NEW INSTRUMENT FOR GRAVITY MEASUREMENTS 23 
beam between the center and the hinged end and the tension in this spring 
is controlled by a micrometer screw above. 
If the instrument is adjusted at a certain location so that the two images 
of the lamp filament are in line and it is then taken to a different location, the 
difference in gravity will cause a slight displacement of the images which are 
then brought back to the zero position by altering the tension in the weighing 
spring; the difference between the two readings of the micrometer dial is 
then a measure of the difference in the force of gravity at the two places. 
The difficulties involved in carrying out this idea to the necessary degree 
of precision have been greatly increased by the requirement that the instru- 
ment be rugged enough to stand transportation over rough roads and small 
and light enough to be carried by two men where there are no roads. 
Suppose a mass of 100 grams or more suspended by a spring of such stiff- 
ness that the total elongation, from no load to full load, is 100 millimeters; 
then, to maintain the tension constant to one part in ten million would re- 
quire; first, that the length be controlled to within one one-hundred-thou- 
sandth of a millimeter; second, that the temperature be maintained constant 
for the whole period required for a series of observations so that the elonga- 
tion of the spring due to temperature effect minus the linear expansion of the 
supporting frame will be within the same limit; third, that eftects of elastic 
hysteresis be eliminated not only from the main spring but from the flexible 
supports of the beam and mirrors also. 
In the present instrument the distance between the thin ribbons sup- 
porting the mirrors is one millimeter and the distance from the mirrors to the 
eye-piece is 600 millimeters, so that the amplification for each mirror is 1200 
times, but as the two mirrors move in opposite directions the relative dis- 
placement of the images is amplified 2400 times. As the beam ratio is 1.8 the 
total amplification is 4320, but as this is observed through an eye-piece with 
a magnification of 14 the apparent amplification is over 60,000, so that a 
movement of the suspended mass of one one-hundred-thousandth of a milli- 
meter will look like six-tenths of a millimeter and be easily observed: If the 
force of gravity is increased by one part in ten million, part of the increase is 
used in stretching the main spring and part in bending the small filaments 
that support the beam and mirrors, so the sensitivity in terms of force is not 
so great as this, but the first requirement is accomplished—the maintenance 
of the length of the main spring to within one part in ten million. 
I expected to be able to make the beam and mirror system so flexible that 
the resistance to movement would not be any greater than that of the main 
spring, but I have not succeeded in doing so. Although the filaments that carry 
the mirrors are only 0.01 mm thick, it is the stiffness of these filaments that 
limits the sensitivity of the instrument. The present instrument is satis- 
factory for readings of one part per million but is difficult to read any closer 
than that so a new beam system is being made which is expected to be at 
least four times as sensitive as the present one. 
The temperature effect on the spring is very large and unless accurately 
controlled will completely mask the small variations in force that are to be 
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