Kvb.] VISCOSITY OF GASES. 285 
tween stop cock and capillary tube until the high pressurePis reached; 
id after closing the stop-cook the compressed air of the dead space is 
•adually discharged. The method of eliminating the positive error 
hich is thus added to the transpiration volume ( V ) has been indicated 
1 page 257. But when the transpiration volume has to be chosen small 
e dead space discrepancy is more serious in character even when re- 
iced to the smallest value compatible with the practical efficiency of 
e apparatus. These difficulties are quite avoided by using tubes of 
rge bore and larger volumes of gas, and hence a second reason why 
e experiments of the present paragraph are desirable. 
Hoffmann's researches. — From a theoretical point of view 1 the con- 
derations involved are, of course, of extreme difficulty and compli- 
ited in mathematical character. As such they must be here omitted, 
rom an experimental point of view, the difficulties encountered are 
rtunately less formidable, and an excellent analysis of the subject, 
ised on a variety of observations, has been published by Hoffmann. 2 
Hoffmann, after recognizing that the chief discrepancy is introduced 
the ends of the tubes, derives his first eq uati on by successively ap- 
ying Navier's equation vp=R 2 n n x \J Ch%^ for the ends of his 
ibes, and the Poiseuille-Meyer equation for the intermediate parts, 
nfortunately, even in the favorable case of slight variation from 
oiseuille-Meyer's law, this process leads to very involvedresults: 
7T X 
(VP) 2 , X2 
E* 7L 1 Op? 
(vp) 2 
7t 2 =p 2 e*«*<W, 
rhere p x and p 2 are the observed pressures just before entering and 
saving the capillary tube, and 7t x and n 2 are the corresponding press- 
res in the first and final section; (7=—^ X^T^ and the remain- 
7 0.00129277 
ag variables have a meaning which is easily understood from the 
iscussion on page 253. 7T=3.1416 and e is the basis of the Naperian 
^be literature is digested by Hoffmann (1. c.) as follows: Navier: Mem. de l'Acad. 
e 8c. de Paris, vol. 6, 1823, p. 389 ; Poisson : Journale de l'dcole Polytecbnique, vol. 
3, 1831, p. 139; Stokes: Trans. Cambridge Philos. Soc., vol. 8, 1849, p. 287; Caucby : 
Sere, de Mathem., vol. 3, 1828, p. 183; de St. Venant: C. R., vol. 17, 1843, p. 1240; 
tefan: Wien. Ber., vol. 46 (2), 1862, p. 8. 
2 Hoffmann: Wiedemann, Aunalen Pbysik, new series, vol. 21, 1884, p. 470. 
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