4 Proceedings of the Royal Society of Edinburgh. [Sess. 
working out completely one example. This particular example corresponds 
to the third entry in the first table given below, the one designated 123 tris. 
It was not included by Andrews in the published Table I. A comparison 
of what is tabulated here with Dr Andrews’ working out will serve to 
show how the present table has been constructed. 
My original intention was to have worked out the true pressures and 
entered them in the sixth column. After prolonged and careful discussion 
of Amagat’s published results for air, I was reluctantly compelled to come 
to the conclusion that they were not sufficient for the purpose. In his 
final “ Memoires sur l’Elasticite et la Dilatabilite des Fluides jusqu’aux tres 
hautes Pressions ” ( Annales de Chimie et de Physique , 1893), Amagat 
gives three tables of numbers. Tableau No. 10 contains the volumes at 
pressures ranging from 100 atmospheres to 1000, at intervals of 50 ; and in 
Tableaux No. 10 bis the volumes are given for pressures ranging from 125 
to 475, also at intervals of 50 atmospheres. These are not detailed enough 
for pressures below 100 to serve for the present purpose. At first sight 
Tableau No. 11 seems to give results in sufficient detail for pressures from 
20 metres pressure to 65 metres pressure, that is from 26*32 to 85*53 
atmospheres. I do not find, however, that this last table agrees well with 
the other two. 
For any limited range of pressure and temperature changes we may 
assume the following empirical formula — 
p(v - b) = RT - ajv + c/v 2 , 
where p, v, and T have their usual meanings, and R, a, b, c are constants 
for any given mass of gas at given temperature and pressure. When 
c = abwe have Van der Waals’ formula 
(p + a/v 2 )(v - b) = RT. 
On applying this formula to the data of Tableau No. 11, and then to 
those of Tableau No. 10 and No. 10 bis, I did not obtain consistent results. 
I have accordingly thought it best to leave the pressure column vacant in 
all cases in which air was the manometric substance. 
On the other hand, the approximately linear character of the hydrogen 
curves, showing the relation between pressure and volume, renders it 
possible to obtain a formula applicable throughout a wide range of 
pressures. 
The pressures which are entered in the tables of Group C below have 
been calculated from the formula 
p(v- 0-001 668) = 0*00366 T - Q ' Q0Q9575 _ Q,QQQQ0Q86 I 7 . 
v 
V‘ 
