Improvements in Logarithmic Calculating Instruments.
Year: 1899

page_text: Date of Application, 23th Aug., 1899-Accepted, 4th Nov., 1899
COMPLETE SPECIFICATION.
Improvements in Logarithmic Calculating Instruments.
I, ROBERT HENRY SMITH, Civil and Mechanical Engineer, of Ellerslie, Bruns-
wick Road, Sutton, in the County of Surrey, do hereby declare the nature of this
invention and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement: -
This instrument consists of three parts each in the form of a tube, but the outer
tube being so short as to be better called a ring. These tubes are arranged one
inside the other and sliding on each other telescopically. The three tubes are all
of the same material and are preferably made of thin metal.
The inner tube is the longest of the three. On it is placed spirally a logarith-
mic scale, that is, a scale of lengths proportional to the logarithms of whole and
fractional numbers from one to ten. It is therefore termed the scale tube.
Throughout the central part of its length upon which the scale is placed, it is made
of slightly less outside diameter than at either end. Thus the second tube which
fits these ends does not rub upon the scale so as to abrade or dirty its surface.
The second tube is called the holder tube because in using the instrument this
tube is held in one hand continuously throughout any series of operations, the
manipulations being entirely performed by the other hand. This second tube
is shorter than the inner one so that at all times there is sufficient length of the
inner or scale tube projecting beyond one or both ends of the holder tube to
enable one to grasp the scale tube in order to slide it inside the holder tube. Each
tube being considerably longer than the one outside it also ensures that the one
may be slid upon the other through a long range and with an easy fit between
the two without rock shake or side-play sufficient to cause inaccuracy in the
settings or readings.
The second or holder tube has cut in it two opposite slots throughout a central
length somewhat longer than that occupied by the spiral logarithmic scale. The
parts not cut away by these slots form two opposite bars rigidly connecting the
two uncut ends of the tube. At the four ends of the two edges of one of these
bars are formed four small rectangular projections whose projecting corners are
used as four reading indices or horns. These reading indices are thus placed
upon and attached to the tube which carries them in a very rigid manner without
overhanging or springy parts so that the pairs of indices cannot be sprung or
bent out of their correct relative positions and so that no adjusting device for
drawing them from time to time into true relative position is necessary. This
arrangement of tubes without overhanging or projecting parts also obviates the
risk of such parts catching each other or the dress or fingers of the operator
when being moved past each other in the process of manipulation, whereby they
are, in other similar instruments, frequently bent out of shape.
The
The breadth of each bar is made about twenty per cent of the circumference of
the tube, leaving the breadth of each slot about thirty per cent of the same.
circumferential distance between each pair of reading horns is intermediate
between these two dimensions being made about twenty-six per cent of the whole
circumference. Each pair of horns at the two ends of one edge have their read-
ing corners placed exactly on the same line parallel to the axis of the tube and at
a distance apart exactly equal to the axial length of the spiral logarithmic scale

page_text: so that when one horn is placed at the beginning of the scale marked 100 the
other horn is precisely at its end marked 1000.
The pair of horns fashioned on the right hand edge of the bar have their read-
ing corners placed precisely 26 per cent of the circumference distant from the right
hand edge of the slot and this edge of the slot is cut with exactitude straight
and parallel to the axis of the tube. With the exception of the parts here par-
ticularly mentioned exactitude in the cutting of the various edges and corners
of the instrument is of no importance whatever for accurate calculation. It is
important that the holder tube should slide upon the scale tube without shake
and that both these tubes should be accurately straight.
The third or outer ring tube is of short length and slides with an easy fit upon
the holder tube. On its two edges there are a top and a bottom reading projection.
These two are alternative indices for setting and reading but there is no necessary
particular relation between their positions nor any necessary particular length
between them.
The three tubes being made of the same material, preferably of thin metal,
change of temperature or the like influence produces equal expansion or contrac-
tion in all three so that such change does not produce either slackness or tight-
ness in the fit of one upon the other tube with consequent easy sliding without
shake or side-play at all times. This result is obtained without the use of felt
or other soft packing between the tubes such as has been required in other similar
instruments.
The instrument being composed of these three parts is called the Ring-Holder
Scale Logarithmic Calculator, or more shortly the R-H-S log rule, this name
being a mnemonic materially assisting the recollection of the correct manipula-
tion of the instrument.
As at present made the outside diameter of the instrument being only about
seven eights of an inch and its length only about nine inches, it is very easily
carried in the pocket, and draughtsmen may use it as a case in which to hold
drawing pencils or like instruments.
Yet the spiral scale is about fifty inches long and it is thus capable of giving
in calculation as high a grade of accuracy as a straight logarithmic slide rule of
double this length. A straight slide rule of this length costs many times as
much as does this construction; is extremely clumsy to use, and is not conveni-
ently portable. The fifty inch scale is sub-divided by lines to three-place figures
and by ordinary and easy eye-estimation of the fractional values of the divisions,
four-figure results are read from it. This degree of accuracy corresponds with
the limits of exactitude required in the great bulk of engineering, architectural
and industrial calculations. But I reserve the right to manufacture the instru-
ment in any larger or smaller size than here stated that may be found convenient
Fig. 1 shews the scale tube apart from the holder and ring tubes. The beginning
of the spiral scale is marked 100 and the end is marked 1000. The intermediate
numbers are marked at suitable points all along the length. Around the top of
the central part of smaller diameter is marked a circular scale of 50 equal parts.
The spiral scale is formed in 20 complete spiral turns. The number of complete
turns from the beginning of the scale to any point of it may be counted by means
of a straight scale of 20 equal parts engraved on the right hand edge of one of
the slots in the holder tube; this scale being numbered however, from 0 up to 10.
The fraction of one complete spiral turn is measured by help of the 50-part
circular scale. By combining the two readings from the straight and circular
scales the length of any part of the spiral scale from its beginning may be
measured in thousandth parts of the whole length from beginning to end. This
reading forms the 3-figure mantissa of the logarithm of the corresponding num-
ber; and by this measurement of the logarithm exponential calculations, such as
compound interest and similar sums in geometrical progression with any positive
whole or fractional powers or roots, may be easily performed. These scales are
not used for ordinary multiplication or division. To take this reading of the

page_text: mantissa of the logarithm the lower right hand horn h of the holder tube is placed
upon the spiral scale at the number whose logarithm is desired, and the logarithm
is read off by the right hand edge of the slot in the holder by help of the straight
scale combined with the uniform circular scale. The zero of the top circular
scale is displaced circumferentially from the beginning of the spiral scale by
twenty-six per cent of the circumference, namely the same distance as from the
horn to the right hand edge of the slot.
Both spiral scale and top circular scale are printed upon paper which is cemented
upon the metal tube, and afterwards covered with special hard and transparent
varnish.,
Figs. 2, 3 and 4 shew the holder and ring together without the scale tube.
Fig. 2 is a view facing the slot containing the right hand horns and the straight
holder scale. Fig. 3 is a view facing the bar which carries no horns, but on
which is marked the above scale. In these figures the two indices on the ring R
are marked r and r¹. Fig. 4 is a view facing the other bar carrying the four
horns hh. In Fig. 4 the ring R is removed. Any calculation performed by
this instrument involves three settings and a final reading of the result. The
three settings correspond to the three factors in M, M, where M₁M, are two
D₂
multipliers and D, is a devisor, or, otherwise stated, correspond to the three given
terms of a sum in proportion. The settings are performed in the order M, D₂ M3.
Firstly, holding the holder in the left hand, the scale tube is slid inside it so as
to bring the number M, as printed on the spiral scale under one of the horns of
the holder. Next the ring is grasped in the right hand and slid on the holder
so as to make one of its horns read D, on the scale. Thirdly, the scale tube is
again taken hold of by the right hand and slid inside the holder until the same
ring horn reads M, on the scale. Lastly the result Q = M₁ M3 is read off the
D₂
scale at the same holder horn as was used in the first operation.
:
If a simple multiplication M, M is to be performed, then in the second setting
the ring horn is placed at either 100 or 1000 on the scale since D₂ = 1.
If a simple division M,÷D, is to be performed, then in the third setting the
scale is set so as to bring 100 or 1000 under the ring horn since in this case M, = 1
Thus the sliding operations are always performed in the order scale tube, ring,
scale tube, or S.R.S; while the settings or readings on S are made by help of the
indices or horns in the order holder, ring, ring, holder or HRR H.
At the end of these operations the holder horn used in the first setting may be
situated beyond the limits of the spiral scale; if so, the reading of the result is
to be taken by the other holder horn in the same axial line; that is, i instead
of h or vice versa, or i¹ instead of h¹ or vice versa. If the scale were extended
these two horns would in every position read the same series of figures, the one
representing a number ten times greater than the other.
If when the first setting to M, is made by one of the right hand holder horns hi,
this setting causes the place of the number D, on the scale S to be hidden by
either bar of the holder, then the first setting is to be shifted to make one of the
left hand holder horns h¹¹ read M₁. This shifting involves a rotation of the scale
tube in the holder tube, equal to the angle between h and i and as this angle
is greater than that covered by the bar but less than that of the slot, the read-
ing M, must now necessarily be visible. In other instruments of this class there
is always a certain series of results which cannot be worked accurately because of
necessary readings on the scale being hidden by parts of the instrument. 'In
my invention there are no such cases.
The alternative indices on the ring R are provided to avoid ever having the
holder indices covered and hidden by the ring. In the second setting if, when the
ring index r is set upon D, the body of the ring covers either set of holder horns,
then the index r must be used instead of r when the holder horns will be neces-

page_text: sarily uncovered. This rule amounts to the direction that the ring is never to be
slid on the holder so that either r or r¹ goes beyond the limits h h¹ or i¹.
Having now particularly described and ascertained the nature of my said
invention and in what manner the same is to be performed, I declare that what
I claim is:-
1. In a cylindric logarithmic calculating instrument with a spiral scale, the
placing of the two needful sets of indices directly on the bodies of tubes sliding
outside the tube carrying the spiral logarithmic scale, so that these indices are
held rigidly in fixed positions in these tubes without any overhanging or slender
and springy parts, the errors due to the springing of the parts supporting the in-
dices being therefore eliminated; and so that in the sliding motions necessary in
the manipulation of the instrument the one set of indices passes the other freely
without possibility of catching these others or the fingers or dress of the manipu-
lator and thereby becoming strained out of true relative position.
2. In the nest of three tubes referred to in Claim (1) making each tube con-
siderably longer than that next outside it the parts of the instrument being thus
readily made so as to slide easily to an accurate fit one on the other without rock,
shake, or side play sufficient to cause inaccuracy in the settings or readings.
3. The making of the three tubes all of the same material and preferably of one
and the same metal, whereby they may be made to fit each other accurately while
sliding on each other easily without packing of any soft material between them
and whereby, the three tubes expanding and contracting in the same ratio with
change of temperature or the like influence they maintain their good fit in spite
of such expansions and contractions.
4. The placing of the primary indices on the edges of two opposite slots in a
metal tube outside the tube carrying the scale so that these slots permit the
manipulator to see all the parts of the scale needed at any one time during the
manipulation while at the same time the two bars separating the slots hold to-
gether the two ends of the tube in a substantial and rigid manner, thereby pre-
venting the indices carried by the tube being sprung out of their true relative
positions and obviating the necessity of any adjusting device to draw these points
from time to time into correct relative position.
5. The proportioning of the circumferential widths of the slots and the bars
referred to in Claim (4) and of the circumferential distance between the pairs of
indices so that, while leaving the bars wide and therefore stiff all possibility of
parts of the scale required to be seen being hidden by the bars or other parts of
the instrument is eliminated, each slot having a width more than a quarter of the
circumference, each bar a width less than a quarter of the circumference and each
pair of indices being placed apart a distance intermediate between the widths
of the slot and of the bar in the manner substantially hereinbefore described and
illustrated.
6. In cylindric logarithmic calculating instruments consisting of tubes sliding
one on the other and the tube carrying the logarithmic scale not being the outer
tube, the making of that part of the scale tube occupied by the scale of slightly
less diameter than its other parts so that the outer tube sliding upon these larger
parts and fitting them, may not rub, abrade or dirty the scale surface.
7. The combination of the parts substantially as hereinbefore described and
illustrated so as to form a logarithmic calculating instrument reading with accu-
racy upon an open scale to three and four figures and yet so compact that it is
readily portable in the coat pocket.
Dated this Twenty fifth day of & novat 1800