360 
Nov. 16, 1874. 
THE PRESIDENT (PROFESSOR BABINGTON) in the Chair. 
Linear partial Differential Equations, and their Germ- 
integrals. By S. HarnsHaw. 
: This paper will be found printed at length in the “Trans- 
actions of the Society.” 
{ Abstract. ] 
Long before it was discovered that 
A — B = 
ge a BA Hen ON 
U ee GNC oi ae: € ! 
=u, it had been known that 
: , TCO) 
is an integral of the equation aay 
every linear partial differential equation with constant coef- 
ficients, whatever be the number of its variables, is susceptible 
of an integral of the form 
a= Ceme $NY +o 
It thus appeared that the above equation admits of two 
integrals of essentially different types. The same was found 
to be the case with the equation ae = ae of which both 
dx dy 
a= Ceme tm y 
and oo es vel 
are found to be integrals; and they are also of essentially 
different types as integrals. This discrepancy of types created 
in me a desire to ascertain the significance and true origin of 
each, and their mutual dependence if any existed. 
