2 
Proceedings of the Royal Society 
Monday , §th December 1880. 
The Right Hon. Lord Moncreiff of Tulliebole, LL.D., Presi- 
dent, occupied the Chair, and opened the Session with an 
Introductory Address on the Rise of the Constitutional 
Idea.* Bishop Cotterill proposed that the Society record 
a vote of thanks to the President, which was agreed to. 
The following Communications were read : — 
1. On the Structure of Eupledella. By Dr F. E. Schtiltze. 
Communicated by Sir Wyville Thomson. 
2. On Equidifferent Multiples of Irrational Quantities. 
By Mr E. Sang. 
Our attention, naturally, is most drawn to the difficult parts of 
an inquiry; the easier steps are apt to be overlooked. Thus, while 
much attention and deep thought have been bestowed on the solu- 
tion of equations, on the computation of logarithms, on the con- 
struction of astronomical canons ; such a simple process as the 
repeated addition of some known quantity, has not been considered 
worthy of the notice of arithmeticians. Yet the tables constructed 
by help of this process are much more numerous, and are as 
important as the others, often indeed serving as their foundation. 
The case when the quantity to be added is expressed accurately 
in numbers, needs no remark; but when that quantity is represented 
only approximately, we have to consider the accumulation of that 
part which is unavoidably left off, and to see that this does not 
lead to an error of so much as the half of unit in the last place 
that is to be retained. 
The obvious and indeed the common plan is to carry the scroll 
calculations to several places beyond what are to be preserved, and 
to rewrite the whole leaving off the surplus figures, only taking care 
to augment the last figure whenever those to be rejected exceed 
5000 Or, if the scroll calculation be put in the compositor’s 
hands, to trust to his care and to that of the reader, in making the 
requisite augmentations. 
* The first part of the President’s Opening Address will he given along with 
the second part. 
