986 REPORT—1885. 
5. The Size of Molecules. By Professor A. W. Retnotp, M.A., F.R.S. 
The four lines of argument by which Sir W. Thomson has been led to form 
an estimate of the size of a molecule are, briefly, as follows :— 
1. Argument from the Refractive Dispersion of Light.—If transparent sub- 
stances like water, glass, &c., were infinitely homogeneous, the velocity of propa- 
gation of light through them would be independent of the period of vibration or 
wave-length. The fact that the velocity of propagation does depend on the period 
is irrefragable proof that such transparent substances are not infinitely homo- 
geneous—2z.e., the coarse-grainedness of such substance is comparable with the 
wave-length of light. Cauchy was the first to arrive at this conclusion, but his 
theory leads to results altogether untenable. The same general principle is, how- 
ever, applicable, and by making certain assumptions as to the connection between 
the ether and the heavier particles of matter, results may be obtained in agreement 
with those derived from other considerations. 
2. Argument from the Phenomena of Contact Electricity—If a plate of zine 
and a plate of copper be brought into contact with each other, they become oppo- 
sitely electrified and attract each other. Let the plates be each a square centimetre 
in area, and, after being made to touch, let them be brought to a distance of 
10—-* centimetres from each other. The work done by electrical attraction while 
the plates are allowed to approach each other is about 2 x 10® x 10-8 =2 x 10-? centi- 
metre-grammes. If now a third plate, of copper, be similarly placed upon the 
zinc platean, equal additional amount of work will be done by electrical attraction, 
and by making a pile of plates, alternately of zinc and copper, an amount of work 
will be done by electrical attraction proportional to the number of plates employed. 
Suppose a pile so constructed of 100 millions and one plates, 50 millions and one 
of zinc, and 50 millions of copper, each plate being the hundred millionth of a centi- 
metre thick, and the distance between the plates the 100 millionth of a centimetre. 
The volume of the metal will be a cubic centimetre, and its mass 8 grammes. The 
work done by electrical attraction will be 2 x 10% centimetre-grammes, or, 3 x 10° 
centimetre-gramme per gramme of metal. To raise the temperature of 1 gramme of 
zinc or copper,the heat required is equivalent to 4030 centimetre-crammes. Hence 
the work done by electrical attraction would, in the form of heat, raise the temperature 
lh 108 
4030 16,120 
our present knowledge of the heat of combination of zine and copper. By suppos- 
ing the plates and intervening spaces to be made yet four times thinner, it is shown, 
in a similar manner, that the temperature attained would be 990°. A result 
requiring more heat than is prodused by the chemical union of copper and zinc. 
Hence plates of zinc and copper ,.\_. centimetres thick, placed close together 
000,000 : c 
alternately, form a near approximation to a chemical combination, if indeed such 
plates could be made without splitting atoms, This argument, therefore, gives 
3y M. (M=millionth of a millimetre) as the diameter of a zinc or copper particle. 
3. Argument from Liquid films.—The surface tension of water is 81 dynes per 
centimetre, corresponding to about 8 milligrammes per millimetre. Therefore in 
the case of a water film with two faces the contractile force is 16 milligrammes per 
millimetre. Hence the work done in stretching a film of water, measured in milli- 
gramme-millimetres, is 16 times the number of square millimetres by which its area 
is increased. But the film is cooled in being stretched, and Sir William Thomson 
has shown that half as much energy must be supplied to the film in the form of 
heat to maintain its temperature constant. Hence the intrinsic energy of a mass 
of water in the shape of a film kept at a constant temperature is increased 24 milli- 
gramme-millimetres for every square millimetre added to its surface. Starting 
with a film ofa thickness of one millimetre, and supposing it to be stretched until 
its area is increased 10,000 fold, the heat equivalent to the work done in stretching 
it, supposing the temperature to remain constant, is calculated. It is thus shown 
that work spent in stretching this film until its thickness is moma Mullimetre, 
would, in the form of of heat, cause a rise in temperature sufficient to vaporise the 
of the mass by ; x 10° x = 62° C, which is not improbable according to 
