WEIGHT AND SUPPOET IN SHIPS. 
437 
of water-borne division. By a simple extension of the method, the cases similar to those 
illustrated by Plate XVII. figs. 10 & 11 can also be shown to come under this rule, and 
the theorem stated above may thus be established generally*. 
It has already been shown that sections of water-borne division coincide with sections 
of zero shearing, and that the number of such sections must be odd ; hence we have this 
rule, that the number of sections of maximum and minimum bending-moment must be 
odd. This rule will be seen to hold in all the preceding cases. For example, in the 
‘ Minotaur ’ there is one section of maximum hogging-moment (a a' in Plate XVII. fig. 8) ; 
in the ‘ Bellerophon,’ and in the ‘ Audacious ’ when fully laden, there are three sections 
of maximum and minimum hogging-moment, the section of minimum moment being 
nearly amidships (a a', bb', c d in Plate XVII. figs. 9 & 10); in the ‘Audacious,’ when 
light, with her engines and boilers only on board, there are five sections of maximum 
and minimum hogging-moment [a a!, bb', &c. in Plate XVII. fig. 11); and in the 
‘ Victoria and Albert ’ there are two sections of maximum hogging-moment and one of 
maximum sagging-moment ( a a!, c c', and b V in Plate XVI. fig. 7 ). In the hypothetical 
case of Plate XVII. fig. 12, based upon the ‘ Audacious,’ there are also three sections of 
maximum and minimum hogging-moment. If sagging be regarded as a negative phase of 
hogging, it appears from all these cases that sections of maximum and minimum bending- 
moment occur alternately, although it must not be forgotten that in its absolute amount 
the sagging-moment, which is termed a minimum, may exceed some of the so-called 
maximum hogging-moments. What is really meant may perhaps be better expressed as 
follows : — Between two sections of maximum hogging-moment there must fall either a 
section of minimum hogging-moment or a section of maximum sagging-moment. In 
the ships with which Dupin was acquainted no sagging-moments were experienced, and 
hence we find him laying down the law, which I believe he was the first to observe, that 
sections of maximum and minimum bending-moment occur alternately. My statement 
is simply an extension of the same principle to more complex cases, such as are met with 
in modern ships. Dupix also indicates a simple method of determining whether a sec- 
tion of water-borne division is one of maximum or minimum bending-moment. It is as 
follows: — If the resultant vertical force immediately adjacent to the section of water- 
borne division acts upward, that section is one of maximum hogging-moment ; if down- 
ward, it is one of minimum hogging-moment. In order to extend this so as to embrace 
ail the ships we have considered I must add, if the resultant vertical force acts downward, 
the adjacent section of water-borne division is either one of minimum hogging-moment 
or of maximum sagging-moment, and vice versa. 
All that has been said respecting the variations in the number of sections of zero 
shearing, or water-borne division, which may be produced by alterations in the stowage 
* In the case previously considered, of ships with a long middle body of which the weight balances the 
buoyancy, this general law also holds ; for any transverse section within the limits of the middle body will 
obviously fulfil the conditions of a section of water-borne division, and of one where the bending-moment is a 
maximum or a minimum. 
3 p 
MDCCCLXXI. 
