( 683) 
quadratic and 2 == 9.0 em. with the linear formula. The uncertainty 
thus introduced into the determination of length, is less than Ly. 
In order to determine the influence of various suppositions with 
regard to the distribution of temperature in the rod, we have 
calculated the change in length which would be produced, if the 
temperature was — 87° C. from O to 4 and O° from 4 to Z, in 
place of the distribution assumed above. The change was hardly 
0.1 uw and thus lies within the degree of accuracy. However an 
important control indispensable for more accurate determinations 
would be obtained by measurements on a rod with similar ends 
AB and CD, but where LC was only a few centimeters long ). 
To apply generally the method of this section for the determination 
of mean temperature it may be necessary to subdivide the portion 
of at variable temperature AB into more parts while for each of 
these separate portions the resistance would have to be found. In 
our case this would have been an unnecessary complication. 
§ 5. Influence of errors. These can be fully considered by the 
RTs ni 
i ek 
The accuracy of the cathetometer reading can be put at 2u (the 
whole contraction being 1200 u). This gives da = 2 x 108. For the 
mean temperature of the portion BC the error is certainly less than 
0.5 deg. C, whence da = 1.5 >< 10-8, and for that of the ends we 
found 1a. Hence a greater uncertainty than da = 4 1078 is not to 
be expected. Although the division of this error between @ and } 
cannot well be made, it is certain that an error in the temperature 
determination has by far the greatest influence on 5. 
aid of « —= 
§ 6. Final results. For the observed lengths Livo, at the tempe- 
rature £vo, in nitrous oxide, Zo, in oxygen, and Lig at ordinary 
temperature we have the three equations 
Lino, = (Lee, + Ai + 4s) (1 + ato, 4- bvo) + 
1 1 
a Tes, sai oe (Zs in ID. Kees i) (: ae 5 atNo, + 3 beo.) 
and two analogous ones for Lio, and Zico, with Liz, = 840 mM., 
Li, =97, L,, =59 for Jenaglass, and Lao, = 834, Lj, — 96, L,, — 60, 
for Thüringerglass. For Lyc¢, (the length of the part LC in the figure 
at 0’ C.), Li, Le, (that of the parts CD and AB in the figure) are 
assumed approximate values; the exact values Zy, and Ls, to be 
1) For Jenaglass in oxygen we found a negative value of a, we made therefore 
the calculation on another supposition viz. that from A in the direction of B the 
rod has the temperature 0’ over a length of A! cm. (ef. Table IV). 
47 
Proceedings Royal Acad. Amsterdam. Vol. VII. 
