298 A. W. Witkowski on the 



a. has been conducted. It takes some time, from 10 to 20 

 minutes, to perform the necessary measurements. At the 

 lowest temperatures this time was considerably longer, because 

 in this case it is necessary to provide a sufficient quantity of 

 the freezing substance (solid carbonic acid, liquid ethylene) ; 

 to regulate the speed of the pneumatic pumps and of the gas- 

 motor by which they were driven, in order to obtain the 

 required temperature ; to compare the electric thermometer 

 for low temperatures with the hydrogen thermometer, &c. 

 Under such conditions it happened that during a day I was 

 not able to make more than one or two determinations — to 

 say nothing of the frequent occurrences, when, after several 

 days of laborious preparations, the intended experiment has 

 been entirely lost, through some mischance or other. I think 

 it necessary to mention these difficulties of experimenting in 

 order to explain the comparatively small number of results 

 obtained at the very lowest temperatures. 



§ 8. Calculation of Results. — By means of the experimental 

 data gathered in the manner described above, the results have 

 been calculated as follows : — 



The bulbs being charged, and the charging- valves closed, 

 we have the following quantities of gas in the apparatus : — 



1. In the bulb of capacity s (index 1 or 2 omitted, since 

 the same formula applies to both) there is the quantity M 

 (§ 3) under the pressure of p atmospheres, at 6 and t (re- 

 spectively) degrees. 



In the stem <x, and the narrow channels r s t connected with 

 it, there is confined a quantity m; under the same pressure p, 

 but at the temperature t of the circumambient air. I shall 

 use the letter a- to denote the small capacity of this space. 



Adding together we find in the apparatus the quantity 



M + m=A 



under the pressure p. 



2. In the copper tubes a 1 and a 2 (fig. 1) — I shall use the 

 same letters to denote their capacities — and also in the eudio- 

 meters themselves (in the spaces denoted above [§ 7] by 

 w ii w 2)j we nave a * r under the barometric pressure b. 



I shall use for brevity the symbol w($, b) to stand for the 

 expression 



w b 



T+yb' 760' 



7 being the coefficient of expansion of air of ordinary density 

 at ordinary temperatures ( = 0*00367, very nearly a constant). 



