JOUBNAL 
OF THE 
EOTAL MICROSCOPICAL SOCIETY. 
FEBRUARY 1897. 
TRANSACTIONS OF THE SOCIETY. 
I. — A New Calculating Machine. 
By Edwabd M. Nelson, F.R.M.S. 
(l?em? lbth December , 1896.) 
This calculating machine, which has been made by Messrs. Watson, 
was designed by Mr. Tamblyn- Watts, and as it possesses much 
interest I ask leave to bring it before the Society, for the particular 
calculation that is performed by it is specially important to optical 
workers, and hence also to microscopists. 
The equation which this instrument is designed to solve is 
1 
■x 
it not only is the focus of two lenses in contact as well as the position 
of conjugate foci found, but also many other problems are determined. 
To solve then the equation by the ordinary method the reciprocals 
of two figures have to be looked up, these have to be added or 
subtracted from one another, and lastly the reciprocal of the answer 
must be found. Now all these several steps are performed at one 
time by this instrument, which consists, as you will observe, of two 
scales placed at right angles to one another. Each of them is 
divided into 100 similar divisions, and each division is sub- 
divided into 5 smaller divisions. Now as a half of one of these 
small divisions can be easily estimated, these scales may be read 
to three significant figures. The third scale bisects the right angle, 
and is divided into 50 equal parts, each of which is subdivided into 
5 smaller ones. These divisions, however, are not the same as those 
on the other two scales; in fact this third scale is not essentially 
necessary, it is only inserted for convenience, as will be presently 
seen. 
In order to solve the equation by means of this instrument all 
that is required is to stretch a piece of cotton thread from the point 
where (a) (fig. 1) is indicated on A C to the point where ( b ) is 
indicated on BC; the answer is found at the point where the thread 
crosses I) C (see dotted line). The correctness of the result may be 
1897 b 
- ± - ; this is of frequent occurrence in optical formulae, for by 
i 
