920 
_ 
The form (5) could not be used for the least-square solution, 
as the left-hand side of that formula is known with greatly difter- 
ent accuracy at the different temperatures, while w has also to be 
corrected. Thus the only expedient is to use the differential formula, 
and this implies a rather accurate couple of values of the unknowns 
to start with. Therefore the second approximation could not be 
dispensed with. 
In computing resistances from formula (5) it is most convenient 
to transform it as follows : 
rs, 100 
Tat + br? a cr—3 + dr—4 
Herefrom we find as the form of the equations of condition : 
Ww 
=|"? tod ee torn ((O)) 
W—wy? W—wy? 
+ Aer-3 (a) + Adx—4 Ga —W—W, 
100 / 100 
in which Aa, Ab, Ac and Ad are negative corrections. 
At the temperatures of liquid hydrogen one same change of 
resistance corresponds to a change of temperature from 5 to 6 
times larger than at the higher temperatures. For that reason a 
weight 30 was given to the 6 corresponding equations of condition, 
taking the weight of the 9 other ones as unity. 
The corrections found from the normal equations were applied to 
the constants of the second approximation, thus yielding the final 
solution stated in Table III. The weights found for these quantities 
have been inserted in the following line of that table. It will be seen 
at once from these weights that 4 and c cannot be determined 
accurately. The mean errors have been derived from the weights by 
assuming the mean error of a single resistance somewhat arbitrarily 
as + 0.001 2. Comparing these mean errors, stated in the fifth 
line of Table III, with the quantities themselves, to which they belong, 
it might seem that these quantities have been given far too accurately. 
Such is indeed the case, if the cunstants found are merely to be 
compared with numbers of the same kind caleulated from other 
experimental data. It is quite another thing however if the constants 
are to be used for interpolation, i.e. for the investigated thermo- 
meter itself. Then they ought not to be rounded off any more, as 
in that case other mean errors apply that are given in the lowest 
line of Table VI. These give namely the precision of each unknown 
separately, i.e. if a definite value is assumed beforehand for 
the other unknowns. The weights from which these errors have been 
