146 
MR. W. GEOFFREY DUFFIELD ON THE 
of Set B, at 3 and 4 atmospheres, show too great a value for the linear relation to 
hold, and in this region the curves are not accurately directed to the origin ; but too 
much stress must not be placed upon the measurements at these pressures, because 
the percentage error in the measurement of a shift is greater at low than at high 
pressures, since in the former the shift of the line is but a fraction of its own width. 
At higher pressures the percentage error is less, because the broadening of the lines 
does not increase as rapidly as their displacement. 
The existence of the linear relation described by Humphreys between the 
displacement and the wavedength is not confirmed by the present investigation. 
The discrepancies in the displacement of the lines of Groups I. and III. are not to 
be accounted for on this hypothesis, since the sequence of the lines on the diagram 
is not the same as their sequence on the photographs. 
The conclusion arrived at from the displacement curves is that the relation between 
the pressure and the displacement is in general a linear one, but that it may be 
affected by a disturbing cause in the region 15 to 25 atmospheres. 
14. Phenomena relating to the Departure from a Linear Relation between the 
Pressure and Displacement . 
The photograph showing the most marked departure from the linear relation is 
D 19, taken at 25 atmospheres pressure, and its measurement by different observers 
is given in Table V., which also contains the readings obtained from three other 
plates, 1)18, D24, D25, taken at the same pressure. The last three agree well, and 
their mean values have been placed in the last columns of the table, where they may 
be compared with the mean values for Plate Dl9, given in the preceding column. 
The table shows that the difference between the two plates is not to be explained 
by errors of measurement, and the fact that the discrepancy is different for different 
lines would in itself indicate that there had been no accidental disturbance of the 
camera, but we have additional evidence of this, because the two exposures of the 
comparison spectrum, which were taken before and after the pressure spectrum, are 
exactly superposed. An irregularity in the magnitude of the displacements might be 
introduced by the unlikely, but still possible, contingency of an alteration in the 
temperature, and therefore of the dispersive power, of the grating, during the 
exposure of the pressure spectrum, and a return to its original value for the second 
half of the divided exposure, but this irregularity would be progressive and should 
not displace the lines of one group more than those of another group when the 
members of the two are interspersed. There is strong evidence in favour of this 
phenomenon being a genuine one. 
In the table the lines are arranged according to their groups, and the ratios of the 
shifts on Plate Dl9 to those on Plates Dl8, D24, and 1)25 for the different groups 
are as follows :— 
