SU31677A1 - Logarithmic line - Google Patents

Description

Log-countable rulers are known with multi-scale scales in which the divisions in the second half of the preceding row are repeated at the beginning of each subsequent row.

The proposed logarithmic calculating line is made of a composite of two equal parts connected by hinges. On the side faces of the ruler, there are grooves for inserting the H-obrg of hot edges in them, which serve as guides for sliders of additional scales. In the line applied additional interchangeable plates with special scales and the corresponding engines. In the directional direction and perpendicular to the length, the ruler is equipped on the slider with a movable additional ruler for indicating the rows.

In the drawing .fig. 1 shows a general view of the ruler from above; FIG. 2, 2, cross sections of the ruler; FIG. 3- view from above; FIG. 4 is a top view of a ruler folded in half; FIG. 5 is a cross section of a ruler according to FIG. four; FIG. 6 is a top view of the spare tire, retractable, if necessary, into the grooves between the edges and the ruler; FIG. 7 - view of a slider with a transverse ruler, a transparent window and a hair

(thread); FIG. 8 is a cross section of FIG. 7; FIG. 9 - side view of the case; FIG. 10-side groove slider.

The proposed ruler (Fig. 1) consists of the ruler itself, made of wood, thick Bristol cardboard, Whatman paper or white opaque celluloid, having a shape C in shape (Fig. 2) with longitudinal grooves B.

Into the grooves are inserted metal edges L, having a W-shaped cross section (Fig. 2, 2 and Fig. 5), under the edges of which along the ruler, the slider O (Fig. 1 and 3) freely consists of a transparent scale. reinforced in an opaque frame. The engine has a size that is two times smaller than the ruler itself. The latter is cut across into two equal parts, fastened together by hinges B (Fig. 1 and 5).

In a folded form, the ruler is shown in FIG. 4 and 5. When the ruler is folded, the edges of A are inserted into the grooves B, not with their middle protrusions, but at the extreme (Fig. 5).

Slider M runs along the ruler with a transparent window E, a hair or a dash (thread) E and an additional p to the indicative movable ticker D (Fig. 7), which runs its protrusions in the lateral grooves P of the slider (Fig. 10). On the side faces of the slider, the numbers from / 1 to 10 are engraved, indicating the places to which the indicatory D line should be adjusted to mark the corresponding scale segment on the ruler or slide.

Scales are printed on both sides of the ruler. In addition to the scales printed on the ruler itself, there are special spare, sliding, opaque scales, equal in size to the engine, printed on thick paper (Whatman paper) or on thin white celluloid (Fig. 6), slid, if necessary, into the grooves between the edges of the L and a ruler, and in storage time, stored separately from the ruler in general with it. The bag I (Fig. 9 and 4, dotted line) has dimensions that make it possible with full convenience to wear a ruler in a side pocket and even in a waistcoat pocket.

On the ruler itself, on the one hand, there is an ordinary logarithmic scale in ten equal in size, parallel segments, plotted in the following sequence:

1st segment from the beginning. stroke from 1000 to 1585 incl. 2nd. . . „„ 1255 „2000„ 3rd 4th 5th bth 7th 8th 9th 10th

If you cut this scale across a ruler into two equal parts, vertically drawn through the stroke with the number of 10.000 of its lower segment, then the left half of the ruler will have segments from the 1st to the 10th inclusive, which are entirely in the right half of the ruler, the only difference is that here on the first Mecte there is a segment of the scale, which is in the left part in second place, etc., i.e. such a combination of scale segments on a ruler is obtained, in which each of the right-hand segments will actually have a continuation of the scale applied on the left-hand segment.

On 1} of the razrachnoy part of the engine, walking in the grooves of the πol of the ruler, ten segments of the scale identical to the segments of the left half of the ruler should also be applied, mentally split into two equal parts (as mentioned above). Therefore, this will be applied in the following sequence:

1st segment from 1000 to 1260 incl.

2nd. 12551535

3rd 15802000

4th 1995992515

5th 25103165

bk31603985

7th 39805015

in 50106310

9th 63057945

10th 794010000

The scale on the ruler has numbers, printed above the strokes, and on the engine, below. The segments of the scales on the engine are printed so that when moving along the ruler, the segments of the scale printed on the engine are between the segments of the scale printed on the ruler: the first is under the first, the second is under the second, etc. (Fig. 1). Due to the transparency of the engine between the segments of the scale of the latter, the segments of the scale on the ruler will be visible.

On the opaque frame of the engine both on the left and on the right side, numbers of segments from 1st to 10th inclusive are printed in bold type, which makes it possible to quickly determine the number of the segment on which at one time or another they perform.

On the reverse side of the ruler, a logarithm-logarithm (Ig Ig) scale should be printed, applied also on ten equal geometrically segments. If the scale of logarithms should be

calculated by the formula - ogj /, where n-

full length of the entire scale from 1000 to 10,000; X. is the distance from the beginning of the scale (from the prime denoting 1000) to any subsequent stroke and the y-number that any bar represents on the scale, the location of the lines of the logarithm-logarithm (Ig Ig) scale is calculated using the formula Iglgy, where

x, y have the same values. Naturally, the Ig Ig scale will not have a left limit, since Ig Ig 1 oo; therefore, the mathematical origin of the Ig Ig scale (its zero) will be against the line marking 10,000 (Ig Ig 10 0). All strokes. Right from 10,000 will have a positive sign.

and left-negative, for Ig Ig of numbers greater than ten is always greater than zero, and less than ten-less than zero.

For ease of use, the Ig Ig scale calculates values (distances from scale zero, i.e., from lOOOQ) for all numbers from 1096 to 2040000000 and breaks the resulting scale into eleven equal segments, arranging them like the logarithm scale , then ten segments of the Ig Ig scale are obtained in the following sequence:

The 1st segment is from 1096 to 1260 incl., The 2nd from 1157 to 1445 incl., The 3rd from 1260 to 1785 incl., The 4th from 1440 to 2510 incl., The 5th from 1780 to 4300 incl. , 6th ot 2500 to 10,000 incl., 7th from 4250 to 38,500 incl., 8th from 10,000 to 326,000 incl., 9th from 38,000 to 10,000,000 incl., 10th from 325,000 to 2,040,000,000 incl.

If you mentally cut this scale into two equal parts, drawing a vertical through the stroke with the number 10,000 on its seventh segment (i.e., through its zero, for Iglg 10,000 is zero), then, like it was with the logarithm scale, you get on the left, the segments from the 1st to the 10th, which are repeated on the right half of the ruler, with the only difference that in the right part in the first place will be the segment of the scale, located in the left half of the ruler in the second place, and in the last (dec tom) the place on the right will be a completely new cut of the scale, missing on the left side and which is a continuation of the 10th segment of the left side.

The engine that runs along this side of the ruler should be no different from the logarithm scale engine, and therefore a special engine will not be required. When working with the Ig scale, it will be necessary to shift the transparent engine from the scale of the scale to this side of the ruler. When working with the Ig scale, the slider can also be rotated to the other side of the ruler. However, in order to avoid frequent rearrangement of the slider and carrying the engine, you can make two identical transparent engines for each ruler, and make the slider two-way in general.

On additional plug-in scales (Fig. 6), in size - p1вных

engine, can be printed, also in ten equal segments, the following scales:

1) uniform for finding logarithms of numbers by numbers and numbers by their logarithms;

2) trigonometric functions — for determining trigonometric values by angle and angle by trigonometric values;

3) electrical engineering - for solving various electrical problems;

4) chemical solution of problems in chemistry (atomic weights, etc.);

5) scales of squares and cubes similar to those found on all lines currently existing.

The latter, i.e. the scales of squares and cubes can also not be attached to the rulers of the proposed device, since the scale of Ig Ig makes it possible, by two movements of the slider, to solve

/ - easily expressed as // "and / and, where and

can be equal to any number, both, whole and fractional (expressed / in decimal fraction).

In order not to complicate the devices of the pinnay, one can stop on two additional scales, making them not even sliding, but printing them on both sides of the ruler case. In this case, it is necessary to choose a uniform scale and a scale of trigonometric functions, depicting them conjugated with an ordinary logarithmic scale identical with the scale on the engine, directing the strokes on the segments in different directions and writing near the strokes of the symbol also from different sides of the segments.

The peculiarity of working with the proposed ruler is that, unlike the cylindrical ruler, when operating on numbers, no matter what scale the actions are performed on (except for additional inserted scales), we cannot combine the initial unit of the engine with any bar (number) on the scale of a ruler when multiplying or raising to a power, just like we cannot - mix any bar, any engine with any on the ruler, when dividing or extracting the root, but are forced to do it, using either the thread or lzynka red or vertical boundaries of the engine E to scale.

By virtue of the above, the reading of the result is also performed here by means of red verticals on the engine (division and extraction of roots) or by means of a slider thread (multiplication and exponentiation). For the same purpose, a p-ruler slide is used. on the slider up and down. The main thing with actions with the ruler of the proposed system will be to accurately determine the number of the segment on which to look for (read) the result of a particular action.

Example 1. Multiply 715 by 23.

Combine the left red vertical of the movement with the number 715 on the ninth segment of the ruler (the segment number is determined by the numbers on the frame of the slider, which are both left and right). The slider is moved until its hair is the same as € 23 on the fourth segment. The segment of line 2 is defined in the mind, on which there must be a result (product), since the sum of the multiplier numbers and the multiplicand without one gives 12, and a decrease by ten - 2. For an error-free reading of the result, put a slider on the slider against the number 2 on his face and read the product, equal to 16445 on the second segment of the scale of the ruler under the hair of the slider. At the same time, the p-indicative ruler .D closes the numbers on the engine and, on the contrary, emphasizes those on the ruler. The result is read at the intersection of the top face of p of the indicative line D and the hair of the sighting device. The result in this case is obtained with an accuracy of one, i.e. , accurate to the nth mark.

Example 2. Divide 4482 by 166.

It is found on the logarithmic scale of the ruler, on its 7th segment, the number 4482. Combine the slider's thread with this number. The number 166 is found on the 3rd segment of the engine and the engine is supplied with this number under the hair of the sight. It is determined that the result should be sought on the 5th segment of the ruler scale, since the ratio of the numbers of the dividend and the divisor is increased

by one, is equal to five. On the fifth segment of the ruler scale, against the left vertical red line of the slider, read the quotient equal to 27.

Example 3. The number 3.2 to raise to a power of 4.7.

Transfer the transparent slider to the log log scale. Combine the left red vertical. With a number of 3.2 on the sixth segment of the Ig Ig scale. Move the slider until its hair coincides with the number 4.7 on the fourth segment of the engine. It is determined that the cut of G1stat should be searched for on the ninth segment of the Ig 1g scale, since the sum of the numbers of the segments of the number and the exponent, reduced by one, is nine. The use of the indicator line D at the point of intersection of the top face of the slider and the hair of the sighting device reads a result of 236.7.

PRI me R 5. Extract the root with the index 3.8 out of 78.5.

Combine the hair of the sight with the number 78.5 on the eighth segment of the log log scale. The number 3.8 is put under the hair of the sight in the third segment of the engine scale. It is determined that the result must be sought on the sixth segment of the log log scale, since the difference between the numbers of the number segments and the root index, increased by one, gives Six. Against the left red vertical of the engine, on the sixth segment of the log log scale read the result of 3.1525.

The subject matter of the invention.

Claims (4)

1. A logarithmic ruler. with multiple scales, equipped with a half-length transparent engine and scales in which at the beginning of each successive row, the divisions repeated in the second half of the preceding row are repeated, characterized in that it is made up of two equal parts connected by hinges ; 2. In the ruler of claim 1, a device on its side faces of slots B for inserting W-shaped rims A in them, which serve as guides for sliders and additional ticks. 3. With a ruler according to claims 1 and 2, the use of additional interchangeable plates with special scales and the corresponding engines. 4. In the line in pp. 1-3 application on a slider mobile in a direction perpendicular to the length of the ruler, ruler D. FIG 4 Fig 5 .. .ff