OF ARTS AND SCIENCES. 47 



(7Z), either at the same or at different temperatures. Now, if we de- 

 note by Fj, i?j, ^p r]^, &c., the vohime of gas transpired by A£, the 

 radius and length of AB, and the coefficient of viscosity of the air pass- 

 ing througii it, while V^, &c., represent the same quantities for CD ; 

 also, if PpP2' 7'" Pi '"epresent the pressure of the gas at A, B, C, and B 

 respectively as obtained from the gauge and bai'ometer readings ; then 

 from (1) we may write, 



and 





But if both baths are at the same temperature F^ = F^ if <^ ^ #05 and 

 11^ = /^i,? whence we may write, 



^V^i ~ Ih'-p-z'' 



(4.) 



Also in general it will be seen from the nature of the apparatus that 



V V. 



1 — — — where 8^ and 8.^ represent respectively the tempera- 



l-l-a5^ 1 -|- "So 



tures at which \\ and F^ are transpired. Hence 



(o.) 



From equation (0) it will be seen that, in order to determine with 

 this apparatus the ratio j/j : //„ between the coefficients of viscosity 

 in the two tubes when the temperature of these is 8^ and 8.^ respectively, 

 we have onl}- to know the ratio of the dimensions as expressed by 



jHrti and to measure jt?p p.^, and p^ by reading three mercury columns. 



Also we can obtain a value of Trrr f™m readings of the gauges when 



8^ = 8.,, which needs only to be corrected for expansion of the glass 

 to be used directly in equation (5). The whole process is thus re- 

 duced to the simple matter of reading columns of mercury, no meas- 

 ure-ments of volumes of gas being necessary. The nature of the 

 correction of Ji and I for temperature appears by putting into the 

 above formuhs in which these values are supposed to be for 0° C, 

 the coefficients of expansion of the glass =: A ; we thus get from (5) : — 



Vj _ R,H\ -}- A6,)% {1 -\- A6.2) Pi'-P^^ 1 + «S2 

 V2 — /?2'( 1 + A6,]iX,( 1 + .4c5j • ;v -7-3- ' I + aS, 



(6.) 

 _ R,H\-\-AdJ^?., pf-pl 1 + oh 



