160 
regards the nodal curve upon the centrosurface: the distinction 
of real and imaginary is of course attended to. The new results 
suitably modified would be applicable to the theory treated from 
the second point of view: but I do not on the present occasion 
attempt so to present them. 
(2) On the correct expressions for the resistance which 
bodies experience, whilst moving in gases and 
liquids; with a description of the verifying expert 
ments. By Ricuarp Porrer, A.M. 
[ Abstract. ] 
The mathematical discussion of the resistance to motion 
which bodies experience whilst moving in fluid media has re- 
mained hitherto in a very imperfect state, although it received 
great attention from Sir Isaac Newton. In the second Book 
of the Principia he discusses the resistance when bodies move 
in elastic and non-elastic media. 
Canton having in 1762 proved the liquids to be elastic as 
well as the gases, though they are subject to different laws of 
compressibility, the consideration which Newton adopted for 
elastic fluids we know now to apply to all fluids. The Problem 
vil. Prop. xxxv. of Book 11. of the Principra, the author held to 
be the problem still to be solved by the instrument of the 
modern analysis which was undeveloped in Newton’s days. It 
is enunciated as follows: 
“Si medium Rarum ex particulis quam minimis quiescen- 
tibus, eequalibus, et ad equales ab invicem distantias libereé 
dispositis constet: invenire resistentiam Globi in hoc medio 
uniformiter progredientis.” 
This involves the method which the author followed in his 
paper on Hydrodynamics published in the Philosophical Maga- 
zine for March, 1851, before he knew that Newton had con- 
sidered elastic fluids to be constituted of distinct molecules in 
