114 
. 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14,15 together 
No. of types is = 1 , 4 , 6 , 19 , 27 , 47 , 55 , 78 , 55 , 47 , 27 , 19 , 6 , 4 , 1 
In the first mentioned point of view the like question 
arises, in regard to the sets belonging to the 5 different types 
separately or in combination with each other ; for instance, 
taking only the 6 symbols of the type AB, these may be 
taken 1,2,8, 4, or 5 together, and we have in these cases 
respectively 
1 ,2,3,4,5 
No. of types =1,2,2,2,1 
as is very easily verified ; but if the number of letters A,B... 
be greater, say this is =8, or, instead of letters, miting the 
numbers 1,2,8,4,5, 6,7,8, then the question is that of the 
number of types of combiuation of the 28 duads 12,18, ...78, 
taken 1,2,8,... 27 together, a question presenting itself 
in geometry in regard to the bitangents of a quaidic curve 
{see “Salmons Higher Plane Curves,” Ed. 2 (1878), pp. 222 
et seq.) ; the numbers, so far as they have been obtained, are 
1,2,8, 4 24,2.5,26,27 
No. of types = l,2,5,ll 11,5, 2, 1 
It might be interesting to complete the series ; and more 
generally to determine the number of the types of combina- 
tion of the J n {n-1) duads of n letters. 
“ On Ternary Differential Equations,” by Eobert Eawson, 
Esq., Hon. Member of the Society. 
1. The following observations have been suggested by 
reading the interesting communication, to the ordinary 
meeting of November 28th, 1876, “On Ternary Differential 
Equations,” by Sir James Cockle. 
With a view of comprehending fully the nature and im- 
portance of the step advanced by Sir James Cockle in the 
communication above referred to, it will be necessary to 
state briefly the exact state of our present knowledge of this 
subject, as given by Boole and other eminent writers on 
Differential Equations. 
