US764074A - Calculator. - Google Patents

Description

No. 764,074. I 'PATBNTED JULY 5, 1904.

A. H. POI-LEN & M. BARR.

CALCULATOR.

APPLICATION FILED we. a, 1902.

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No. 764,074. PATENTED JULY 5, 1904. A. H. POLLEN & M. BARR.

CALCULATOR.

APPLIOATION FILED AUG. 8, 1902.

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i ji/fffiivwg UNITED STATES Patented July 5,1904.

PATENT OFFICE.

ARTHUR H. POLLEN AND MARK BARR, OF LONDON, ENGLAND; SAID BARR ASSIGNOR TO THE LINOTYPE COMPANY, LIMITED, OF LON- DON, ENGLAND.

CALCULATOR.

SPECIFICATION forming part of Letters Patent No. 764,074, dated July 5, 1904.

Application filed August 8, 1902.

To all whom it may concern.-

4 Be it known that we, ARTHUR HUNGERFORD POLLEN, of 69 Elm Park Gardens, Kensing-' ton, and MARK BARR, of 25 Kensington Court Gardens, Kensington, London, England, have invented a certain new and useful Calculator, of which the following is a true, clear, and full description, such as will enable others skilled in the art to which it appertains to make and use the same.

Thepresent invention relates to improved apparatus for the mechanical determination of the linear elements of triangles, and the principle on which it is based will be best understood from the following formulae and equations and from the accompanying diagramsanddrawings, which are to be taken as S to the object E sighted for, and A and B are respectively the complementary and internal angles which the lines of sight form with the base-line. Now

1. It is well known that as in any other triangle S is to R as sin. (AB) is to sin. B, or

S sin. (AB) R sin. B. from which we have S sin. B (a) Now if the length of S is short in comparison with the lengths of the other two sides of the triangle then the length of R can be taken as the' nicely-approximate distance of the apex E from all points along the line S. We therefore express thedistance R in terms of the base-line S and the sines of the angles of sight from the respective ends of the base-line.

2. Referring to Fig. 2, if we draw from 0 two lines 0 P 0Q, at any convenient angle (not Serial No. 118,938. (No model.)

Hence if for convenience we call the distance 0 GZU and make 0 (0 equal to some number of times-say Vtimes-the sine of the difference of the anglesA and B, or, to wit, 0 a V sin. (AB), and if we make 0 6 equal to some number of timessay T times the sine of the angle B, or, to wit, 0 b T sin. B, then we can rewrite the equation given for L (or 0 (Z) as follows:

U T sin. B i L B) (1) Now-remembering that S sin. B R sin. (AB) or as differently expressed R sin. B s sin. (AB) (2) we see that the results (1) and (2) combined give us the following equation:

L, as before explained, being the distance 0 (Z i found by constructing the diagram Fig.2 and R the range indicated in Fig. 1.

From the equation (3) we have That is to say, we find that the range R is equal to L multiplied by the quantity Y and when we decide upon certain convenient numerical values for V, S, U, and T, as hereina fter exemplified, we know the numerical value of the quantity Whence L is proformulaand always state the same relation-- ships among the individual quantities contained in the formula (4), and though each may have a value of unity their respective values and functions are alike constant, and these constants must always be embodied in every mechanical development of the invention.

The result of the line of reasoning detailed above is the basis of the present invention, or, in other words, the improved apparatus is the mechanical embodiment of the fourth equation. In carrying the invention into effect any'mechanical linkage capable of dealing with that equation may be employed. Thus in the arrangement represented in Figs. 4:, 5, and 6 of the accompanying drawings the linkage is the equivalent of the geometric diagram Fig. 2, inasmuch as the arms thereof may be set in such positions as will solve the proposition illustrated by Fig. 2. To facilitate the identification of the various parts of. the apparatus shown in Figs. 4, 5, and 6 with the corresponding parts of the diagram shown in Fig. 2 the said parts are,wherever possible, marked with the same reference-letters in all of these figures. In this linkage when lengths are given proportional to the sines of the angles as described above these lengths are set ofi along a linecorrcsponding to 0 Q and read the range along a line corresponding to 0 P; but it is necessary now to show by what means the sines of the angles mentioned may be directly obtained without reference to trigonometrical tables.

The sine of an angle being the ratio between the perpendicular and hypotenuse of a right-angled triangle, when the given angle is included between the base and the hypotenuse, as shown inFig; 3, we have Q T sin. B,

where T is the arm length and is supposed to with reference to Fig. 2. The pivot 0, being have opened out the angle B from the base.

f Now suppose we describe a-circle 6, having the radius T, and then draw a straight line 0.1 at one side equal in length to one-half the circumference of that circle and suppose the line '0 P and the half-circumference to be divided into corresponding numbers of parts. Then if we erect heights, such as 2, above the straight line 0 P corresponding to the heights, such as 2, from the circle diameter from the corresponding divisions and draw a line connecting the ends of all these heights we produce a curve, as shown at the right of Fig. 3. This curve can be said to form a cam, and if moved backward distances from 0 toward P it will raise a point above the line 0 P to heights equal to T times the sines of the corresponding angles made by the radius T with the diameter f.

, of the tube 1.

If a micrometer-screw be used for I operating such a cam, the device may he graduated in terms of fine angular measurement, and thereby a movement can be produced which is proportional to the sine of any angular measurement so made, and it is in this way that mechanical movements are obtained in the above-named linkage which are proportional (0 a and 0 b), to the sines of the angles obtained in the manner described. In this linkage, as represented more particularly in Fig. 5, the points a, I), c, and d of Fig. 2

arerepresented by pivots bearing the same reference-letters, on which two links 1 and 2 (representing, respectively, the two lines a 0 and I) d) are free to turn, and the lines 0 Q 0 P are represented byguides or trammels 3 and- 4:, along which the pivots a, b, 0, and (Z are capable of receiving their only motion. The two pivots a b and the pivot c are mounted so as to be finely adjustable along the guides or trammels 3 (or 0 Q) and 4, (oi- 0 P,)

"convenient way of securing this result is, as

shown in Figs. 5and 6, to provide the pivots -64 and I) on two tubes '1 and 2, respectively, through which the links 1 and 2 (directly pivoted on c and d, respectively) are free to slide. axially, and by parallel links 8 and 9 connect the tube 2 with a sleeve or slide 1',

capable of sliding in the directionv of the axis The pivots a and c are adjustable directly by their respective micrometerscrews 5 and 7; but the pivot I) is adjustable through the abovenamed sine-cam 10, which is itself adjusted by the micrometer-screw 6.

Now consider the operation of the linkage fixed in a position determinate upon the length of the base, (S of Fig. 1,) if we move the pivot a so as to produce the distance 0 a along 3 (or 0 Q) it follows that the link 1 (or ac) will take the position shown, the link 2 (or b d) re' maining parallel with l, (or a 0,) though in a position which is undetermined, because the pivot d is free to slide along 4 (or 0 P) and because the length 0 I) has not been determined.

If now we move the pivot I; so as -'to produce the distance 0 6 along 3, (or 0 Q,) the link b d (always parallel with a 0) will take the position shown in Figs. 2 and 5. We then have a mechanically-produced diagram corresponding to Fig. 2, in which Tt'is to be remembered that '0 is any fixed length chosen at will, equal, say, to U, Fig. 2;

I also, that it is 0 a which. is to be set to a length of Vtimes the sine of (A-B), while 0 Z) is to be set to T times the sine of B, and that it has furtherbeen shown how a cam-block 10 and micrometer-screw 6 can produce the length T sin. B when B is'known; preferably, two scales 11 and 12 are provided for reading adjustments of the micrometerscrew 6, oneviz., the fixed scale 11con jointly with the index 11, which is fixedto the slide block or nut 13, carrying the cam 10, serving for reading the adjustments in terms of grades-that is to say, four-hundredth parts of a circumference-and the otherviz., the scale 12 on the edge of the disk 14, which is adjustably fixed on the micrometer-screw 6 serving, conjointly withan index 12, fixed to the scale 11, for reading'the adjustments down to one-thousandth grade, (about three and one-half seconds are.) The distance 0 a, which is to be set to V times the sine of (AB), is regulated not by a sine-cam, but simply by a micrometer-screw 5, because the: angles .set for are so exceedingly small that within a nice approximation their sines are proportional to them;

Indesigning the linkage taken of-the limits of the motions of a and b. We know that the lengths 0 a and 0 b are respectively V sin. (AB)-and T sin. B, and having decided what shall be the maximum and minimum values for B and for (AB) we decide upon such values for V and T as will give rational dimensions for the linkage. Those values should be such as to bring. the lengths 0 a and 0 b to the same order of magnitude as the lengths of Uand Lthat is to say, no

length in thediagram Fig. 2 orin the-representation Fig.5 of the mechanical embodiment ofv this diagram should be very'long or very short as compared with the other lengths in that diagram. .Thu's'it is found that 8'is a good value for T and, that 333.33 is a good value for V. Now a sine-curve plotted from the expression .2: 8 sin. B (see Fig; 3) be tween the limits fifty grades and one hundred grades?. 6., forty-five degrees. and ninety degreesgives a cam which must be-moved forward one grade at each rotation of its adjusting-screw; but as the maximum value for (AB) is only aboutOA: gradez'.e. thirty-sixminutesand a multiplier V, equal to 333.3, is required it follows that only a small proportion of a large sine-curve'would be used for In the linkage,-

account is first range, which is taken 'guished from a sine-cam, is used to move the pivot a proportional distances, for the reading of which latter preferably two scales 15 and 16 are provided, as in the arrangementfor reading adjustments in the length of 0 b.

The scale 16 is depicted on the edge of a disk 18, adjustably fixed on the micrometer-screw 5, and conjointly with a relatively fixed index 16 gives readings down to one-thousandth grade. Hence when given the angles B and A we adjust the pivot b'by means of the micrometer-screw 6 and through the sine-cam 10 to give the value of B, and by means of the micrometer-screw 5 we adjust the pivot a to give the value of (A -B), and we haveo dis to0casobistooa,orListoUasTsin.B is to V sin. (AB), which is simply this:

L I U T sin. B

V 'sin. (A-B) This equation, through the combination .of

equations (2) and (3), leads to the equation (4):

as previously explained. Hence if a scale 19 of ranges adjacent to the pathof the pivot d bemarked off in uniform divisions in which unity shall be one of a yard then a pointer 19, connected to said pivot, will read yards-range for the surveyed" triangle shown in Fig. 1. As to adjusting the distance 0 cor U. From equation 1), which is V S T U T we have U V T where U is the adjustable distance 0 c in inches. S is base-line in yards. L is distance along range-scale. R is actual range in yards, and V and T are mere multipliers chosen at convenience. Now assuming, for example, that twelve inches is a convenient length for the range-scale to represent the maximum at twenty thousand yards, then I 12' r R 20,000 and y 333.33, T 8 Therefore That is to say,

This means that we adjust the distance U to be in inches one-fortieth of what the base is in yards, and afterv in accordance therewith numbering the base-scale 20, which is adjacent to the path of the pivot c and readable conjointly with an index or pointer we have only to keep the pivot 0 set at the number corresponding to the length of base in yards and the linkage will solveall surveyed triangles as described, whatever may be the length of base. The index or pointer 20 is conveniently attached to the slide-block or nut 21 carrying the pivot c.

The before-described slide-block or nut 13, on which is secured the sine-cam 10, is adjustable by the micrometer screw 6 along guides 22, which, like the other guides 3 and 4, are provided in the base-plate 23.

The before-mentioned screw 7 is provided with a micrometer-disk 24;, the scale on v which, in conjunction with a relatively fixed index or pointer 25, gives readings in fractions of the lntegers given by the base-scale 20 and index 20.

To facilitate the working'or adjustment of the instrument, the before-described slide 1 and sleeve 2 are fitted with grooved antifriction-rollers 26 26 and 27 27, adapted to travel freely along or allow'of the free travel between them of the tube 1 and link 2, respectively, and for the same reason an antifriction-roller 28 is pivoted on the lower end of the pivot 5 to travel over the surface of the sine-cam 10.

Each of the micrometer- disks 14, 18, and 24 is, for the purposes of initial adjustment only, adjustably secured upon its respective screw-shaft by means of a bush 29, fast on the said shaft, and each of the three micrometer- screws 5, 6, and 7 is rotatable by means of a detachable handle 30, engaging the said screw through a hole in the case 31, which in other respects completely incloses the entire instrument; At its top the case 31 is provided with three glazed wickets 32 32 32, through which the various scales 11, 12, 15, 16, 19, and 20 and appropriate indices 11, 12, 15, 16", 19, and 20 are visible, all other parts of the instrument preferably being concealed from view'by and within the said case.

To hold the roller 28 constantly in contact with the sine-cam 10, a spring 33 is provided, which may conveniently be connected at one end to the tube 2 and at the other end to the link 8, as shown in Figs. 5 and 6.

It is not necessary to provide for the exposure to view of the scale 25 and index 25, (nor, indeed, of the scale 20 and. index 20,) because the screw 7 need only be adjusted once to the specific length of base from which the observations are to be taken and left in l that position of adjustment' A glazed wicket may, however, if desired, be provided to expose the said scale and. index in the sameway as is done with the other scales.

To determine the distance of a distant object from a given position of observation, two observers stationed apart at the length of the given base S, Fig. 1, measure the angles A B, Fig. 1, and communicate said measurements to the operator stationed at the beforedescribed instrument. The instrument has previously been adjusted in accordance with the lengthof base S, this being determined by means of the scales and indices 20 20 and 25 25. The operator then turns the screw 6 until the scales and indices 11 11 and 12 12 register the angle corresponding to B, Fig.

1, and then turns the screw 5 until the scales and indices 15 15 and 1 6 16 register the angle corresponding to A B, these adjustments bringing the index 19 opposite the particular mark of the scale 19, which indicates the distance of the object sighted for.

We claim 1. In apparatus for the mechanical determination of thelinear elements of triangles, the combination of two guides at an angle to each other, the length of the first from the meeting-point of the two guides to a given point in the said first guide re presentingthe length, symbolized as U, of the base of the triangle in inches, and from the said meeting-point to a point adjustable along the said first guide,

representing a variable distance, symbolized as L; different scale-markings along the first guide representing respectively the length of the base-line in yards, symbolized as S, and the actual range in yards, symbolized as R; j and two parallel links extending from the two before-mentioned points in the-first guide to two points in the second guide, these members having the relationship expressed by the formula V S R U T L Q wherein V and T represent the distances of the two points in the second guide from the above-named meeting-point, in terms of the number of times they are longer than respectively the sine of the difierence-of the internal and complementary angles, and the 1 sine of the internal angle.

2. In apparatus for the mechanical determination of the linear elements of triangles, the l combination with two telescopic links, and two other parallel links in pivotal connection therewith, for maintaining the telescopic links constantly parallel, of two pivots on each of the telescopic links, and two fixed guideways l or trammels at an angle to each other, each guideway receiving two pivots, one of each l f tile telescopic links substantially as set i OIt 3. In apparatus for the mechanical determi- IOC nation of the linear elements of triangles, the combination with two telescopic links, two other parallel links in pivotal connection therewith for maintaining the telescopic links constantly parallel, two pivots on each of the telescopic links, and two fixed guideways or trammels at anangle to each other, each guideway receiving two pivots, onepivot of each of the telescopic links, of micrometer-screws in operative connection with the pivots for adjusting their position along the gu'ideways or trammels substantially as set forth.

4- In apparatus for the mechanical determination'of the linear elements of triangles, the combination with two telescopic links, two other parallel links in pivotal connection therewith for maintaining the telescopic links constantly parallel, two pivots, on each of the telescopic links, two fixed guideways or trammels, each guideway at an angle tothe other and receiving twopivots, one pivot of each of the telescopic links, of a micrometer-screw in operative connection with each of the two pivots of one telescopic link, a sine-cam in operative connection with one of the pivots of the other telescopic link and a micrometerscrew in operative connection with the said sine-cam substantially as set forth.

5. In apparatus for the mechanical determination of the linear elementsof triangles, the combination of two telescopic links, two other parallel links in pivotal connection therewith for maintaining the telescopic links constantly parallel, two pivots on each of the telescopic links, two fixed guideways or trammels, each guideway at an angle to the other and receiving two pivots, one pivot of each of the telescopic links,micrometer-screws in operative connection with the pivots for adjusting their position along the guideways or trammels, indices in operative connection with the pivots, scales along the paths of the indices and micrometer-disks on the screws substantiallyas set forth.

6. In apparatus for the mechanical determi nation of the linear elements of triangles, the combination of two telescopic links, two other parallel links in pivotal connection therewith for maintaining the telescopic links constantly parallel, two fixed guideways or trammels, 5 each guideway at an angle to the other and receiving two pivots, onepivot of each of the telescopic links, a micrometer-screw in op erative connection with each of the two pivots of one telescopic link, a sine-cam in operative connection with one of the pivots of the other telescopic link, a micrometer-screw in operative connection with the sine-cam, in dices in operative connection with three of the pivots and the sine cam and scales along the paths of the indices substantially as set forth.

7 In apparatus for the mechanical deter-mi .nation of the linear elements of triangles, the

combination of two telescopic links, two other parallel links in pivotal connection therewith 5 for maintaining the telescopic links constantly parallel, two fixed guideways or tramm'els, each guideway at an angle to theotherand re-' ceiving two pivots, one pivot of eachof the telescopic links, a micrometer crew" in op- 7 erative connection with each of the two pivots of one'telescopic link, a sine-cam in opera tive connection with one of the pivots of the other telescopic link, a micrometer-screw in operative connection with the sine-cam, indices in operative connection with three of the pivots and the sine-cam, scales along the paths of the indices and micrometer-disks on the screws substantially as set forth.

In testimony that we claim the foregoing as our invention we have here unto signed our names in the presence of two subscribing w1tnesses.

ARTHUR H. POLLEN. MARK BARR.

Witnesses:

CHAS. S. WOODBOFFE, GODFREY HEDGES.

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