400 
Proceedings of the Royal Society 
roundabout fashion : the equation referred to can readily bo solved. 
For it is clear that 
must be integral : 
and as P is prime to Q, this is the same as saying that 
2P2a + PP' . . I 
— must be integral. 
Q 
But P^ = QP' + (-l)* if I be the number of terms in the cycle 
(6, Cf ... 7 c, b). Hence 
2aQF + 2a(-l)' + PF 
Q = an integer. 
(-iy2a + PF 
7^; = an integer = m say 
H 
a = (-l)'HQM-PP'}. 
By substitution now in the original equation we find 
a = (-iy{PM-F2}. 
Hence the required expression is 
J{Qm-PF}2+(-1)^(Fm-P'2). 
M. Catalan’s equation, the solution of it here given, and this final 
result, are to be found in the The Expression of a Quadratic Surd^ 
&c., p. 30. 
o. New Forms of Nerve Terminations in the Bkin of 
Mammals. By George Hoggan, M.B, (Edin.), Com- 
municated by Professor Turner. 
{Abstract.) 
The new forms have been found in the palms of the raccoon, 
the Procyon lotoi\ so named from its habit of dipping its morsels in 
water before eating them. These forms are three in number, and, 
in order to prevent any morphological or physiological appellation 
being applied to them, they have been named, for purposes of 
description and differentiation, after three ladies respectively, the 
Browne, the Hoggan, and the Blackwell bodies. The Browne 
bodies occupy the apices of the dermic papillse, exactly where the 
