of Edinburgh, Session 1885-86. 
539 
[After integration as to a and to </>, the part in braekets becomes a 
multiple of cos 2 /? + sin 2 /?.] 
The average value of the product of the velocity-components along 
the line of centres (uv of (1)) is 
Thus it appears that the average value of (1), written in the form 
so that Maxwell’s Theorem is proved. 
[March 15, 1886. — There is an error here, due to a wrong 
assumption as to the probabilities of various positions of the line of 
centres. It does not vitiate the proof, as it introduces a mere 
numerical factor of the whole quantity. See p. 644.] 
4. On Water-Bottles, with the Description of a new form of 
Slip Water-Bottle. By Hugh Bobert Mill, D.Sc., 
Scottish Marine Station. (Plate XX.) 
The various forms of apparatus employed for procuring samples 
of water from beneath the surface are either designed to take up as 
a sample a mixture of the water in a certain vertical range, or to 
secure their entire charge at one definite position. The former 
description of water-bottle has been used almost invariably in deep- 
sea work ; the latter is necessary only in shallow water. 
The most common type, on the principle of the force-pump, 
appears to have been originated by Hooke* two hundred and twenty 
years ago. A box provided with a valve above and one below, 
both opening upwards, is lowered by a weight; the water runs 
f nnfo sin fidfi sin adad<£> 
which is easily by the foregoing process reduced to 
-l/6(p + $). 
is, term for term, 
P(u 2 — uv) - Q(v 2 - uv) 
2P/3p - 2Q/3g, 
or, in the usual notation, 
* Described and figured, Phil. Trans., ii. (1667), p. 442. 
