1889-90.] Lord McLaren on Reflexion- Caustics of Curves. 297 
class. These are of the looped or foliated type. Those of the 6th 
degree are figured in my paper on homogeneous equations. An in- 
finite number of such curves (all traceable) may be formed for a 
given degree (n-p) by augmenting the values of n and^>. 
It is evident that the caustic will not in general be the locus of a 
homogeneous equation. If we take, for example, the solution in 
(Equation 10), p. 288, 
B 
cos 
<srr i)- 
sin 
the condition that the curve shall be a homogeneous equation of the 
second class, or of the form <j> p (x, y ) = <£</#, y), is that the coefficients 
1 
of 0 shall be whole numbers ; that is, 
2m - 1 
and — — A must be 
2m- 1 
integers, in order that the expansions of the two trigonometrical 
quantities may each be a homogeneous expression in sin 0 and 
cos 0, and so be transformable into homogeneous equivalents in x 
and y. 
Synthesis by Means of Electrolysis. — Part III. Synthesis 
of n-Dicarbodecahexanic Acid. By Prof. Crum Brown 
and Dr James Walker. 
(Read June 16, 1890.) 
(Abstract.) 
The synthesis of the diethyl ether of this new acid was effected by 
the electrolysis of a strong aqueous solution of potassium ethyl 
sebate, COOC 2 H 5 (CH 2 ) 8 COOK. This salt was prepared by adding 
the calculated quantity of alcoholic potash to an alcoholic solution 
of diethyl sebate. After some time the potassium ethyl salt began 
to separate out : the whole was then boiled, allowed to cool, and 
filtered. What remained on the filter was dissolved in water ; the 
aqueous solution was extracted twice with ether, and then evapo- 
rated to a concentration suitable for electrolysis (cf. this vol. p. 54). 
When the electric current was passed through the cold solution, 
it rapidly diminished in intensity, and in a few moments ceased to 
flow altogether. This we found to be due to the fact that the pro- 
duct of electrolysis is solid at the ordinary temperature. Heating 
