US1163294A - Computing instrument. - Google Patents

Description

J. l. WHITE.

COMPUTING INSTRUMENT.

APPLICATION FILED SE'PT.21. 1914.

Patented Dee. 7, 1915.

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I. I. WHITE.

COMPUTING INSTRUMENT.

APPucATIoN FILED sEPT.21.1914.

Patented Dec. 7, 1915.

2 SHEETS-SHEET 2.

314 @e1/dro@ Wmme@ cuLUAmlA 'PLANOGRAPM co., WASHINGTON. D. c.

UNITED STATES PATENT OFFICE.

JOHN J'. WHITE, 0F ARVADA, COLORADO, SSIGNOR OF ONE-FOURTH TO J'. A. PIERCE, OF ARVADA, COLORADO.

COMPUTING INSTRUMENT.

Specification of Letters Patent.

Patented Dec. '7, 1915.

To all whom t may concern Be it known that I, JOHN J. WHITE, a citizen of the United States, residing at Arvada, county of Jefferson, and State of Colorado, have invented certain new and useful Improvements in Computing Instruments; and I do declare the following to be a. full, clear, and exact description of the invention, such as will enable others skilled in the art to which it appertains to make and use the same, reference being had to the accompanying drawings, and to the characters of reference marked thereon, which form a part of this speciiication.

My invention relates to improvements in a computing device, and more particularlyto a device for computing the circumferences and areas of circles when the diameters are known.

4 The object of this invention is to produce a device of the character stated whichy shall be simple in construction and easily operated, not requiring a knowledge of mathematics. l y

Generally speaking, the device consists of a combination of disks and an indicator mounted in a circular casing and operating in connection with a train of gears in such a manner that the circumference or area of the circle of any given diameter may be readily obtained, all of which will be hereinafter more fully described and pointed out in the claims.

Having briefly outlined my improved construction, I will proceed to describe the same 1n detail. reference being made to the accompanying drawing, in which is illustrated i an embodiment thereof. In this drawing,-

Figure 1 is a face view of my improved device, showing a table of areas of circles radially arranged from a given center. Fig. 2 is `a view of the opposite face of the device, showing the manipulating disks. Fig. 3 is a vertical section taken on the line 3-3, Fig. 1, looking toward the left. Fig. 4 is a section taken on the line 4-4, Fig. 3, looking toward the left. Fig. 5 is a view taken on the line 5 5, Fig. 3, looking toward the left.

The same reference characters indicate the same parts in all the views.

Let the numeral designate a metal ring provided with an annular flange 6 formed on one edge thereof for retaining a transparent disk 7 preferably composed of glass.

and which is fitted into said ring, the outer edge of the glass engaging the flange on the inside. Also fitted into the ring 5 is a casing S which consists of an inner or `bottom plate 9 having an annular liange at its outer edge and projecting in a direction opposite the glass disk 7. To the outer edge of this flange is secured a cover composed of a plate 10, the latter being held in place by suitable fastening devices as screws 11. Yithin the casing 8 as thus defined are mounted gear or toothed wheels 1Q, 18 and 1'1, on spindles 15, 1G and 17, respectively. The gear 12 has eight teeth and its spindle 15 protrudes through the plate 10 and a disk IS, which is mounted and made fast to its protruding extremity. The opposite extremity of this spindle is journaled in the bottom or inner plate 9 of the casing. The gear 13 has thirty-two teeth and its spindle 16 protrudes through the bottom or inner plate 9 of the casing, and to this protruding extremity is secured an indicating arm or pointer 19. The gear 142 has seven teeth and its spindle 17 protrudes through the plate 10 and has a disk 20 mounted on and made fast to its protruding end. The opposite end of this spindle is journaled in the inner or bottom plate 9.

The outer portion of the disk 1S adjacent its periphery is divided by radial lines into eight equal sections. This disk will for convenience, be herein termed the traveling or manipulating disk. The disk 20 which I will term the fractional disk, is divided adjacentits periphery by similar radial lines, into sixteen equal sections.

On the inner face of the corresponding disk 9 is mounted a chart 21 divided by radial lines, whereby sect-or shaped or partially sector shaped spaces are formed in which the areas of circles are expressed by suitable idicia as numerals; the circles whose areas are thus indicated on this particular chart have diameters from four to twentyfour inches, inclusive. The chart is divided by circles or circular lines into live Zones, t-he aforesaid radial lines being employed to subdivide the innermost zone into sixteen equal parts; the next outer Zone immediately adjacent the innermost zone being divided by the radial lines into thirty-two equal parts; and the remaining zones each into sixty-four equal parts. In the innermost Vzone are printed or otherwise suitably formed, the areas of circles'from four t o seven and three-fourths inches in diameter, each` successive expression being the area of a circle whose diameter is 1/4 of an inch greater than the preceding expression. That is to say, the diameters of the circles whose areas are expressed in the innermost Zone are l inches; l 1 inches; el 1/2 inches; Ll; 3/1- inches, and so on. In the next zone, areas are formed of circles from eight to eleven and seven-eighths inches in diameter, each successive expression being the area of a circle whose diameter is 1/8 of an inch greater than the preceding expression. That is t0 say, the diameter of the circles whose areas are expressed in the zone next to the innermost zone are 8 inches; 8 1/8 inches; 8 2/8 inches; 8 3/8 inches, and so on. In the next outer Zone are found areas of circles from twelve to fifteen and fifteen-six- Vteenths inches in diameter, each successive expression being the area of a circle whose diameter is 1/16 of an inch greater than the preceding expression. That is to say, the diameter of circles whose areas are ex` pressed in this rone are 12 inches; 12 1/16 inches; 12 2/16 inches; 12 3/16 inches, and so on, and continuing in this order to the last zone, where the areas of circles having diameters from twenty-three to twenty-l three and fifteen-sixteenths inches, respectively, are given, each successive expression being the area cf a circle whose diameter is 1/16 of an inch Greaterlthan the preceding expression, as heretofore explained. The next or final division of the fifth Zone, being the completion of the cycle, and corresponding to a circle whose diameter is twentyfour inches, has its area printed in the center of the chart, as all ofthe other spaces have been previously filled. The chart is further divided into quadrants by heavy lines A, B, C and D, respectively, and the table printed in each zone starts from the line A, reading toward the right.

In operation, the device is set with the indicator 19 parallel with the line A, its point being exposed through Vthe glass 7 at the outer edge of the chart, the latter being of slightly less area than the exposed surface of the disk (see Fig. 1) and with the traveling disk 18 and the fractional disk 20 in the position shown in Fig. 2. A small recess 22 is formed in the traveling disk 18 to receive a pointed instrument in order to facilitate the manipulation of the disk and the operation of the instrument for determining the circumferences and areas of circles.

To find the circumference of a circle of a given diameter, the traveling disk is turned toward the left or in the direction indicated by the arrow in Fig. 2, as many revolutions as there are inches inthe diameter of the circle, and by virtue of the gear connection with the fractional disk 20, it will be seen that each revolution of the disk 18 will cause the disk 20 to travel one revolution and a fraction. The aggregate of this additional travel of the fractional disk during Ythe several revolutions of the traveling disk, added to three times the number of revolutions of the traveling disk, will give the circumference of the circle. It will thus be seen that the gearing connection between the traveling disk and the fractional disk is such that the additional travel of the fractional disk beyond the corresponding number of revolutions of the traveling disk, will be approximately the fraction expressed by the decimal .111-16 multiplied by the number of complete revolutions of each disk. For instance, to find the circumference of a circleI four inches in diameter, it will be seen that in turning the traveling disk 18, four times, the fractional disk will have made four revolutions, and approximately nine-sixteenths of a revolution, or nine-sixteenths of a revolution more than the traveling disk. Ninesixteenths added to three times four, the number of revolutions of the traveling disk, equals 12 9/16, or 12.56, which is the circumference of a circle of four inches in diameter.

To read the area of a four inch circle, the casing is reversed, so that the side containing the chart is brought into view, and it will then be found, assuming the completion of the operation just explained, that the indicator having made a complete circuit or revolution by virtue of its gea-r connection, is again at the line A and the area of a four inch circle as 12.56, is found in the space included between the radial lines intersecting the innermost zone, being what I will term the first section, or that immediately adjacent and on the right hand side of the radial line A when the instrument is held in the position .shown in Fig. 1 and so that the pointer has its exposed extremity uppermost. We look for the area of the circle under consideration within the innermost zone, because this is the zone in which the areas of the series of circles having diameters beginning with four inches and increasing up to seven and three-fourth inches are found. Again, to find the circumference and area of a circle whose diameter is fourteen inches, I turn the traveling disk 18,

fourteen times, when the fractional disk 20 will have made sixteen revolutions, or two more than the traveling disk. Two added to three times fourteen, the number of revolutions of the larger disk, equals forty-four, which is the circumference of a circle of fourteen inches in diameter. As the true circumference of a circle having a diameter of fourteen inches is L13.98, two figures only of the decimal being expressed, it will be seen that my improved instrument will come within one-two hundredth of an inch of a true circumference, which will answer, most purposes where the said dimensions of circles are required.

In the example last above, the indicator 19 will have traveled three and one-half circuits and will rest at the radial line C from which may be read the area of a crcle fourteen inches in diameter, as 153.94 square inches.

Having thus described my invention, what I claim is,-

1. A computing instrument comprising a casing, two disks mounted to rotate thereon, and an operative connection between the two disks whereby for each revolution of the first disk, the second disk will be given one revolution and a fraction of a revolution, the said fraction being approximately equal to the decimal expression .1416.

2. A computing instrument comprising a casing, a spindle journaled in said casing, a manipulating disk fast on said spindle, a toothed wheel also fast on the spindle, a second toothed wheel larger than the first wheel and meshing therewith, a third toothed wheel smaller than the first named wheel and carrying a disk graduated to indicate parts of its circumference, the arrangement being such that for each revolution of the first named disk, the second disk will be given one revolution plus a fraction of a revolution, the said fraction being approximately equal to the decimal expression .1416.

3. A computing instrument comprising a casing, a spindle journaled in said casing, a manipulating disk fast on said spindle, a toothed wheel also fast on the spindle, a second toothed wheel larger than the irst named wheel and meshing therewith,athird toothed wheel smaller than the first named toothed wheel and carrying a disk graduated to indicate parts of its circumference, the arrangement being such that for each revolution of the first named disk, the second disk will be given one revolution and a fraction of a revolution, the said fraction being approximately equal to the decimal expression .1416, a spindle upon which the said larger gear is mounted and made fast, and a pointer also attached to said spindle, whereby a complete revolution of the larger gear will impart a corresponding travel to the pointer.

In testimony whereof I aiiix my signature in presence of two witnesses.

JOHN J. WHITE.

Witnesses MAZE KIRBY, A. EBERT OBRLEN.

Copies of this patent may be obtained for ve cents each, by addressing the Gommissoner of Patents, Washington, D. C.

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