Improved Safe Distance Finder for use at Sea.
Year: 1891

page_text: COMPLETE SPECIFICATION.
Improved Safe Distance Finder for use at Sea.
JAMES SMITH care of Messrs. Lilley and Son 10 London Street London E.C.
Master Mariner 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 :-
A sliding scale with five columns, each of which is figured and marked in equally
divided spaces, the figures being so arranged, that by using the slide, it will solve
navigational problems.
This instrument is a sliding scale as shown in the accompanying drawing and
herein referred to. It is made up of two parts viz.: the fixed part marked Å and
the slide marked B.
On the fixed part marked A will be found three columns of spaces containing
figures. These are marked with the abbreviations ANG., HGHT., and ALT.,
meaning respectively Angles in degrees, Heights in feet, and Altitudes in degrees
and minutes.
The angles in the ANG. column are distant from each other in proportion to the
logarithms of their natural cosecants. The column is filled up in the following
manner commencing from the top. 90° is placed in the top space. Its log.
cosecant is 10.000000. Take the log. cosecants of the other angles, subtract 10.
from all indices, and use the first two figures of the decimal. Divide these figures
by 02, (the proportion obviously remains unaltered) and the quotient will be the
number of the space below 90° in which to write the corresponding angle.
73° will be the nearest angle to log. cosecant 10-02. Subtract index 10 and divide
by 0.2; the quotient is 1. 73° is therefore placed in the first space below 90°.
66° will be the nearest angle to log. cosecant 10.04. Subtract index 10° and divide
by 02; the quotient is 2. 66° is therefore placed in the second space below 90°.
The places of the other angles are found in the same manner.
The heights in HGHT. column are distant from each other in proportion to the
logarithms of their natural numbers. The column is filled up in the following
manner commencing from 100 feet, which is written in the 53rd space from the
top, because it is necessary for practical purposes, to have on the scale, heights
ranging from 1100 feet to 36 feet. The log. of 100 is 2.00. Subtract index 2
from all logs also divide by 02, (the proportion obviously remains unaltered) and
the quotient will be the number of the space above 100 feet in which to write the
corresponding height. The log. of 105 is 2-02. Subtract index 2 and divide by
02; the result is 1. Therefore 105 is written in the first space above 100 feet.
The log. of 110 is 2.04. Subtract index 2. and divide by 02. The result is 2.
Therefore 110 is written in the second space above 100 feet. The places of the
other heights above 100 feet are found in the same manner. The places of heights
below 100 feet will be in proportion to those below 1000 feet. 950 is one space
below 1000, therefore 95 will be one space below 100; and so on down to 36 feet.
The altitudes in the ALT. column are distant from each other in proportion to
the logarithms of their natural cotangents. The column may be filled up in the
following manner commencing from the top. By trigonometry 1100 feet, at a
distance of two nautical miles subtends an angle of 5° 10. This altitude is placed
in the top space in a line with the height 1100 feet. The log. cotangent of 5° 10'
is 11-04. Use this as a constant log. The log. cotangent of 4° 56' is 11.06.
Subtract the constant log. 11-04 and divide by 02. The result is 1. Therefore
4° 56' is written in the first space below 5° 10%. The log. cotangent of 4° 43′ is

page_text: 11-08.
The result is 2.
Subtract the constant log. 11-04 and divide by 02.
Therefore 4° 43' is written in the second space below 5° 10' and so on down the
column the places of the other altitudes are found in the same manner.
On the slide marked B on the drawing will be found two columns of spaces
marked with the abbreviations DIST. meaning distances in nautical miles and
tenths. These columns are filled up in the following manner commencing from the
top space in which is written 10 miles. The distances marked in these columns
are distant from each other in proportion to the logs. of their natural numbers.
The log. of 11 is 04 which divided by 02 is 2. Therefore 1.1 is written in the
second space below 1.0. The log. of 1-2 is 08 which divided by 02 is 4. There-
fore 1-2 is written in the fourth space below 1-0. The places of the other distances
in these columns are found in the same manner.
Having shown how the columns are filled in, it is now proposed to show how
the following problems can be solved by the scale.
Problem 1. From the bridge of a steamer a 20-mile light was sighted 6 degrees
on the bow, how far off will it be when abeam?
By trigonometry the problem may be stated thus: as cosecant of 6º, is to
20 miles; so is cosecant of 90°, to B C 2.1 miles, which is the distance required.
By the scale, set 20 in the DIST. column to 6 in the ANG. column. Opposite
to 90 in the ANG. column will be found 2-1 in the DIST. column.
Problem 2. A lighthouse bore 35 degrees on the bow, and after running 5 miles
it had changed its bearing 27 degrees; how far off is the lighthouse?
20
By trigonometry it may be stated thus: as cosecant of 35°, is to 5 miles; so is;
cosecant 27°, to BC 6.3 miles the distance required.
By the scale, set 5 in the DIST. column to 35° in the ANG. column. Opposite
to 27° in the ANG. column will be found 6-3 in the DIST. column.
Problem 3. The altitude of a lighthouse 345 feet high, was observed to be 0° 45'
by the sextant; what is its distance off?
By the scale, set 2 miles in the DIST. column to 345 in the HGHT. column.
Opposite to 0.45 in the ALT. column will be found 4.4 miles in the DIST. column,
which is the distance required.
5° 10' being the angle which 1100 feet subtends at 2 miles, therefore 345 feet
would subtend 1° 38' because the heights are arranged in the columns in proportion
to their logarithms and the altitudes in proportion to their log. cotangents. If
345 feet subtend 1° 38′ at 2 miles, it would subtend 0° 45' at 4.4 miles, because the
distances are arranged in proportion to their logarithms.

page_text: Having now particularly described and ascertained the nature of my said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is :-
That the figuring of this scale is arranged in a novel and improved manner to
show the distance a ship is from an object on shore, or the distance she will pass
from it by one setting of the slide when the usual data are given.
Dated this 16th day of July 1891.
JAMES SMITH.