10 Mr. Ivory on the Theory of Capillary Action^ $c. 



in terms of s. The necessary operations being performed, we 

 finally obtain, 



_ 1 / jl _5f_ 119s7 393 s9 \ 



2 — "497 V + 16 + 256 T 12288 + 65536 / 



1 x v 192 T 512 y 



The term multiplied by I 3 being omitted, as it does not affect 

 the value of a in the fifth decimal place. In order to find s, 

 we must compute <r, for which purpose we readily obtain this 

 series, 



_ jL * 5 35 z> 137 & « . 



r "" 16 128 12288 98304 + 



and * being 0*735, we get <r = 0*70805. Then 



•70805 



A being computed by the formula (A). 



As the diameter I decreases, s approaches indefinitely to cr, 

 and u to z ; so that, for tubes of an extremely small bore, the 

 depression is, 



z -015 



q ~~ 49* ~ I 

 On the other hand, the diameter of the tube increasing, s de- 

 creases very rapidly ; and when the diameter is half an inch, 

 or greater, all the powers of s are inconsiderable, and we have 

 simply, 



- s - '70805 _ -Q1445 



? ~~ 49 1 49 i ' >. ~~ 1 . * 



The first term of q in the formula (B) being the expansion of 

 a known function, it may be continued to any degree of ap- 

 proximation ; but the terms set down are sufficient even for 

 very small tubes. Suppose I = fa thus A = 1*01539, s = 

 •69736, and 



Next, let I = i, then A = 1*5460, 5 = *1997, and 

 •1997 



I have subjoined a Table of the depressions in tubes of va- 

 rious bores, and have added the experimental determinations 

 published by Lord Charles Cavendish ; by which it will be 

 seen that the agreement of the theory with experiment is very 

 satisfactory. 



Depression 



