On the Summation of Singular Series Associated with Certain Quadratic Forms (II)

In a recent paper on the same subject an account was given of a method, an alternative to the standard one, of effecting the summation of the singular series which arise when we consider the representation of numbers in the forms.
a(x²+y²)+c(z²+t²) (1)
a(x²+y²)+2c(z²+t²) (2).