US1453078A

US1453078A - Instrument for the survey and solution of plane triangles in field work

Info

Publication number: US1453078A
Application number: US494200A
Authority: US
Inventors: William S Moses
Original assignee: Individual
Current assignee: Individual
Priority date: 1921-08-22
Filing date: 1921-08-22
Publication date: 1923-04-24
Anticipated expiration: 1940-04-24

Description

-Apr. 24, 1923.

W. S. MOSES INSTRUMENT FOR THE SURVEY AND SOLUTION OF PLANE TRIANGLES IN FIELD WORK Filed Aug. 22, 1921 7 2 Sheets-Sheet 1 William 5.1505425 I INVENTOR' ATTORNEY 1,453,078 w. s. MOSES Fil ed Aug. 22' 1921 2 Sheets-Sheet 2 INVENTOR wuuam 3. Moses Apr. 24, 1923.

INSTRUMENT FOR THE SURVEY AND SOLUTION PLANE TRIANGLES IN FIELD WORK .Qaa

ATTORNEY Fatented Apr. 24, E923.

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INSTRUMENT FOR THE SURVEY AND SOLUTION D1 BLAKE ERIANGL'ES IN FIELb wean.

Application filed August 22, 1521. Serial No. {St-94,200.

\ To all whom it may concern:

Be it known that I, FVILLEAM lviosns, a citizen of the United States, residing at Onamia, in the county of Mille Laos and State of Minnesota, have invented a new and useful Instrument for the Survey and Solution of Plane Triangles in Field l/Vork, of which the following is a specification.

This invention relates to a new and improved means for finding a numerical ratio triangle for the solution of trigonometric problems comprehended by the art of surveying or for the survey and solution of all plane triangles in field work.

An object of this invention is to provide an instrument for determining the numerical values of the angles and sides of a triangle through a similar triangle whose angles are equal and its sides proportionate to said triangle, the construction of the numerical unit triangle being determined by the positioning of certain elements of the instrument with respect to the similar position of the lines and angles forming the triangle which it is attempted to compute.

The invention will be best understood from a consideration of the following detailed description taken in connection with the accompanying drawing 'lorming part of this specification, with the understanding, however, that the invention is not confined to any strict conformity with the showing in the drawing, but may be changed and modified so long as such changes and modifications mark no material departure from the salient features of the invention as expressed in the appended claims.

In the drawing Fig. 1 is a side elevation of the device.

Fig. 2 is a plan view of the same.

Fig. 3 is a transverse section taken along the line 3-3 of Fig. 2.

Fig. 4- is a transverse section taken along the line 4+4 of Fig. 2.

Figs. 5, 6 and 7 represent diagrammatic views of the various positions of the pivoted arms of the instrument and the unit base line.

In the drawings, 1 designates a tripod for supporting the instrument provided with a table 2 having an upstanding boss 3 which is perforated. I Arotatable disk 4 hasa depending pin 5 inserted in the perforationin the boss, the pin being engaged by one end of a set screw 6 ,to prevent rotation or the pin. r

The rotatable disk 4113s anupstanding per orated' lug 'Twhich is engaged upon op- POSliBSldQS byperiorated ears 8 depending rrom a disk 9. A pin 10 havinga threaded portion passes through the alined perforations 'otthe ears 8 and the lug? and is provided with a wing nut 11 adapted tobe screwed upon the threaded end of the pin to securely hold the disk 9 in adjusted relation with the rotatable disk 4. Mounted centrally uponthe disk 9 is a vp'in'12 secured in the bottom of a base-line bar l An eye-sight 14 and an object sight 15 are 10- cated upon oppositeen'dsof the base bar.

The base-line bar 13 is provided with a central horizontal line 16 placed upon one side of the bar which forms the base of a numerical unit triangle presently to be described and designated more particularly throughout the specification as the radix. A leveling tube 17 is secured in a socket located in the base bar. The central portion of the tube which is designated by the numeral 18, is disposed in av'ertical line passing through the center of the instrument and is adapted to determine the horizontal level of the base-line bar 13 and likewise the radix 16. A handle 19, secured toone end of the bar 13 and at the sighting end or". the instrument, is adapted-to rotate or t-ilt the bar when the wing nut 11 is loosened, for positioning the instrument ina horizontal, oblique or vertical plane.

Firmly secured to a vertical side of the bar 13 are two

protractors

20 and 21. the centers of which fall upon the ends of the radix or base of the unit triangle. A graduated arm 22, designated at the secant arm, is pivotally mounted on the bar 13, at the center 20 otthe protractor 20 and is secured to a right angle operating rod 23 and spaced from the protractor 20 by means of a washer or shim 24.

A telescope 25 is mounted upon the secant arm 22 by means of the straps 26 Another graduated arm 27, designated at the tangent arm, is pivotally mounted on the bar 13 at the center 28 of the protractor 21 and secured to a right angle operating arm 29 which is mounted in bearings in the bar 13. By reason of the washer 24:, the arm 27 may be freely oscillated by the sides of the arm 22, and bar 13. Both operating

arms

23 and 29 are fitted tightly in their bearings in order to insure against ready displacement of the secant and tangent arms after they have been adjusted.

The inner edge 30 of the arm 27, designated as the tangent ratio line, is adapted to form with the edge 31 of the arm 22 and designated as the secant ratio line, an angle B which is called the angle of limitation.

The

lines

30 and 31, together with the base line 16, form a numerical ratio triangle which is capable of being made equi-angular with any triangle, the numerical values of the sides and angles of which it is desired to compute, employing the base or radix 16 as a unit line and which is divided into ten equal parts. The arms 22 and 27 are similarly graduated by means of the same scale, each tenth part being divided into tenths and hundredths, thus graduating a unit decimally into tenths, hundredths and thousandths.

iinother telescope 32 is secured by means of straps 33 to the base bar 13, and it will be seen that when the secant arm 22 has its secant ratio line 31 in alinement with the base or radix, that the

telescopes

25 and 32 will be in the same horizontal plane, and furthermore that when the arm 22 is oscillated upwardly and away from the line 16, the telescope 25 will be oscillated and form an angle with the telescope 32, while the arm 22 passing over the protractor 20 will determine the numerical value of the angle between the

telescopes

25 and 32, and likewise between the radix and the secant ratio line 31. This angle, represented by A, is designated as the secant angle in Figs. 1, 5 and 6. 'lVhen the arm 27 is oscillated above or beneath the radix 16, the tangent ratio line 30 will form, with the radix 16, an angle designated as the tangent angle and represented by C, the numerical value of which may be read upon the protractor 21. The angle B formed by the intersection of the tangent ratio line 31 and the secant ratio line 30, forms the angle of limitation of the triangle and is determined by adding angles A and C and subtracting the sum from 180, or 180(A+C):B.

The secant arm 22 is provided with the eye-sight 3a and the object sight 35.

The telescope 32 is provided with the eye piece 36 while the telescope 25 is provided with eye-piece 37.

The graduated semi-circular part of protractor 21 located above radix line 16 is adapted for reading angles less than 180, that are formed by the radix and the tangent ratio line above the radix, while the graduated semi-circular partof the protractor below the radix is adapted for reading angles formed by the tangent ratio line and the radix when tangent arm 27 is rotated few of them will suffice to demonstrate they application of my device.

If the two angles and a side of a triangle be given, the other angle and the other two sides may be readily determined in the following manner In Fig. 5, let ABC be any triangle, the angles A and C and the side AC being given.

To find angle B and sides AB and BC by means of the ratio triangle ABC of Figs. 1 and 5 formed by base line 16, secant line 31 and tangent line 30, in the following manner I Rotate 22 until the secant angle A equals A of the triangle. Also rotate tangent arm 27 until the tangent angle C equals angle C of Fig. 5.

The angle of limitation B of Fig. 1 is equal to the angle 1 of Fig. 5. Since two angles of a triangle are equal to two angles of another triangle, the third angles are equal respectively to each other.

In the unit or ratio triangle shown in Fig. 1, line 16 being a unit and also proportional to the side AC will bear the following ratio to

lines

30 and 31, respectively, of Fig. 1. Therefore, we will have the following formulas from the triangles ABC of Fig. 1 and 5.

=secant ratio line;

I ig,-= tangent ratio line.

Suppose, for instance, that the known side AC, Fig. 5, is equal to 100 feet, and as the line 16 of the ratio triangle in Fig. 1 is a unit line, and the length of the line 31 between the point 20 and the intersection of the line with the line 30 of the arm 22, designated as AB, is read as 61; (that is 6-1- tenths of unit line 16), line AB of the similar triangle ABC would be equal to 65 feet. The length of the line BC on arm, 2'? between the point 28, and the point where the line 31 cuts the line 30 is read as 4.9, the

anemone line BC will be -49 'hundredths of the unit line 16, andtherefore theside BC ofthe triangle ABC would be equal to 49 feet.

Any triangle may be computed through the numerical ratiotriangle shown in Fig. 1, when certainpa-rtsof the triangle are given, as, when I A side and two angles are given, and when Two sides and-the included angle, or opposite angles are given.

Also when the three sides are given.

For surveying and the solution of triangles in field work, telescope 32 is mounted on the base-line bar 13 having its line of sight parallel with the radix or unit baseline 16.

The telescope 25 is'inounted on the secant arm 22, having its line'of sight parallel with the sec-ant ratio'line 31., The sight line of each telescope being equally spaced respectively from the unit base line 16 and the secant ratio line 31, thereby producing two triangles which have two of their respective sides in coincidence and the third side paralleled. Therefore, their angles are equi-angular and their homologous sides proportional.

In sighting the angles formed by the telescopes, or by the

sights

14 and 15, and the sights 85 and 3 1, the angle formed by the intersection of the respective sight lines is called the angle of sight and this-angle is placed over the point or station popularly known as the sight station and from which the survey is to be made. After the sight station has been located, the first step is to measure a side and locate an angle between that side and some unknown side which is necessary in the solution of tri angles in surveying.

It will be noted that the line of sight through the eye sight 1% and the object sight 15 is so placed on the base line bar 18 that it will be found to beat one side of and parallel with the radix line 16 for determining the position of the radial line of sight. Likewise, the

sights

34 and 35 are so positioned on the secant arm 22 that their line of sight will also be to one side and parallel with the secant ratio line 31 for determin- F ing the position of the arm 22, or more par- "ticularly the secant ratio line 31 or secant angle A.

It may further be stated that the

sights

14, 15 and '34:, 35 may be used jointly with the telescopes, or independently thereof.

Referring to :Fig. 6 of the drawings, D designates the ordinarystaif used in surveying and which is accordingly graduated and supplied with the vanes B and C, the base d of the stafi resting upon the ground.

The instrument is located at the sight station A, while the staff D is located at a point distant from the sight station. The distance between the staff D and the sight station A is a line ofthe triangle A, :B, C, which is required to be determined and which may be accomplished in the following manner The instrument illustrated in Fig. 1 is located at the sight station A, and by means of the leveling instrument 17, the base-line bar 13 is horizontally positioned, and by means of the sights 141- and 15 and telescope 32, the horizontal line AC which is an ex tension of the line AC, is determined. The line AC cuts the staff D as indicated by the vane C. The secant arm 22 is then rotated by means of the arm 23 and by means of the telescopes and the

sights

35, 34, the angle betweenthe secant ratio line 31 and the unit base line 16 is determined, so that an extension of the line 31 will pass through I the highest point of the staff D which is located at B forming the line AB.

The line B C on the staff being known, and which is say 10 feet, it will be easy to findthe length of the line AG by means of the formulas just given which are applicable to the ratio triangle ABC. Lines BC and B C are perpendicular to the horizon tal line AC, and therefore the tangent arm 27 .will be located perpendicularly to the unit base line 16. Since B C is the sight tangent, BC the tangent ratio line, AC-

the unitbaseline and AC the line to be determined, the numerical value of the line AC is found as follows Reading the dimensions from the ratio triangle we have,

AC:1 BO:1/100.

In Fig. 1, let an and Ache the sight lines and BC the third side of the ratio triangle.

Let A be the sight station. From the sight station A, sight the radix line 16 on the base line bar 13 tostation or angle C, the line AC passing through C." Sight the secant line AB to angle B. The angle A is read from protractor 20.

Now measure angle C. Angle B which is the angle of limitation is determined by the position of lines AB and BC. This completes the ratio triangle, making the ratio triangle and the triangle to be determined equi-angular. The following solution is appropriate 2- The side A'C is measured, (Fig. T To find BC and AB' AC times tangent ratio BC AC times secant ratiozA'B Therefore, if AC is known, BC may be readily found by reading the value of the tangent line BC of the ratio triangle or the instrument and that number multiplied by the base AC will give the length of the side BC. AB may be found in the same manner lVhat is claimed is p 1. A surveying instrument comprislng, 1n combination, a base-line bar, graduated arms pivotally mounted at spaced fixed points on the base-line bar, the dlstance between said points representing a unit base of a numerical triangle, the other two sides of the triangle being formed by the adjacent edges of the pivoted arms, means tor rotating the pivoted arms, and telescopes one of which is collimated with the baseline bar and the other with a pivoted arm.

2. A surveying instrument comprising, in combination, a base-line bar, graduated arms pivotally mounted at spaced fixed points on the base-line bar, the distance between said points representmg a unit base of a numerical triangle, the other two sides of the triangle being formed by the adj acent graduated edges of the pivoted arms, means for rotating the pivoted arms, and telescopes collimated with the base-line bar and with one or" the pivoted arms, one of said telescopes adapted to be positioned at an angle to the other telescope. r

3. A surveying instrument comprising, in combination, a base-line bar, graduated arms pivotally mounted at spaced fixed points on the base-line bar and normally rotatable in a vertical or oblique plane, the distance between said points representing a unit base of a triangle, the other two sides of the triangle being formed by the adjacent edges of the pivoted arms, means for rotating the pivoted arms, telescopes collimated with the base-line bar and with one of the pivoted arms, and sight means located on one of the pivoted means and on the base-line bar, the sight means and a telescope forming equal angles with a line passing centrally of the base-line bar at all positions of one of the arms.

4. A surveying instrument comprising, in combination, a base-line bar, graduated arms pivotally mounted at spaced fixed points on the base-line bar and normally rotatable in any plane, the distance between said points representing a unit base of triangle, the other two sides of the triangle being formed by the adjacent edges or the pivoted arms, means for rotating the pivoted arms, and sight means located on one of the pivoted means and on the base-line bar, the lines of sight through said sight means being collimated with two sides of the triangle to determine the sight angles of the triangle.

5. A surveying instrument comprising, in combination, a base-line bar graduated arms pivotally mounted at spaeed fixed points on the base-line bar and normally rotatable in avertical or other plane, the distance between the fixed points reprev senting a unit base of a triangle, the other two sides of the triangle being formed by the adjacent edges of the pivoted arms, telescopes collimated with the base-line bar and with one of the pivoted arms, and sight means located on one of the pivoted means and on the baseline bar, said telescopes and sight means being respectively located normally in the same horizontal planes.

6. A surveying instrument comprising, in combination, a base-line bar graduated arms pivotally mounted at spaced fixed points on the base-line bar and normally rotatable in a vertical plane, the distance between said points representing a unit base of a triangle, the other two sides of the triangle being formed by the adjacent edges ot the pivoted arms, means for rotating the pivoted arms, telescopes collimated with the base-line bar and with one of the pivoted arms, sight means located on one of the pivoted means and on the base-linebar, the sight means being in alinement with the pivotal points of the oscillating arms, and means for alining one edge oi a pivoted with line passing through the sight means and the pivotal points of the arms.

7. In a surveying instrument comprising base bar provided with a base line, means for determining the horizontal position of the line, graduated arms pivotally mounted at spaced fixed points on the line, the distance between said points representing the unit base of a triangle, the other two sides of the triangle being formed by the adjacent edges of the pivoted arms and the length or the sides of the triangle being determined by the intersection of said pivoted arms, one of said arms adapted to be positioned perpendicular to the base line, the other arm forming an acute angle with the base line, and sighting means on the base bar and arranged in a plane passing through the base line.

8. A surveying instrument comprising,

in combination, a base-line bar graduated arms pivotally mounted at spaced fixed points. on the base-line bar, the distance between said points representing a unit base 01"" a numerical triangle, the other tWo sides of the triangle being formed by the adjacent edges 01 the pivoted arms, means for rotating the pivoted arms, and telescopes one of which is collimated with the base' line bar and the other with a pivoted arm, and means for adjustably supporting the instrument.

In testimony, that I claim the foregoing as my own, I have hereto aflixed my signature.

WILLIAM S. MOSES.