4 
: 
a 
_ 
a 
‘ 
: 
: 
‘ 
T. Russell—Calibration of Thermometers. 373 
Art. XLVIL—Neumann’s Method of calibrating Thermometers, 
with ways of getting columns for calibration; by T. RussELL, 
U. S, Lake Survey. 
_ NeumANn’s method of calibrating thermometers has very con- 
siderable advantages over those of Bessel and of Hallstrém,which 
are the onesincommon use, In the computations of the corree- 
tions by this method the numbers used are always small, and 
there is entire freedom from arbitrary assumptions. ithout 
at all increasing the work of reduction, the calibrating columns 
can be used to the greatest advantage, and even when’fall the 
regular observations required by the method are not obtained, 
the corrections can nevertheless be derived in a definite man- 
ner. The method combines, in short, the greatest simplicity, 
elegance and exactness. 
An essential feature of the method is that the columns used 
must be as nearly as possible equal in length to a whole num- 
ber of intervals between the points for which the corrections 
are required ; if, for instance, for every ten degrees, the lengths 
@ 
ble columns of this kind, yet the greater the number obtained 
the simpler becomes the reduction. Calling the points for 
which the corrections are required principal points, the col- 
umns obtained are to be measured with the lower ends near 
all of the principal points, as far as the lengths of the columns 
will permit. The lengths of the columns being as stated 
above, the upper ends will also be in the vicinity of principal 
points 
For a knowledge of this method the writer is indebted to an 
article by M. Thiesen, in the November number for 1879, of the 
Zeitschrift der dsterreichischen Gesellschaft. fiir Meteorologie. 
The notation given there is followed here. Denote the calibra- 
tion corrections at the principal points of a thermometer by 
4, 4, 4,....4,, and the corrections to the intervals between 
successive principal points by 3, 6, 4,, ete., then we have in 
general: 
0; — Ain -J4; 
Let the general designation of principal points near the upper 
ends of columns be &, and that of points near the lower ends be 
% Denote the volume of any column by /y_,» and its appar- 
ent length, that is the difference of the readings of the upper 
end and lower end in a given positiou, by (4, 7). If the cor- 
rections of the small spaces which lie between the ends of the 
