ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
Ill 
fundamental plane, is drawn at right angles to the axis. In this plane 
a circle of any given radius k and with its centre on the axis is drawn. 
If rays from a given point be considered before refraction as passing 
through this circle, after refraction they will form on any plane at right 
angles to the axis a curve. This curve the author calls the aberration 
curve for the radius k. 
With respect to this curve the author has demonstrated the following 
properties : — 
It is an algebraic curve of the fourth degree. The coordinates can 
be represented by trigonometrical functions thus : 
V = (fa + V i sin <t>) cos 4> 
z = A 0 + cos </> + A 2 cos 2 4> 
where is an angle in the fundamental plane between the y axis and 
the radius vector to the incident ray ; and the five magnitudes A and ju 
depend on the constants of the system of lenses and on the position of 
the plane of the image. 
The Secret of the Brownian Movement.* — Mr. R. Meade Bache 
gives an account of the experiments which he has made in order to de- 
termine the cause of the Brownian movements. Robert Brown found 
as the result of a series of experiments which he made on finely 
crushed glass, various minerals, and many organic substances, that ex- 
tremely minute particles of solid matter, whether organic or inorganic, 
when suspended in water, exhibit motions resembling in their irregu- 
larity the less rapid motions of some of the simplest animalcules of 
infusions, and states his belief that the motions “neither arose from 
currents in the fluid containing them, nor depended on the intestine 
motion which may be supposed to accompany its evaporation.” More 
recently Herren Wiener, Exner, and Schultze have investigated these 
movements. Wiener concluded from his experiments that they have for 
their basis the movements which, by virtue of their molecular constitu- 
tion, belong to fluids. Exner considered that the liveliness of the 
movement was heightened by light and heat. 
The author, in his experiments, made use of finely divided carmine 
suspended in water. He found that no effect was produced upon the 
movement by the passage of a galvanic current through the liquid, by 
placing the liquid in the lines of force of a permanent magnet, nor by 
the application of heat and cold. Herr Wiener had been inclined to 
attribute the movement to the action of the red wave of light, but the 
author could detect no alteration in the movements when either a violet 
or a red glass was interposed between the source of light and the par- 
ticles. 
By observation for weeks, both with water-immersion lenses and also 
with a 1/15 dry lens, of liquid enclosed in a hermetically sealed 
cell the author could find no alteration in the movement, and concludes 
that evaporation has nothing to do with it. As the result of all his 
experiments the author therefore concludes “ that it is not the particles 
which are moved by their own energy, or moved by any energy directly 
imparted to them from outside sources, but that it is the fluid that moves 
them.” 
* Proc. Amer. Phil. Soc., xxxiii. (1894) pp. 163-77. 
