JPH02299083A - Logarithmic scale instrument - Google Patents

Abstract

PURPOSE:To obtain a logarithmic scale instrument which reads data from a logarithmic graph with the high precision and generates logarithmic graphs of various measure sizes by providing a plate material with the point where the meaning of logarithmic value '0' is given, and three straight lines which intersect this point and the meanings is given as prescribed. CONSTITUTION:A first straight line 3 and a second straight line 4 are intersected orthogonally with each other on a transparent thin plate. The straight line 3 indicates true value X=10 of Y=log10X, and the straight line 4 indicates true value X=1. Concentric circles 5 as logarithmic reference lines are arcs having a point O as the center. A third straight line 6 indicates the true value X of logarithm, and the true value is indicated in the upper part of each picture. L/R=log10X is obtained by sintheta=log10X and sintheta=L/R. Consequently, an intersection P on the circle 5 is obtained by a logarithmic scale L at the time of giving R, and the true value X of the logarithm is found by the straight line 6 crossing the point P. When the true value X is given, the length as the logarithmic scale is obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION <Field of Industrial Use> The present invention relates to a logarithmic scale that can read data from and write logarithmic graphs.

(Prior art) Conventionally, when reading data shown on a logarithmic graph,
It is fine as long as the scale is finely divided to the degree of accumulation that one wants to read, but in many cases, the intervals between the scales are coarse and are on a logarithmic scale, making it difficult to estimate data values. In some cases, it may be necessary to calculate the value, but
It was difficult to determine by simple calculations, and it was necessary to use function tables and calculators with function functions.

On the other hand, when creating a logarithmic graph, there is no problem if you use commercially available logarithmic graph paper, but if you need to create a logarithmic graph on a paper size other than the specified paper size, or if there is no commercially available logarithmic graph, Since the scale of the graph is on a logarithmic scale, it was difficult to determine the scale by simple calculations, and a calculator with a function table or function function was required9 (Problem to be solved by the invention) Function table or function function Data can be read accurately from logarithmic graphs without using an attached IT calculator, etc.
To provide a logarithmic scaler that can create logarithmic graphs with various scale sizes.

(Means for Solving the Problems) This invention provides a point O which is marked on a plate as a logarithm value of "0", and a true value of the logarithm that is the same as the base of the logarithm that intersects the point O. a first straight line that intersects the point O and is orthogonal to the first straight line and is set to the true value of the logarithm ゛°1''; a point S on the first straight line and the second straight line Orthogonally project a logarithmic reference line that passes through point T on the two straight lines and an arbitrary point P on the logarithmic reference line whose length is R between the point O and the point S onto the first straight line. Draw a third straight line that is not significant to the true value Equipped with the above.

(effect) In this invention configured as described above, the logarithm value ゛.

When the length R between the point 0 and the point S of the logarithmic reference line, which corresponds to a length of 1'°, is given in advance and the logarithmic scale is given as an arbitrary length on the first straight line, the logarithm Find the true value X of the logarithm from a third straight line whose value is predetermined as the true value of the logarithm passing through the intersection point P obtained by orthogonally projecting the length L onto the reference line and the point O, and write it to the correspondence. When the true value X of the logarithm is given, the logarithmic scale for the true value The length can be obtained by orthogonally projecting the point P onto the first straight line (Embodiment M) Next, an embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a diagram showing an embodiment of a logarithmic scaling device for common logarithms constructed using a plurality of concentric circles centered on point O as the logarithmic reference line.

A suitable plate material for the logarithmic scale device 1 is a transparent thin plate. The first straight line 3 and the second straight line 4 are orthogonal to each other, and the first straight line 3 indicates the true value X210 at Y=log, , X, and the second straight line 4 indicates the true value x=1.

The numerical values shown above the first straight line 3 and the second straight line 4 indicate their respective true values.

The concentric circle 5 as a logarithmic reference line is a circular arc centered on the point O.

The third straight line 6 shows the true value "x" of the logarithm, and the true value is shown above each straight line.9 The angle θ showing this third straight line 6 is: θ=sin-'(log, X). On the other hand, this angle θ is θ−
Since it can be expressed as s in = (L/R), L
The relational expression /R=Iog X holds true.

Therefore, the radius l of the concentric circle 5 in 10groX21
If ma is given in advance, the true value of the logarithm "x" can be found by finding the intersection P on the concentric circles from the length of the logarithmic scale and from the third straight line 6 that intersects with the intersection P.

Since a logarithmic scale corresponding to log, oX=1 is usually given, a concentric circle 5 with a required radius R can be set in advance.

If the true value of the logarithm is given to the correspondent, the true value of the logarithm”
By finding the intersection point P between the third straight line 6 representing "x" and the concentric circles, it is possible to find the length as a logarithmic scale.

In the embodiment, 10 to 12 concentric circles are provided with the third straight line 6, but the number may be further increased and divided into smaller circles to improve reading accuracy.

Here, in order to read the length L by orthogonally projecting the point P onto the first straight line 3 and to find the position of the intersection P from the length value, we use a guide line that is perpendicular to the first straight line 3 and parallel to the second straight line 4. A large number of straight lines may be displayed directly on a transparent board.

Also, instead of displaying the straight line for guidance, the guide plate 8 is made to slide over the 6th and 8th planes of the logarithmic scale main body 7 as shown in FIGS. 3 and 4. Alternatively, the 0 plane may be the guiding straight line.

Figure 5 shows the horizontal axis value (X+
, Xz) is measured using a logarithmic scaler according to the present invention.

Align the first straight line 3 of the logarithmic scale with the vertical line set to "l" on the horizontal axis of the logarithmic graph.

Concentric circles with a radius that matches the length between the vertical line set to "" and the vertical line set to "io" (the concentric circles shown as thick lines in the figure) and the measurement Data point Q+
The value of the true value X1 can be found from the third straight line passing through the point where the first straight line 3 intersects with a parallel straight line. In the case of the measurement data point Qt, Xl is 5 according to the embodiment. Similarly, in the case of the measurement data point Qz, Xl is 1.5.

Here, on the horizontal axis of the logarithmic graph in Figure 5, "
If the vertical line set to ``1'' is ``10'' and the vertical line set to ``10'' is 100'', then the measurement data point Q.

, X, , xz at point Q2 can be simply multiplied by 10.

Therefore, the value of Xl is 50, and the value of Xl is
It becomes 15.

FIG. 6 shows an example of a logarithmic scaler for common logarithms in which a straight line is used instead of concentric circles centered at point O as a logarithmic reference line.

As the logarithmic reference line, the fourth straight line 13 passing between the point S on the first straight line 11 and the point T on the second straight line 12 is used as shown in the seventh VA.

Here, the third straight line 14 is a straight line assigned to the true value of the logarithm as described above. Let the intersection of this third straight line 14 and the fourth straight line 13 be P, and let the point obtained by orthogonally projecting this point P onto the first straight line 111 be P'.

The length between point P- and point 0 is R, the length between point S and point 0 is R5, the length between point T and point 0 is W, and the length between point P and point 0 is r.
shall be.

Further, when the angle between the second straight line 12 and the third straight line 14 is θ, L/R as a logarithm value is expressed as L/R=1/(1−a/lanθ). Here, a is the slope of the fourth straight line 13 (R/W
) is shown.

FIG. 6 shows an example in which the slope a of the fourth straight line 13 is "-1".

From the above, the value of L/R as a logarithm value is related only to the angle θ, so if it is on the third straight line 14, which is meaningfully assigned to the true value of the same logarithm, which logarithm reference line The fourth straight line 13 also shows the same value 9, indicating that the logarithmic scaling device according to the present invention can be used for logarithmic tables of arbitrary sizes.

In addition to the function as a logarithmic scale, the first straight line 11 may be graduated at intervals of, for example, 1 mm, as shown in FIG. 6, and may have the function of a ruler and a measuring stick, thereby adding value.

So far, we have described a logarithmic scaler for common logarithms, but it can also be used as a logarithmic scaler for natural logarithms.

A logarithmic scaler for natural logarithms will be explained using the embodiment shown in FIG. The first straight line 3 has the same value as the base (e) of the natural logarithm as the true value of Yn=log, Xn=2.71
8... is assigned, and the second straight line 4 is assigned the true value Xn=1.

The third straight line 6 is assigned a true value between 1 and 2.71.8. The angle θ of this third straight line 4 is θ=sln
(log, 2Xn) is given.

On the other hand, since this angle θ can be expressed as θ−s i n−1 (L/R), the relational expression L/R=log, If R is given in advance, it is possible to find the intersection point P on the concentric circle 5 from the length L of the logarithmic scale, and from the third straight line 6 that intersects with the intersection point P, the true value of the logarithm °''X n '' can be found.

When the true value of the logarithm Xn is given to the correspondence, the intersection point P of the third straight line 6 representing the true value of the logarithm "Xn" and the concentric circles can be found, and the length L as a logarithmic scale can be found.

Here, by writing the true value X of the common logarithm and the true value Xn of the natural logarithm together on the third straight line 6, it can be used as a logarithmic scaling device for both the common logarithm and the natural logarithm.

The true value Xn of the natural logarithm is the base (e) of the natural logarithm (log
, , X).

Also, there is another method as follows.

In this case, the first straight line 3 is given the true value Xn=10 at Yn=logeXn, and the second straight line 4 is given the true value Xn=
1 is given. The third straight line 4 is given a true value between 1 and 1°.

The angle θ of this third straight line 4 is set to θ=srn (logeXn/loge10). As a result, the angle θ of the third straight line -1 will be the same value if both the common logarithm and the natural logarithm have the same true value. Yes, 9 However, 1,,,y' expressed as the logarithm value of the common logarithm
R is.

In the natural logarithm, Iogelo (2,3026>(n) must be.

(Effects of the Invention) As explained above, the present invention enables data to be read accurately and easily from a logarithmic graph without using a function table or a calculator with a function function. You can easily create it.

[Brief explanation of drawings]

FIG. 1 is a perspective view of the present invention FIG. 2 is a diagram illustrating the present invention shown in FIG. 1 FIG. 3 is a front view of the present invention using a guide plate FIG. 4 is a diagram 3 FIG. 5 is a partially enlarged cross-sectional view showing an example of the use of the present invention. FIG. 6 is a perspective view showing another embodiment of the present invention.
1 and 9 for explaining the present invention shown in FIG. , the third straight line 7 is the logarithmic scale main body 8, and the guide plate 13 is the fourth straight line.

Claims (1)

[Claims] A point O marked on the board as a logarithm value of "zero", a first straight line marked as the true value of the logarithm that is the same as the base of the logarithm that intersects the point O, and a first line that intersects the point O and a second straight line that is perpendicular to the first straight line and is assigned the true value of the logarithm "1", and one or more logarithmic references that pass through the point S on the first straight line and the point T on the second straight line. line, and the length between the point P and the point O obtained by orthogonally projecting any point P on the logarithmic reference line with a length R between the point O and the point S onto the first straight line. By providing one or more third straight lines that are assigned to the true value X of the logarithm whose logarithm value is the ratio L/R of L and the length R,
When the length R between the point O and the point S of the logarithmic reference line that corresponds to the length of the logarithmic value "1" is given in advance, and the logarithmic scale is given as an arbitrary length L on the first straight line. , the true value X of the logarithm is obtained from the third straight line whose value is predefined as the true value of the logarithm passing through the point O and the intersection point P obtained by orthogonally projecting the length L onto the logarithmic reference line. and conversely, when the true value X of the logarithm is given, the logarithm scale of the true value A logarithmic scale that can be determined as the length L obtained by orthogonally projecting the point P that intersects the reference line onto the first straight line.