On Laplace's Theory of Capillarity . 309 
be applied to the human sciences have been prejudiced by 
its pretensions to arithmetical precision. The mathematical 
forms of the science have been unnecessarily weighted with 
numerical content. The logic of Mr. Venn is supposed to fall 
with equal force on those who pretend to estimate numerically 
evidence and inverse probability, and those who hold that the 
entangled quantitative relations which are presented in this 
as in other departments of the human sciences are best un- 
ravelled by the aid of symbols representative, not of number 
indeed, yet of quantify. But if the extravagant pretensions 
to numerical accuracy be abandoned, the moderate claim put 
in for mathematical reasoning may be received with more 
favour. If our First Part has shown that the calculation of 
"probable error" is often not arithmetical, our Second Part 
may show that the calculation of disadvantage is often mathe- 
matical. 
(2) The property of divergence in the average, in so far as 
it is connected with extent of error in the individual, may be 
looked for in moral measurements, which seem to admit of 
more nearly infinite error than physical observations. Accord- 
ingly the process of taking a mean between different judgments 
is not necessarily advantageous in the case of bad authorities. 
By multiplying authorities we may go further and fare worse; 
but in touching on the art of measurement we have already 
reached our Second Part. 
King's College, London. 
Postscezpt, September 27. — If the limits of the elemental errors 
are finite, the proof of the Law of Error by way of equation (2) 
becomes rigorous — analogous to Fourier's reasoning, Theorie de 
Chaleur, art. 377 sqq. 
XLIII. On Laplace's Theory of Capillarity. By Lord PtAT- 
leigh, D. C.L., F.R.S., Cavendish Professor of Physics in 
the University of Cambridge*. 
EROM the hypothesis of forces sensible only at insensible 
distances Laplace f, it is well known, arrived at the con- 
clusion that the pressure within a sphere of liquid of radius b 
may be expressed bv 
K +f CD 
H is the constant on which capillary phenomena depend, and 
* Communicated by the Author. 
t Mecam'gue Celeste, Supplement to Tenth Book. 
