Vol.. 6, 1920 
PHYSICS: C. BARUS 
497 
by diminishing this diameter further; but it is by no means proportional 
to the sectional area. 
3. Equations. — If M is the mass of the diver, m that of the air contained 
at the absolute temperature r and pressure h -\- {H — Tr)pm/pw in centi- 
meters of water {h being the incidental water head, figure 1, H the residual 
mercury head, and tt the vapor pressure in centimeters of mercury, p^, 
p^, pg, the densities of mercury, water and glass, all read off at r), we 
may write for the gravitational acceleration, g: 
RntT 
^ ^ lh + {H- 7r)p^/p,][(l - pJp,)M + m]' 
The first term in the denominator is to be multiplied by p^ at r, to get 
the water head at 4° C; the second term to be divided by p^ to get the 
volume of the air bubble. These reductions, therefore, cancel each other. 
Mercury, water, and air are necessarily at the same temperature, at least 
in a proper installation of apparatus. 
Thus it follows that variations of g are determinable with the same 
accuracy as r and H. The former being of the order of 290°, 0.03° C, 
must be guaranteed if g is to be correct to 10""^. Furthermore, H, which 
is over 1000 cm. of water, must be read to 1 millimeter for the same ac- 
curacy. Both of these requirements are moderate. By tapping the 
tables from below, the swimmer is slightly separated from the thermometer 
above, and the degree of flotation may thus be estimated with great pre- 
cision, by the speed with which the swimmer rises again into contact. 
An accuracy of 0.01% in g may thus be expected, provided m is adequately 
constant. This paper indicates to what degree this may be insured; 
for in a heated room, in winter, with very variable temperatures, the test 
is extremely severe. 
The absolute determination of g is dependent on the value of m. To 
measure this, large swimmers would be needed such as would make the 
apparatus too cumbersome. With regard to small quantities or small 
changes of the quantities p^, p^, etc., equation (1) may be stripped of its 
less important terms and written in an approximate form. The cor- 
rections are then found by logarithmic differentiation. 
4. Observations. — Figure 2, curve B, contains the most complete series 
of observations made with this apparatus, g/m in ten thousands, being 
shown in its variations within a lapse of somewhat less than two months. 
Readings were made about at noon daily and the corresponding tempera- 
tures are given (increasing downwards) in the graph marked Cor- 
rections for the temperatures, etc., have been applied. As the air con- 
tent was too small for persistent flotation, the diver was liable to sink 
at low temperatures, or high barometers, or both {s, in the figure). It 
is under these circumstances that the irregularities of the curve are usually 
marked. 
