ADDRESS BY PROFESSOR TRAILL. XXXLE 
This Report is an excellent specimen of the method of comparing 
the Faunz of distant regions, and presents a model of a philosophical - 
disquisition on the geographical distribution of animals. 
The Association has, at different times, received three able Reports 
from Professor Challis, of Cambridge, on the Mathematical Theory of 
Fluids. In the first he showed how the application of mathematical 
analysis to investigating the properties of an imaginary fluid, supposed 
incompressible, or so compressible that the density should always be 
proportional to the pressure it sustains, admits of comparison with 
facts observed in the equilibrium and motion of water, or in the exist-_ 
ing mechanical qualities of air. In the second, the author considered 
the modifications which these theories had, in later times, sustained by 
the introduction of certain molecular hypotheses on the constitution of 
matter, and how a comparison of the consequences of these hypothe- 
tical speculations with experimental results, served to establish the 
basis of the mathematical reasoning, and to make known properties 
and conditions of bodies not cognizable by our senses. 
The present Report treats of several very important points in the 
Mechanical Theory of the Atmosphere. Mr. Atkinson’s* attempt to 
ascertain the law of variation of temperature, at different heights in the 
atmosphere, would seem to require, for its establishment, a more ex- 
tensive series of observations over a greater portion of the earth’s sur- 
face than we now possess. 
The difference between the velocity of sound, as determined by ex- 
periment, and Newton’s deduction from Boyle’s and Mariotte’s law of 
elastic fluids, amounting to one-sixth of the whole, has given rise to 
many attempts to solve the problem, especially by Euler, Lagrange, 
and Laplace. The latter gave the true solution of the discrepancy— 
namely, that it arises from the evolution of heat, and its absorption, 
which accompany every sudden compression or expansion of air. The 
application of analysis, to afford a formula of correction, was first at- 
_ tempted by Biot and Laplace, and more lately by Ivory ; but when we 
compare the theoretic deduction with the best experiments on the 
propagation of sound by Moll and Van Beck, at Utrecht, by Golding- 
ham at Madras, and Parry and Foster in the Arctic regions, the slight 
_ diserepancies between experiment and calculation are more to be at- 
_ tributed to some imperfection in our formule than to error in experi- 
_ ments, which in their results agree so nearly, though made under very 
_ different circumstances. 
* Trans. Royal Astron. Soc., vol. ii. 
