534 
MR. HENNESSY’S researches IN TERRESTRIAL PHYSICS. 
Abstracting these irregular causes, an examination of the question of the directions 
of the fissures in a spheroidal and nearly spherical shell, composed of strata each 
possessing in itself an uniform cohesive strength, but differing in this respect from 
every other, would assist in pointing out what should be the predominant directions 
of the fissures, if the greater effectiveness of general over particular causes be allowed. 
The problem which is here to be examined is therefore simply to find the directions 
of the fissures in a thin, solid and nearly spherical shell, resulting from the pressures 
of a mass of fluid inclosed in it, the cohesion of the shell being supposed to vary, 
according to some continuous law, along a vertical line from its inner to its outer 
surface. 
If the constant pressure referred to in Section I. alone acted on the shell, the ten- 
sions at any point in one of the shell’s indefinitely thin strata would be equal to each 
other and situated in the tangent plane at that point. The position of the maximum 
resultant tension would therefore be indeterminate, and consequently there would be 
no tendency to form a fissure in any particular direction rather than in any other. 
If the variable pressure be superimposed on the constant pressure, the direction of 
the maximum resultant tension would be determinate, and consequently also the line 
in which a fissure would commence. At first, if the intensity of the pressures should 
gradually increase, a portion of the shell at each side of the equator bounded by 
parallels would be subjected to tensions sufficiently great to produce fissures, while 
beyond these parallels the shell would remain unfractured. The portion where the 
tensions would be sufficiently great to produce fissures, would thus constitute a dis- 
turbed district with nearly fixed boundaries. At a point where there is a tendency to- 
wards the formation of a fissure, the direction of the maximum resultant tension will 
be in the direction of the tangent to the meridian ; the greatest tendency to form a 
fissure will therefore be parallel to the equator. From the nature of the variable 
pressure the maximum tensions must be equal, at equal distances from the equator; 
hence such a fissure, when once commenced, would tend to be propagated along a 
parallel of latitude until the force of the tensions become sufficiently lessened by the 
separation of the extended portion of the shell. Similar fissures would be formed 
simultaneously and symmetrically at each side of the equator. As long as the ten- 
sions in the directions of the tangents to the meridians continued sufficiently great, 
such fissures would be formed ; but, as already mentioned, their formation would tend 
to annul these tensions, and a new system would result, having a tendency, as may be 
readily deduced from Mr. Hopkins’s investigations*, to produce fissures perpendicular 
to those previously formed. If the maximum intensity of the variable pressure be 
not inconsiderable compared to the constant pressure, it will follow, if the pressures 
continue to act with sufficient energy, that all the shell’s fissures will be either parallel 
or perpendicular to the equator. 
If, on the contrary, the constant pressure were far greater than the variable pres- 
* Cambridge Philosophical Transactions, vol. vi. 
