( 675 ) 
then serve as a control and as the starting point for further measure- 
ments. The present investigation forms the first part of this general 
program and gives the linear expansion of glass with an accuracy 
which suffices for our present purpose. From the description of our 
measurements it will be seen that with practically the same apparatus 
and in nearly the same way it will be possible to determine the 
absolute expansion of pentane. 
§ 2. We have determined the two coefficients a and 4 in the 
formula for the linear expansion = L, (1+ at + bt’), for the 
two varieties of glass from three observations for each. These 
were made at ordinary temperature, at about — 90°, C. and at about 
— 180° C., by measuring directly and at the same time the lengths 
of the rods of the two substances. 
The rods were drawn out at each end to a fine point which could 
be accurately observed with a microscope. At the bottom and top, the 
two rods project out of a vertically placed cylindrical vessel. The 
bath is closed at the lower end and is filled with a liquefied gas giving 
the required temperature. Care is taken that the points shall be kept 
as nearly as possible at the temperature of the surrounding air, and 
also that the air between the points and the objective of the microscope 
shall be at the same temperature. The lengths are then read directly 
against a scale by a cathetometer arranged as a vertical comparator. 
Although this arrangement gives a convenient method for the deter- 
mination of length it necessitates a considerable difference in temperature 
between the middle and the ends of the rods. To correct for this, use is 
made of the method employed in Comm. N° 83 (Febr. ’03) for the deter- 
mination of the corrections along a piezometer or thermometer stem. 
This depends upon the use of a uniform platinum wire wound uniformly 
round the rod. Its use depends upon the assumption, that the change of 
resistance of a wire wound in this manner is nearly proportional to the 
mean change of temperature of the rod. This will be further considered in § 4. 
After this general view we may consider certain details. 
1st. The glass rods were about 1 m. long and had diameters of 
5 mm.'). Round these 0.1 mm. thick platinum wires were wound 
spirally and soldered to brass rings A, B, C, D (PLL fig. 1.) which 
were tightened by screws. 
Between B and C, the part which was immersed in liquified gases, 
there were 140 turns with a pitch of about 0.5 em. Between A and B 
or C and D where the temperature changes rapidly there were 25 
and 40 turns respectively with a pitch of 0.25 em. Care is taken 
1) A platinum tube provided with glass ends similar to those described above 
was used for the determinations on platinum. 
