PARALLELOGRAM DIVIDED TO SUSTAIN EQUAL FLUID PRESSURES. 57 



and from this, by evolution and transposition, we get 



Pursuing still the same mode of induction for the fifth value of p, 

 and substituting the respective values of v, w, x and y, as we have 

 determined them above in terms of I and n ; then we shall have 



z { |/5 \/4n~}. 



And in like manner we may proceed for any number of divisions at 

 pleasure ; but what we have now done is sufficient to exhibit the law 

 of induction. 



The formulae which we have investigated, for determining the 

 several sections of the given parallelogram, may now be advantage- 

 ously collected into one place ; for it is manifest, that by exhibiting 

 them in juxta-position, the law of their formation is more easily 

 detected, and the difference which obtains between the co-efficients of 

 the successive terms becomes at once assignable. 



The several equations therefore, when arranged according to the 

 order of the corresponding sections, will stand as under, viz. 



3 - x = (V^- 



&C.&C.ZZ &C. &C. 



71. The practical rule for determining the points of section, in 

 reference to their respective distances from the upper extremity of the 

 parallelogram, may be expressed in words, as follows, viz. 



RULE. Multiply the number of parts into which the paral- 

 lelogram is proposed to be divided, by the number that indicates 

 the place of any particular section; then, multiply the square 



