434 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OF 
of facilitating comparison, Mr. Love’s notation will be employed for strains and 
directions. It will also be convenient to denote the values of the various quantities 
involved, at a point P on the middle surface of the shell by unaccented letters; and 
the values of the same quantities at a point P' on the normal at P, whose distance 
from P is h', by accented letters. The radius of the shell will also be denoted by a, 
and its thickness by 2h. 
The theory which it is proposed to develop for cylindrical and spherical shells 
is identical, except in matters of detail, with the theory of plane plates which I 
recently communicated to the London Mathematical Society,* but for the sake of 
completeness a short outline will be given. 
In the flnure let OADB be a small curvilinear rectang^le described on the middle 
surface of the shell, of which the sides are lines of curvature ; and let us consider 
a small element of the shell bounded by the external surfaces, and the four planes 
passing through the sides of this rectangle, which are perpendicular to the middle 
surface. 
The resultant stresses per unit of length which act upon the element, and which are 
due to the action of contiguous portions of the shell, are completely specified by the 
following quantities ; viz., across the section AD, 
T]^ = a tension across AD parallel to OA, 
Mo = a tangential shearing stress along AD, 
N 2 = a normal shearing stress parallel to OC, 
G 3 = a flexural couple from C to A, whose axis is parallel to AD, 
= a torsional couple from B to C, whose axis is parallel to OA. 
Similarly the resultant stresses per unit of length which act across the section BD are, 
T 3 = a tension across BD parallel to OB, 
M] = a. tangential shearing stress along BD, 
= a normal shearing stress parallel to OC, 
= a flexural couple from B to C, whose axis is parallel to BD, 
H 2 = a torsional couple from C to A, whose axis is parallel to OB. 
* ‘ London Math. Soc. Proc.,’ vol. 21, p. 33. 
