphs, and taking a fraction, thus : — 
individual chequer error in best graph /difference between best and\ 
same in second best graph ~ \ second best graphs / * 
This is the true measure of the errors of the best graph. 
It depends, of course, on a general mental estimate or appreci- 
ation, and is consequently not susceptible of exact definition. 
But this does not much matter, for if the value of an error 
be known within two times either way it is usually sufficient. 
The difference between the best and second best graphs is 
less dependent on a mental estimate, and consequently sets a 
firmer limit to the possible error. 
Taking, for example, the graph of the field round a helical 
line source given in section III. c, and laying over it the 
tracing of the unpublished second-best graph, one sees that 
the difference in position of the lines in the two graphs 
nowhere exceeds \ the linear dimension of the chequer, at the 
point and in the direction considered. Now I should estimate 
that the error of the shape of individual chequers in the 
published graph averaged \ of the same quantity in the other ; 
so that \ of the linear dimensions of the chequer may be taken 
as the error of position of the lines in the published graph. 
Now the graph exhibits ten tubes of flow ; so that \ of one 
tube is 2-J- per cent of the range. This is in the worst parts 
of the field. Elsewhere the error will be less, but it may 
still be expected to exceed the errors found when the graph 
is drawn on a surface normal to the guiding lines, because in 
the case of screw symmetry we have the added difficulty that 
the shape of the chequers depend upon its orientation. 
Phil. Mag. S. 6. Vol 15. No. 86. Feb. 1908. U 
