Defence of the Newtonian Law of Molecular Action. 199 
clude with him, “that M. Cauchy’s are at variance with ex- 
periment?” I believe very few persons will be found to join 
in this opinion. M. Cauchy’s name, in the first place, isa 
sufficient guarantee for the accuracy of results which he has 
repeatedly obtained at different remote intervals. But, in the 
next place, the same problem has been solved, in different 
forms, by Mr. Airy (Tracts, Art. 110), by M. Naumann, by 
myself, by Mr. Green (Trans. Camb. Phil. Soc., 129), and 
lastly by Mr. O’Brien (Phil. Mag., March 1842, p. 210), all 
2 
arriving at like results, viz. that the equation ears n* &, 
&e. correspond generally to three directions determined re- 
lative to the front of the wave, not to the axes of symmetry 
in the medium only, or in a medium of symmetry at all. [See 
Mr. O’Brien’s paper, Phil. Mag., March 1842, p. 211.] But, 
lastly, Mr. Earnshaw says he effects his reductions on eape- 
rimental grounds. On what kind of experiments? let me ask. 
In the next page (442) we find again, “The forms of the new 
equations of motion 
nee d*y d? 
rie —h?t, Tea key ad =— 126) 
show that these axes cre axes of dynamical symmetry,—those 
in fact which are better known as the axes of elasticity. Now 
from experiment we know that k,*, £,”, 4° are constant quan- 
tities, i. e. independent of the wave’s front.” The inference 
which Mr. Earnshaw here draws from his equations is directly 
opposed to that drawn by all the authors quoted above. Other 
writers consider their symmetry to refer to the front of the 
wave. But, not to waste words on an error so obvious, let 
me ask Mr. Earnshaw a question. Are k,*, £,, £37 equal or 
unequal in uncrystallized media? If they are not, on what 
does their inequality depend? If they are equal; then can 
it be shown that D=0, E=0, F=0, and A= B=C, 
so that the transformation is no transformation at all. If 
Mr. Earnshaw will carefully examine this remark, he will be 
convinced, I am sure, that the problem he conceives himself 
to be engaged in is the following :—* To find those directions 
within any medium, in which if a particle be disturbed, the 
resultant of the forces acting on it will tend to move it back in 
the same line in which the displacement is produced.” This 
problem has been solved by Fresnel (Mém de l’ Institut, 1824), 
by Herschel (Light, Art. 1001), and by A. S. in the Cam- 
bridge Mathematical Journal, vol. i. p. 3. Now this is a 
totally different problem from that against which Mr, Karn- 
shaw brings his conclusions to bear. In the latter we are not 
