WITHOUT THE USE OE THE SOUNDING-LINE. 
677. 
The instrument of which the results have been chiefly recorded in the Table given 
further on has cups of 90 millims. in diameter and a height of mercury of 600 millims , 
representing an available force of 51 ‘9 kilogrammes susceptible to variation in gravi- 
tation ; whilst the instrument of which the drawing is given has cups of 50 millims. 
diameter and a mercury column of 500 millims., representing an available force of 
13*35 kilogrammes. These amounts are amply sufficient to overcome by their variations 
any slight frictional resistance in the liquid column or in the diaphragm. But this 
frictional resistance is really eliminated from consideration by oscillations of the vessel, 
which cause certain pumping-action (kept within narrow limits by the contracted orifice), 
and bring the diaphragm into the true mean position, notwithstanding slight frictional 
resistances. 
Mange of Scale . — Under this head we have to consider what will be the effect on the 
instrument by a given change in the total attraction. Assuming a diminution of gravi- 
tation equal to say representing about 10 fathoms of depth, this would be equalized 
by a reduction in the height of column of millim. = ’00162 millim. The column 
of mercury in rising under this changed condition of equilibrium will, however, not 
become shortened, as in the case of the barometer when affected by a diminution of 
atmospheric pressure, or as was the case in the instrument before described, but for 
every fraction of a millimetre which the top level rises the centre of the diaphragm 
will rise also, and in an increased ratio, depending upon the proportion of the diameter 
of the solid central portion of the diaphragm to the diameter of the cup. If the central 
solid part of the diaphragm was only a point, it is easy to see that for every fractional 
rise of the mercury in the upper cup the centre of the diaphragm would rise three 
similar fractions, and the real height of the mercury column would diminish two 
fractions instead of increasing one. But in reality the central portion of the diaphragm 
is so proportioned to the cup, that for a rise of one increment of height of mercury 
the centre of the diaphragm would rise to about double that amount, and the effectual 
height of the mercury column would decrease instead of increasing to the amount of 
readjustment required. If the elastic range of the springs balancing the pressure of 
the mercury were equal to the height of the mercury column, the increase of height on 
the one hand would be exactly balanced by the increase of elastic force on the other, 
and the instrument would be in a condition of unstable equilibrium, similar to that of a 
balance-lever suspended at its centre of gravity. If, on the other hand, the elastic 
range of the springs were equal to one half the height of column, the increase of elastic 
force would proceed at double the rate of the increase of potential of the column, and 
the result would be a scale proportionate to the simple height of column. 
It follows from this that the elastic range of the springs must be less than the length 
of the mercury column. In the actual instrument the elastic range of the spring exceeds 
to some extent half the length of the column, so that one division of the instrument 
represents less than its seeming proportion of the total gravitation. It would be difficult 
to determine the actual scale of the instrument a priori ; and I therefore adopted the 
