BY J. GC. BRUNNICH, F.1.C. 4] 
ever, on account of their length, become unwieldy. The 
lengthening of the scale may also be achieved by dividing 
the seale into two halves, with the first half of the scale 
on the upper part of the rule, and the second half on the 
lower part, and to make the instrument with two slides, 
as in the slide rule invented by E. Peraux, which although 
only 25 centimeter long, corresponds in accuracy with a 
rule 1 metre long, and gives results accurate to at least 
four figures (Plate I11., B.). Of still greater accuracy 1s 
the cylindrical slide rule of Prof. George Fuller, in which a 
logarithmitic scale over 40 feet long, is wound round a 
movable cylinder, and with which calculation with an 
approximation of 1+10,000 are obtained. On this imstru- 
ment we have only one scale of numbers and the operations 
are based on the same principle as originally employed by 
Gunter, by taking the first factor from the scale with the 
aid of two indices, and then moving the scale and reading 
off the result on the scale with one or the other of the indices. 
This shderule gives by far the most accurate results, but 
has the disadvantage that if several operations with a 
constant factor have to be made, the scale has to be shifted 
every time. This drawback is avoided in the horizontal 
cylindrical slide rule by Thacher, which has a scale of 30 
feet length, divided into 40 parts of equal length arranged 
parallel on a moving cylindrical slide, which is surrounded 
by a framework of triangular bars carrying similar scale. 
With this rule nearly the same approximation as in Fuller’s 
rule is obtained, but with the great advantage that a series 
of multiplications or divisions in which one of the factors 
is constant can be made with only one setting of the slide. 
The bars further carry a scale of squares which gives a 
much greater range of possible calculations. Futhermore 
the shde has two series of scales running parallel so that 
the results may be generally obtained at two different 
places, and unnecessary shifting and drawing out of the 
slide is avoided. Both Fuller’s and Thacher’s rule are 
only for office use. 
Quite of late years the ordinary Mannheim rule has 
been greatly improved by Prof. A. Beghin, who introduced 
his new slide rule (Plate III., D and E.) towards the end 
of 1898, and which now almost entirely replaces the older 
