OF ARTS AND SCIENCES. 19 



of gases, and hence also for the viscosity itself, are incomplete for this 

 phenomenon, in the same general way as are the analogous hypotheses 

 regarding the compressibility of gases and other phenomena. The 

 hypothetical deductions fail to accord completely with the results of 

 quantitative measurements. 



Discussion of Eesults of all Researches on Air 



AND CO.,. 



The experimental results which I have given in the foregoing tables, 

 and the deduced equations, show that, unless some considerable and 

 regular source of error affects them, the viscosity of both dry air 

 (freed from CO.,) and carbonic acid increases with the rise of tem- 

 perature according to a rate which varies with the temperature and is 

 smaller as the temperature is higher. The ratio rj^ : 77^ is therefore 

 not proportional to the first power (Maxwell) of the absolute tem- 

 perature ; it is not expressible by a linear equation of the first degree, 

 e. g. ?/( = t;^, (1 -|- hi), where t = temperature C. and i = a constant; 

 nor is it given by the equation t;^ = 7/g (1 -f- at)", or its equivalent 

 r/; -4- T/y = c r", where t = absolute temperature. The last three equa- 

 tions are the only ones thus far used by observers in discussing their re- 

 sults, although the work of E.Wiedemann and A. von Obermayer shows 

 a decided departure from these expressions. The insufficiency of the 

 latter equations may be shown by discussing the observational data 

 by the logarithmic method which I used in my former paper. Nor 

 could the equation ;;, = »;., (1 -|- a<)" be more than an empirical equa- 

 tion at best, unless possibly when a. were expressed as a function of t 

 and the pressure, a condition which I have not thought worth consid- 

 eration at present. For the expression of my own results, I have 

 employed merely the empirical equation wuth increasing powers of t, 

 as I have found no theoretical hypothesis which led to results cor- 

 responding to the observed relation of ;; and t. 



The deviation of both air and carbonic acid from the equation 

 V/ = '7o (1 + ^ t) is so small, and the difficulties of precise measure- 

 ment so considerable, that these deviations may often be masked by 

 accidental errors of measurement, and by "constant errors," arising 

 from imperfect drying or purification of the gas, from differences 

 between the thermometer indications and the actual temperature of 

 the gas, from faulty proportioning of apparatus, and from other 

 sources. Tliis discussion of my own method in these regards I give 

 at page 25 ; that of others, I cannot advantageously attempt. But I 



