Motion of Solid and Fluid Bodies. 159 
dy dg dg d&t d&t dy 
dz dy dx dz dy da’ 
this form of the function being deduced from the equation 
d 
+480, 
dx dz 
which expresses that the medium refuses to change its density. 
It follows from this difference of form of the two functions, that in light the 
molecules of the medium cannot act on each other in the direction of the line 
joining them, for if they did, the function corresponding to the medium should 
contain terms depending on the quantities 
dé dyn dé 
ay ae U; V, W. 
Previously to investigating the differential equations of equilibrium and 
motion, produced by the function v,, it is important to examine whether the 
function v, itself is capable of any simplification in its form by means of a change 
in the direction of the axes of coordinates, to which it is referred; as, if it be 
possible to refer it to particular axes, for which it becomes simplified, this will 
also simplify the equations of equilibrium and motion depending on it, and will 
prove the existence of three rectangular axes in the body at each point, which will 
have an intimate connexion with the molecular structure of the body at every 
point. The equations for transforming &, y, ¢ are 
ae + br! + Ges 
y= dl 4+ by + ¢?¢, 
G = al b+ Cae 
d&é dy dé : 
da’ dy? de’ U, V, w, must be transformed by the aid of these 
three equations, and the transformed values substituted in the function v,; adopt- 
the six quantities, 
ing, for brevity, the following expressions, 
p =2a'a", q = 2b'b", te D2GiCits 
p = 2aa", gq = 2bb", r’ =2cc", 
p= 2aa’, q’ = 2bb’, ri’ = 2Qcc'" 
VOL. XXI. Z 
