"Ants] VISCOSITY OF GASES. 253 
of larger bore. Methods of doing this will be described below. Such 
apparatus would, however, be expensive, and in an introductory in- 
vestigation, in which easy variatiou of the capillary bore is one of the 
desiderata, the use of fixed forms of apparatus is unadvisable. Hence 
I have made use of platinum capillary tubes with cold ends in the way 
described in the preceding paragraph, inasmuch as these can be drawn 
down from the original to any smaller radius, and then inserted into the 
pneumatic apparatus with comparative facility. The cold ends, how- 
ever, introduce an error of a serious kind, for which allowance must be 
carefully made. Fortunately this can be done with ease and accuracy 
by successive applications of Meyer's equation. 
As before, let R, L, 0, t be the symbols of radius, length, temperature, 
and time. Let the platinum capillary tube be supposed to be made up 
of three parts, V, I", V", so that l / +l // + l /, '=L. Let the variables refer- 
ring to these parts be similarly accentuated. Then the following scheme 
of variables presents itself: 
PF^V'.^iV/'.etc. p' V",R",l", B", t", V " , etc. p" V", B 1 ", V", B'",t"\ ?f", etc. p 
Of the three partial tubes thus given the first and third are ends, and 
hence I' and V" are small as compared with I", and 6' and 6'" small as 
•compared with the high temperature 6". Applied to the apparatus 
described, the following simplifications are admissible: R'z=R'" — R' i) 
fy=r/"=r f ; 6' =6'" =6; moreover V'p / =V"p"=V'"p'"= Vp, and 
t'=t" — t'"=t. The successive application of Meyer's equations thus 
leads to 
Vkp(l + a0)~ t 
E 
77 i_i_ a 0n r /i 
(i + 4)' '— *"(!«•;) 
= P 2 -f 
Now, if ft be the mean coefficient of expansion of platinum, so that 
R"=R {) " (1+/5 6") (R and R being supposed identical), I find finally that 
rj' 
1 + 4 P/7 
R' 
n Ri-tf t Rn"* 
V SR »\H<+1 
16 p V I" 
>"1 l+ad 
(i+ft^r 
(5) 
If this equation is to express if absolutely, and if P and p are meas- 
ured in heights of columns of mercury, the factor 6g must be inserted 
in the right-band member, as before (page 252). Regarding the other 
quantities it is clear that they are measured in terms of c. g. s. units. 
The temperature of Fis 6. 
Equation (5) is capable of much simplification. In the above appa- 
ratus R "=R () ; hence care must be taken either in making — p— as 
small as possible, or V and V" must be correctly measured. In the 
above apparatus very close contiguity of hot and cold parts of the spiral 
(907) 
