617 
lished in 1855 and subsequently. Referring next to the direct 
experiments of Messrs Fairbairn and Tate on the density of steam, 
published in the Philosophical Transactions for I860, he gives a 
tabular comparison of the volumes of one pound of steam as de- 
termined by these experiments, and as computed theoretically from 
M. Regnault’s experiments on the latent heat of steam, with the 
aid of Joule’s mechanical equivalent of heat ; and from that com- 
parison he draws conclusions which may be summed up as follows : — 
1. At temperatures below 212°, the differences between the 
results of theory and experiment are inappreciable. 
2. At temperatures above 212°, the differences, although too 
small to be of any consequence in practical calculations connected 
with steam-engines, are appreciable, the volume of a pound of steam 
by theory being slightly greater than by experiment. 
3. Small as those differences are, there exist no known sources 
of error either in the data of the theoretical calculation or in the 
method of experimenting sufficient to account for them. 
4. They are therefore most probably caused by some unknown 
difference in the molecular condition of the steam in M. Regnault’s 
experiments on latent heat, and in Messrs Fairbairn and Tate’s 
experiments on density. 
5. That difference of condition is probably connected with the 
fact, that in M. Regnault’s experiments the steam was in rapid 
motion from a boiler towards a condenser ; whereas in the experi- 
ments of Messrs Fairbairn and Tate the steam was at rest. 
6. Further experimental researches are desirable. 
7. Formulae connected with small continuous Displacements 
of the Particles of a Medium. By Professor Tait. 
Although most of the results deduced in this Note have been 
long known, I venture to offer it to the Society on account of the 
extreme simplicity of the analysis employed, and the consequent 
insight it affords us into the connection of various formulae. I 
intend on a future occasion to give large further developments 
especially bearing on physics. I employ the calculus of quaternions 
throughout, but where some unusual expressions occur, I have given 
them in their common Cartesian form, as well as in the quaternion 
one. 
