288 
NATURE 
[May 13, 1915 

tions of the intermediate and large ions were obtained 
on many occasions, but with vapour pressures exceed- 
ing seventeen millimetres, while the observations of 
the large ion were equally good, all trace of the inter- 
mediate ion disappeared.! Disintegration of the ion 
at a critical vapour pressure is unlikely, and it is 
much more probable, assuming a rigid nucleus, that 
the adsorbed fluid is in the condition of a dense 
vapour, and that at the critical pressure it changes 
its state to that of a liquid, like the moisture adsorbed 
by glass and shellac in Trouton’s experience. 
Such a change means a decrease in the energy of 
the aggregation, and is to be expected when the mole- 
cules of water vapour around the nucleus become 
sufficiently closely packed. The advent of a liquid 
surface involves a diminished rate of molecular escape ; 
rapid condensation will therefore occur, with a de- 
creasing unit-surface energy, until further increase in 
the size of the ion means an increase in the total energy 
of the mixture of ions and vapour. The final result 
is no other than the large ion. The assumption of a 
rigid core for the intermediate ion appears, thus, to 
be justified. 
Se | 


VAPOUR PRESSURE 
ro) 

5)0 10}0 
MOBILITY —RECIPROCAL 
Fic. 2.—The relation between the reciprocal of the mobility of the 
intermediate ion and the vapour pressure, 

To sum up the whole evidence, the large ion con- 
sists. of a rigid nucleus surrounded by moisture in the 
liquid condition, the size of the drop at constant tem- 
perature depending on the vapour pressure. The 
intermediate ion is to be considered as a_ similar 
“nucleus enveloped by a dense atmosphere of water 
vapour. The mass of the ion increases with the 
vapour pressure, until at a critical pressure the ad- 
sorbed fluid assumes the liquid state, and the aggre- 
gation develops, by the rapid condensation which 
ensues into the large ion of Langevin. 
It is not quite clear how the electrical energy of 
the ions is related to their diameter. The charge is, 
however, not essential to the equilibrium of molecular 
structures such as those just mentioned, and it is not 
unlikely that the conclusions as to the nature of the 
ions, only rendered possible by the happy chance of 
their electrification, may apply with, perhaps, little 
modification to the far more numerous class of un- 
electrified nuclei which exists in ordinary air. 
University of Sydney. JeeaeePorrock. 
1 Details of these observations will be found in two papers published in 
the Philosophical Magazine for April and May, 1915. 
NO. 2376, VOL. 95| 

Similitude in Periodic Motion. 
Ir may interest those of your readers whose atten- 
tion has been direction to periodic motion to know 
that by reducing extremely large and extremely small 
frequencies to a musical base, and employing the 
middle C (256) as a standard the following results 
are obtained :— 
Green light (frequency 5-6 x 10"*) corresponds to the 
note C in the forty-first octave above the standard. 
The colours—orange, green, and _violet—roughly 
correspond to the musical chord ACE. 
Human heart-beats (seventy-five a minute) corre- 
spond to the note E (320) in the eighth octave below 
the standard. 
The earth’s daily rotation corresponds to the note 
G (384) in the twenty-fifth octave below the standard. 
Neptune’s sidereal period almost corresponds with 
E flat (422) in the forty-first octave below the 
standard. HerrBERT CHATLEY. 
Tangshan Engineering College, Tangshan, 
North China, March 17. 
A Simple Direct Method for the Radius Curvature of, 
Spherical Surfaces. 
Tue following device was developed to. obtain the 
radius of curvature of some lens surfaces that were 
too small for the available spherometers. It has 
proved so satisfactory that, not finding it in any of our 

Fic. 1. 
laboratory manuals, it has been thought to be of 
possible interest to others. 
Two brass strips, A and B (Fig. 1), are connected by 
a flatspring,C. To B is soldered a brass ring, D, to 
serve as a bed for the lens, L, the surface of which 
is to be examined. A is pierced with two triangular 
holes, P and Q, as indicated in the sketch, the for- 
ward one having its vertex over the centre of the 
ring. A three-legged optical lever, E, is set with its 
legs on the glass surface, the front leg being as far 
forward as possible in one of the triangular holes, P 
(as shown). The other legs straddle the strip A, one 
being in contact with A. The lever E is not shown 
in the lower sketch. 
If the mirror be lifted from its position in P to a 
similar one in which the front leg is at the vertex 
of Q, it will have been given a linear displacement 
(s) and an angular displacement (@). The former of 
these quantities is the same as the distance between 
the vertices of P and Q. It is a constant of the 
instrument, and may be determined by means of a 
travelling microscope. The angular displacement (6) 
depends on the lens surface, and may be obtained by 
telescope and scale in the usual way. The radius of 
curvature is then written by p=s/@. 
The vertex of Q is placed over the centre of the 
ring, as this is the simplest way to ensure that the 
displacement lies along a great circle of the surface. 
Witt C. Baker. 
Physical Laboratory, Queen’s University, 
Kingston, Ont., April 19. 

