121 
11. When m, n, and r are positive, u = 0 is a solution of (1) 
Yet the positive values of m, n, and r may be such as, while 
making u = 0, to make U = ©o. This is a paradox. But U 
contains the term mm m_1 (M - 1)(1 - 1), which is suppressed 
in the above calculation. Now, although this suppression is 
in general allowable, it may (but will not necessarily) cease 
to be so when the above term takes the form oo(l - 1). It 
would therefore seem that X - X is not necessarily null when 
X is infinite. 
12. The oo(l - 1) will not occur unless one at least of the 
^ be rendered infinite. The general 
theorem is (not that of Du Bourguet but) this, viz., Retain 
in the calculation of U all terms whatever, whether they 
seem to cancel one another or not. Write the result in the 
form U=Q + X(1-1). Then □ = 0, or, failing that, X = oo 
(which can only arise from C ~ = coor^ = oo) may yield a 
.... dM -| aN 
quantities and 
dz 
single solution. 
March SO , 1881. 
2, Sandringham Gardens, 
Ealing, near London, W. 
The President said that he had, on several occasions, 
brought before the Society a notice of the Eucalyptus glo- 
bulus growing near to the sea in his garden at Douglas in 
the Isle of Man. It was planted in 1875, and grew about 
7 feet in height annually during the three following years ; 
after these its top reached higher than the wall sheltering 
it, and it was exposed to the east winds from the sea, which 
stopped its rapid growth. It now has attained a height of 
thirty feet. During the present winter it fared pretty well 
until the beginning of March, when the strong gales made 
bad work with its foliage, but the tree is still alive, and he 
has every hope it will rally again in the summer. It grows 
about six feet above the ordinary high water mark of the 
sea in Douglas Bay. 
