( 239 ) 
from the observations, if we accord the weight determined by equation 
(5) to each of those observation equations *). 
This treatment of the equations with several observed quantities 
agrees with the solution for two measured quantities given by ANDRADE. 
For the case that a linear relation exists between two measured quan- 
tities this one is simpler than MeRrRIMAN’s solution. 
§ 3. In the following way it is easily shown that the mean error 
in the result is also found according to the usual rules, as applied 
to equations with one measured quantity. From the normal equations 
(6) we find 
Ro te! le ea Parse a, Fn 
Here zv is expressed as a function of the measured quantities 
OE ER © nal! APU feral 
The mean error in « is obtained from: 
1) For the equations, which Scraukwijk used (Comm. Nr, 70, Continued, Pro- 
ceedings June 1901; Thesis for the Doctorate, p. 115) viz. 
PV,,—1.07323 = Bg,,(d—0.93177) +- Cs,,(d?— 0.868), 
1 
where P and Vas have been measured, BS, and C's, are to be calculated 
according to the method of least squares, we find from (5) the weizht of each 
observation equation: 
Oe 1 
aero NA AE DE TAR TLE 2 
{la fs 1 y loo ("py i dE eb log | Bs, ,d oO Sy d ) U, 
if Ey, and Ld, respectively represent the mean relative error in the pressure- and 
density measurement, and py the mean relative error for a measurement to which 
‘ : 5 1 3 
the weight 1 is assigned. If we put bi, = Ba, = Ko (= —~—), then if: 
10000 
5 1 
d= 6.2394: g—=-—, 
: 2.23 
== 55.988: = : 
0) === aay . TE 
The terms with d will have little influence in the value for g, as long as d does 
not become very large, as appears a priori from the fact that the coefficients 
BS, and CS, are small. (Comp. Semarkwik’s Thesis for the Doctorate p. 115, 
where he gives: BS, 0.0006671, Cs, 0.00000099%), In this case errors of 
observation in d will have little influence on the second member, and this second 
member may be considered as precisely known. As the values of PV, differ com- 
paratively little for the different densities at which the observations are made, an 
equal weight has been assigned to each observation equation. This is the more 
justified if we consider that he was able to measure the higher pressures with 
greater precision than the lower, as in the former in adding the measured lengths 
of each column of mercury the accidental errors partly neutralise each other, 
