536 
MR. HENNESSY’S researches IN TERRESTRIAL PHYSICS. 
it must be a zone bounded by two parallels, both of which may become coincident with 
the equator, or evanescent, according as the pressures are very small or very great. 
If it be admitted that any great disturbances in the shell must have been chiefly due 
to the action of such pressures, it would be useful to examine the problem of the de- 
termination of the boundaries of the zone of least disturbance. By comparing the 
results of our investigation with observed phenomena, we may be able to deduce some 
conclusions directly applicable to geology. 
I proceed therefore to determine the analytical expressions for the latitude of the 
limiting parallel of rupture on the side of the zone nearest to the equator. Let ^ re- 
present this latitude, 63 the latitude of a parallel in the supposed undisturbed part of 
the shell. 
It will appear that the general equation between the rupturing and cohesive forces 
upon which the position of the parallel of mean pressure depends, can, when the 
influence of temperature is abstracted, be made to contain but two independent 
variables 62 and a,, or that it will be of the form F(4, ai)=0. The value required of 
^2 must evidently be a maximum, and hence we must determine it in general by eli- 
mination between the equations 
di 
dF 
F(^2, «i), da—^’ da—^ ’ 
the fact of the resulting value being a maximum or minimum can be determined as 
usual by the sign of 
19. Let two infinite planes be conceived to pass through the axis of rotation of the 
shell, making so small an angle with each other that the curvature of the arc of the 
equator intercepted between them could be considered as insensible. The ratio of 
the rupturing to the cohesive forces in either of the opposite portions of the shell thus 
intercepted, will be the same as for the whole shell under our assumed conditions. 
The conditions for finding the section of rupture of one of these bands will therefore 
be the same as those for the entire shell. 
Let dlj represent an element of the area of the section of rupture, I its perpen- 
dicular distance from the neutral surface, k Rnd 4 the perpendicular distances of the 
neutral surface from the outer and inner surfaces of the shell, s the resistance 
measured by the number of units of force required to rupture a square unit of section 
of the material of the shell at the distance 1. The meaning generally attached, in 
works on mechanics, to the term neutral surface, is that here attached to it, namely, 
the surface at which the portions of the band subjected to the rupturing forces are 
neither compressed nor extended. 
Let, as is generally assumed, .s be a function of I, and let be its value at the 
distanee 4- 
If the deflection of the band, in a state of tension and bordering on rupture, be very 
small, as must undoubtedly be the case from its physical structure, the directions of 
