IMPROVEMENTS IN MEASURING TAPES OR SCALES to be as follows:
Year: 1885

page_text: I, WILLIAM ROBERT LAKE, of the firm of Haseltine, Lake, & Co, Patent Agents,
Southampton Buildings, in the County of Middlesex do hereby declare the nature
of my invention for "IMPROVEMENTS IN MEASURING TAPES OR SCALES
to be as
follows:-
"
The object of this invention is to obviate the use of tables of logarithms in
calculations from measured lengths, especially in calculating the cubical contents of
receptacles in distilleries, breweries, and manufactories, and also in computing the
weight of animals.
The invention consists in providing upon a measuring tape or scale in addition to
the usual divisions into meters, centimeters and millimeters or other indications,
other divisions which show the decimals of the common logarithms corresponding
to the units of length contained in the measured distance.
If, accordingly, a given distance is to be measured with this scale, the length of
the same is obtained in units of length, and simultaneously the decimal of the
logarithm corresponding to the number of units is obtained so that it is merely
necessary to add to the said decimal the known integer in order to obtain the real
logarithm.
In calculation of contents and weights for the purposes stated above, the
decimeter will generally be taken as the unit, because the volume is then directly
obtained in liters and the weight in kilogramms.
For this reason at the point marked 1 decimeter on the length measure will be 0
on the logarithmic decimal division; at 2 decimeters 30, and so on. At 10 deci-
meters the decimal division indicates 00; at 20 decimeters 301, and so on, which
indications can of course, be preceded by the corresponding integer, the logarithmic
decimal being independent of the value of the digits.
For the sake of greater accuracy it is advisable to show in the large intervals
the logarithmic decimals to 3 or 4 places.
If the calculation has been made and the logarithm of the required number found,
it is only necessary to find on the long measure division the value corresponding
Prine C71

page_text: to the logarithmic decimal, which value gives immediately the number, regard
being had to the integer of the logarithm found.
In order to explain the use of the scale, suppose that the cubical contents of
a pan are to be determined. If the interior diameter d of the same be taken at
42 decimeters and the height h at 8.3 decimeters, the cubical contents are found
according to the formula v = which when directly calculated, gives 11498 liters.
"
4
dhn
When the improved measure is used, at the division line 42 of the long measure
division, 6232 is found as the logarithmic decimal; at 8.3 the logarithmic decimal
found is 9191; and as the logarithm of = 0.8951-1 must be regarded as known,
πT
4
division, 6232 18 found as the logarithmic decimal; at 8-3 the logarithmic decimal
found is 9191; and as the logarithm of 4 = 0·8951-1 must be regarded as known,
the result is
log v = 2 log. 42
3.2464
+
log. 8.3
0.9191
+
log
0.8951-1
4
4.0606
The logarithmic decimal division shows that the decimal 0600 corresponds to the
number 115, therefore the cubical contents of the pan are equal to 11500 liters,
almost exactly agreeing with the result obtained by direct calculation.
If it is required to attain for small measures a greater accuracy, the logarithmic
decimal is sought for, the tenfold number of the measured length thereby obtaining
one place more.
It is, of course, immaterial whether, in practice, the two divisions are upon one
side of the measuring tape or scale or upon different sides of it; the latter
arrangement, however, renders the reading difficult.
In case the lengths are not measured in decimeters but in meters, the logarithmic
decimals read off retain their value and only the integer is less by 1 for the number
in meters than for the number in decimeters, and greater by 1 when the lengthis are
measured in centimeters.
Dated this 20th dox of Tonuam 100
HASELTINE, LAKE & Co.,
For the Applicant.

page_text: Improvements in Measuring Tapes or Scales.
I, WILLIAM ROBERT LAKE, of the firm of Haseltine, Lake, and Co Patent Agents,
Southampton Buildings in the County of Middlesex do hereby declare the naturė
of my invention for "IMPROVEMENTS IN MEASURING TAPES OR SCALES". and in
what manner the same is to be performed, to be particularly described and
ascertained in and by the following statement:-
The object of this invention is to render unnecessary the use of tables of
logarithms in calculations from measured lengths, especially in calculating the
cubical contents of receptacles in distilleries, breweries, and manufactories, and also
in computing the weight of animals.
The said invention consists in making upon the measuring tape or scale in
addition to the usual divisions of meters, centimeters and millimeters or other
indications, other divisions which show the decimals of the common logarithms
corresponding with the units of length contained in the measured distance.
If, accordingly, a given distance is to be measured with this scale, the length of
the same, is obtained in units of length and simultaneously the decimal of the
logarithm corresponding to the number of units is obtained so that it is merely
necessary to add to the said decimal the known integer in order to obtain the real
logarithm.
In calculations of contents and weights for the purposes stated above, the
decimeter is generally taken as the unit of length because the volume is then
directly obtained in litres and the weight in kilogramms.
For this reason at the point marked 1 decimeter on the length measure will be 0
on the largarithmic decimal division; at 2 decimeters 30, and so on. At 10 deci-
meters the decimal division indicates 00; at 20 decimeters 301, and so on, which
indications can, of course, be preceded by the corresponding integer, the logarithmic
decimal being independent of its value.
For the sake of great accuracy it is advisable to show in the large intervals the
logarithmic decimals to 3 or 4 places.
If the calculation has been made and the logarithm of the required number
found, it is only necessary to find on the long measure scale the value corresponding
to the logarithmic decimal, which value immediately gives the number, regard being
had to the integer of the logarithm found.
The accompanying drawing shows a scale of the class described; a is the long
measure scale, and b the logarithmic decimal scale.
In order to explain the use of the scale, suppose that the cubical contents of
a pan are to be determined. If the interior diameter d of the same be taken at
42 decimeters and the height h at 83 decimeters, the cubical contents are found
according to the formula v =
h =
4
'
which when directly calculated gives 11498 litres.

page_text: When the improved measure is used, at the division line 42 of the long measure
scale 6232 is found as the logarithmic decimal; at 83 the logarithmic decimal
found is 9191; and as the logarithm of * = 0.8951-1 must be regarded as known,
The logarithmic decimal scale shows that the decimal 0606 corresponds to the
number 115, therefore the cubical contents of the pan are equal to 11500 litres,
almost exactly agreeing with the result obtained by direct calculation.
The method of calculating the weight of cattle by means of the improved scale
is as follows:
Suppose an ox to be standing on level ground, and holding its head straight.
It is first measured around the body behind the forelegs, and next from the front of
the shoulder to the extremity of the rump, near the tail. If the first measurement
is 32-3 and the second 22.5 on the scale b then the weight of the ox will be
approximately 743 Kilogramms, because the sum of the numbers 32.3, 32.3 and 22-5
is 87.1 and on examining the tape the number 743 will be found on the scale a
next to the number 87.1 on the scale b. This estimate is good for a well fed ox,
for a lean ox the number 87.1 ought to be reduced by 1, so that in such case it
should be 86.1. If the ox is large bellied the number should be increased by 1, so
that it would be 88.1, the corresponding weight indicated on the scale a being 760.
If it is required to attain for small measures a greater accuracy, the logarithmic
decimal is sought for the tenfold number of the measured length, thereby obtaining
one place more.
It is, of course, indifferent whether in practice the two scales are upon one side
of the measuring tape or scale or upon different sides of it, the latter arrangement,
however, renders the reading difficult.
In case the lengths are not measured in decimeters but in meters, the logarithmic
decimals read off retain their value and only the integer is less by 1 for the the
number in metres than for the number in decimeters, and greater by 1 when
the lengths are measured in centimetres.
Having now particularly described and ascertained the nature of the said
invention, and in what manner the same is to be performed, as communicated to
me by my foreign Correspondent I declare that what I claim is
Measuring tapes or scales in which a logarithmic decimal scale is arranged beside
the metric long measure scale in such a manner that the number read off from the
decimal scale and corresponding to a fixed point of the long measure scale, indicates
the decimal of the logarithm for the number of metric units of length which are
comprised between nought of the long measure scale and the given point, it being
of no importance whether the long measure scale and logarithmic decimal scale are
arranged upon the same or upon different surfaces of the measuring scale.
Dated this 20th day of October 1885
HASELTINE, LAKE & Co.,
For the Applicant.