The Lost Art of Nomography

Ron Doerfler
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The Art of Nomography I: Geometric Design
Ron Doerfler
 DOI: 10.1109/MAHC.1986.10059
Annals of the History of Computing ( Volume: 8 , Issue: 4 , Oct.-Dec. 1986 )
Origins and Development of Nomography
H.A. Evesham
Early developments that preceded nomography are cited, and the development of the subject is examined in outline. The special problem of nomograms in three variables is considered in a general way. Uses of nomography, both old and recent, are given. The tone is intended to be descriptive, not technical, but references are provided so that the interested reader can investigate the subject further.
Mysteries of the Smith Chart
Stephen D. Stearns
The Smith Chart

The Smith Chart was originally created many years ago as an RF engineering aid by Phillip Smith of RCA. Actually, Smith may not have been the first inventor of this tool -- a Japanese engineer named Kurakawa independently created a similar chart about a year before Smith. In any event, the Chart is a clever, complex number nomograph in a circular format which is an invaluable tool in RF design...
Smith Chart Basics

What is a Smith chart? It's really just a plot of complex reflection overlaid with an impedance and/or admittance grid referenced to a 1-ohm characteristic impedance. That's it!...
Normalized Impedance and Admittance Coordinates
A Color Smith Chart in PDF format

Reverse Engineering Nomographs
Nomograms for Wargames
Smith Chart -- 264k .zip file format
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The History and Development of Nomography
H.A. Evesham

Elements de Nomographie
G. Knovanski
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International Journal of Mathematical Education in Science and Technology, Volume 50, 2019 - Issue 8

A brief introduction to nomography: graphical representation of mathematical relationships
Leslie Glasser & Ron Doerfler

Nomographs (or nomograms, or alignment charts) are graphical representations of mathematical relationships (extending to empirical relationships of data) which are used by simply applying a straightedge across the plot through points on scales representing independent variables, which then crosses the corresponding datum point for the dependent variable; the choice among independent and dependent variable is arbitrary so that each variable may be determined in terms of the others. Examples of nomographs in common current use compute the lift available for a hot-air balloon, the boiling points of solvents under reduced pressure in the chemistry laboratory, and the relative forces in a centrifuge in a biochemical laboratory. Sundials represent another ancient yet widely familiar example. With the advent and ready accessibility of the computer, printed mathematical tables, slide rules and nomographs became generally redundant. However, nomographs provide insight into mathematical relationships, are useful for rapid and repeated application, even in the absence of calculational facilities, and can reliably be used in the field. Many nomographs for various purposes may be found online. This paper describes the origins and development of nomographs, illustrating their use with some relevant examples. A supplementary interactive Excel file demonstrates their application for some simple mathematical operations.
Heat and Mass Transfer volume 54, pages2661–2673(2018)

Original methodology and nomography tool for dimensioning multi-packed-bed dehumidifiers
Rached Nciri, Kamel Rabhi, Faouzi Nasri, Chaouki Ali & Habib Ben Bacha
This work deals with the dimensioning of multi-packed-bed dehumidifiers used in solar air-conditioning systems. An efficient dimensioning methodology is elaborated, explained and visualized by a chart. The proposed methodology permits to ensure an appropriate packed-bed dimensioning based on a compromise between the highest possible amount of heat and mass transfer and the lowest possible level of pressure drop within a packed-bed-dehumidifier. Nomography tool is implemented in order to simplify, speed up and expand the possibilities of dimensioning. The proposed nomographs permit to determine the appropriate values of the diameter, the porosity and the height of the packed-bed. The mathematical construction techniques of all nomographs are presented in detail. Applied examples are carried out in order to show the effectiveness of each nomograph.

Mathematics of nomography 

Mathematik und Anwendungen, Chapter 5,
Traditionally, history of mathematics was more interested in the production of abstract concepts and major theories than in the one of methods and tools of calculation. As a result, it has often neglected to consider the mathematical practices of engineers. I want to sketch here a sample of these practices through the example of nomography in the second half of 19th century and first half of the 20th century, precisely at the time when the professional community of engineers structures itself and deepens its mathematical culture.

Pressure-Temperature Nomograph Interactive Tool
Boiling Point vs Pressure Calculator
Edward Otto
John H. Fasal
L. Ivan Epstein / Interscience Publishers, 1958
The History and Development of Nomography Name ...
by HA Evesham - ‎1982
Mathematics of Nomography
Mathematik und Anwendungen, Michael Foote,Michael Schmitz, Birgit Skorsetz, Renate Tobies (Hrsg.), p. 26-32, 2014
Dominique Tournès

Alignment Charts for Engineers and Students

The Online Books Page: Nomography
Some Reference Texts on Nomograms & Nomography

Best Approximation by Linear Superpositions ( Approximate Nomography)
S.Y. Khavinson
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Die Grundlagen der Nomographie
B.M. Konorski
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The History and Development of Nomography
Harold A. Evesham
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Normalized Impedance and Admittance Coordinates
Smith Chart Form ZY-01-N -- Microwave Circuit Design
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Lehrbuch der Nomographie
H. Schwerdt
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On Jargon : The Lost Art of Nomography
Ron Doerfler
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TUGboat, Volume 30 (2009), No. 1
An Introduction to Nomography: Garrigues' Nomogram for the Computation of Easter
Denis Roegel
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Dr Habil H. Athen
[ DJVU ]
Interactive Nomogram Creation Tool
by T. B. Jones, R. Camara, and A. Marrero
A.S. Levens

L. Ivan Epstein
[ DJVU ]

Edward Otto
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Nomography -- Theory and Application
Douglas P. Adams
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A slidable nomograph device having an erasable and slidable rule moved beneath a plurality of partially transparent nomograph fields, charts, curves, etc. The user writes on the rule surface by (pressure) writing on the fixed nomograph fields and the writing is moved from one nomogram field to the next, and so on. Different nomograph fields may be used by sliding out one field set and substituting another field set.

Nomograph system based on cloud computing
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The invention belongs to the technical field of cloud computing, and particularly relates to a nomograph system based on the cloud computing. The nomograph system based on the cloud computing comprises an information base level, a nomograph service level, a nomograph engine level, a service management level and an access interface level, wherein the levels are communicated through network devices, and the information base level is entirely deployed in a cloud computing virtualized service environment. The nomograph system based on the cloud computing has the advantages that the problems of massive data storage, data safety and large time consumption demands of a common nomograph system are solved; through the powerful storage and computing power provided by a cloud platform, nomograph can be carried out efficiently, the operating cost of the nomograph system can be lowered, and users can use resources conveniently.

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A system and method for graphically representing on a computer system the relationship between a plurality of variables related by an equation. A graph having a plurality of axes is displayed on a display device and each axis represents one of the variables. Grips are located on each of the axes to indicate the value of the variable represented by the axis. A user can lock one of the grips on its axis and then select one of th e unlocked grips and slide the selected grip to a new position indicating a new value o n the axis. The remaining grip will slide in relation to the grip being moved by the user an d indicate the value of the remaining variable.

Nomograph calculator 
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A method for to calculation of actual astigmatism correction and nomographs for corneal laser treatment includes performing a post-operative measurement of the cornea of a patient to determine actual astigmatism coefficients. The actual astigmatism coefficients are compared against the expected astigmatism coefficients to generate a nomograph value or a nomograph curve over a sample population. The nomograph is used to calibrate subsequent laser treatments for improved accuracy of clinical results.

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 A method for to calculation of actual astigmatism correction and nomographs for corneal laser treatment includes performing a post-operative measurement of the cornea of a patient to determine actual astigmatism coefficients. The actual astigmatism coefficients are compared against the expected astigmatism coefficients to generate a nomograph value or a nomograph curve over a sample population. The nomograph is used to calibrate subsequent laser treatments for improved accuracy of clinical results.

Constructing method of predicting model and nomograph for HCC recurrence and RFS and application thereof
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The invention belongs to the field of predicting model and nomograph construction technology, and discloses a constructing method of a predicting model and the nomograph for HCC recurrence and RFS and application thereof. The method comprises the steps of by means a minimum redundancy maximum relevance algorithm (MRMRA), respectively extracting 647 radiomics characteristics from liver 3-period enhanced CT scanning images of all patients; confirming a radiomics label by means of a least absolute shrinkage and selection operator (LASSO)-Cox regression model; and establishing a predicting model and a predicting naomograph for HCC recurrence after therapeutic ablation treatment and teh RFS by means of clinical and pathological factors and the radiomics label. According to the method of the invention, the predicting model and the predicting nomograph are constructed through the radiomics method. The method is used for predicting tumor recurrence and RFS of an HCC patient after therapeutic ablation treatment of a focus.

Device for interpreting a nomograph.
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 The device exhibits a backing plate (1) for the nomogram and an arm (15) which is arranged on the plate and is mounted capable of rotating parallel to the front side (2) of the plate about an axis (14) that moves with it. The shaft (14) is arranged to extend and the length of the arm (15) is dimensioned, such that it is possible for the arm to cover all the relevant nomogram scales (a, b, c, d) and for the arm (15) to be able to be aligned on significant positions of the nomogram scales by means of at least one marker line (17) on the arm and running along its longitudinal direction.

Logarithmic scale nomograph for fast dose computation.
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The monogramme has 3 parallel logarithmic scales (S1, S2, S3) of respective length (M1, M2, M3), spaced one from the other by given distances (1,b), with all 3 scales (S1, S2, S3) lying on the same side of a level line (2). Pref. each of the scales (S1, S2, S3) is marked on a respective support. The 3 supports are coupled together via a beam which is pivoted to the centre of each support, allowing the latter to slide relative to one another.

Insulation resistance nomo-ruler
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The utility model discloses an insulation resistance nomo-ruler and relates to the field of surveying and mapping. The nomo-ruler is convenient to use, high in reliability and capable of enabling a working person to grasp the insulation performance of electrical equipment more conveniently. The insulation resistance nomo-ruler comprises an insulation resistance measuring instrument; a temperature measuring instrument; a probe connected with input ends of the insulation resistance measuring instrument and the temperature measuring instrument; an image display unit connected with output ends of the insulation resistance measuring instrument and the temperature measuring instrument, wherein the image display unit is used for displaying an insulation resistance nomograph, and the insulation resistance nomograph comprises a practical insulation resistance value shaft, a temperature value shaft and a theoretical insulation resistance value shaft; and a control unit electrically connected with the insulation resistance measuring instrument and the temperature measuring instrument, wherein the control unit is used for displaying a practical insulation resistance value measured by the insulation resistance measuring instrument on the practical insulation resistance value shaft of the insulation resistance nomograph and displaying a temperature value measured by the temperature measuring instrument on the temperature value shaft of the insulation resistance nomograph.

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SUBSTANCE: group of inventions refers to medicine, namely to resuscitation and intensive therapy, and can be used in executing cardiopulmonary resuscitation (CPR). That is ensured by chest compressions with using a device comprising a bar with an anteroposterior chest size scale, a force transfer contact element representing a strain-free support plate adjusted on a patient's chest, a sound-and-light indicator generating a sound and light signal of fixed frequency 100 times a minute a case of which comprises the bar to be mounted and fastened thereon, a contact element horizontal position sensor comprising a laser pointer, and a nomograph to determine an optimum excursion depth in length units. The nomograph has points 14 to 24 cm corresponding to the anteroposterior chest size, and dial graduations are provided in the form of steps formed by upper borders of nomograph columns which have height equal to 2.247xi cm where xi is a number of dial graduation specifying the anteroposterior chest size. The laser pointer is fixed on the support plate and directs a light ray in a field of the nomograph columns. Chest compression is executed in a projection of the middle one-third of breast bone by pressing through the strain-free flat surface of the contact element at frequency 100 in a minute at an excursion depth, with first 2-3 pressings made 50-70 % of the specified excursion depth. Compression is accompanied with sound and light signals radiated at pressing frequency, and the contact element is followed visually by projecting with a ray its position in a nomograph column field within upper and lower limits of the corresponding column. ^ EFFECT: invention allows providing the most effective CPR ensured by creating optimum artificial blood-groove volume in great vessels with simultaneous simplification of technical compression control facilities, and higher correct chest compression data reliability.

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A ballistic nomograph for determining a firing solution for small arms fire includes a first member and a second member. Alignment of first indicia on the first member with the first indicia on the second member aligns the value of a range to a target with a first environmental condition to align a first adjustment value with an indicator positioned on the first member to provide a firing solution adjustment to a user. A method of determining a firing solution for a small arm by manually manipulating a ballistic nomograph includes determining environmental conditions and aligning the value of a range to a target with a value of environmental condition. The method also includes visually identifying a firing solution adjustment value that corresponds to the particular combination of the range to the target and environmental condition, and making a firing solution adjustment based on the firing solution adjustment value.

Method and apparatus for sizing an environmental control system
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A method is provided for sizing an environmental control system for controlling a temperature of a target. The method comprises the steps of: identifying the target that is to be temperature controlled by the environmental control system; selecting a desired temperature of the target that is to be temperature controlled; and determining optimal characteristics of the environmental control system. Preferably, the step of determining optimal characteristics of the environmental control system includes referring to a nomograph that charts numerical relationships of a plurality of variables. Preferably, variables charted on the nomograph include a temperature of discharge air that is to be discharged from the environmental control system, a temperature of ambient air surrounding the target, a distance between a discharge portion of the environmental control system and the target, and a volumetric flow rate of the discharge air.

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A method for determining the distance between a cased well and an open well using resistivity measurements made in the open well using long electrode spacings and a resistivity is calculated from data that is not influenced by the casing in the cased well. A calculation is made of the anticipated reduction in the resistivity measurements caused by the presence of the casing using the calculated resistivity and assuming varying distances between the cased well and the point at which the resistivity is measured. A nomograph is prepared by plotting the calculated reduction versus the assumed distances for each calculated formation resistivity. The measured resistivity is used to determine the actual reduction in the resistivity caused by the casing and the distance between the two wells is then obtained from the nomograph.

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A method for determining combinational frequencies, based on the calculation and construction in a Cartesian coordinate system of a nomogram of the combinational frequencies of a frequency converter, which is a functional dependence of the ratio of the frequency of the converted signal to the local oscillator frequency on the ratio of the input signal frequency to the local oscillator frequency and includes a straight line segment that determines the main form frequency conversion...

Multiple nomograph system for solving ranging and ballistic problems in firearms
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The multiple nomograph system for solving ranging and ballistic problems in firearms includes a series of graphs or nomographs for the determination of a series of factors affecting the ballistic trajectory of a bullet in flight. The nomographs may be placed upon the reticle of a firearm scope, or provided on media external to the scope, as desired. The scope reticle includes at least one aiming point or aim point field to compensate for elevation and windage, with the vertical axis preferably being offset to compensate for precession at longer ranges. Stadia for determining angular target dimension(s) are included on the reticle, with a nomograph for determining apparent distance from the apparent dimensions being provided either on the reticle or external to the scope. Additional nomographs are provided for the determination and compensation of non-level slopes, non-standard density altitudes, and wind correction, either on the reticle or external thereto.

Controlling superplastic forming with gas mass flow meter
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The forming time necessary to superplastically form an object from a metal sheet is estimated by empirical analysis. The required rate of gas mass flow into a forming cavity is then determined using either a nomograph composed of four interrelated graphs, or a single graph which requires the input of fewer variables than the nomograph. The present invention may also be used to form cells of multiple sheet panels from a stack of sheets. In the latter application, forming time necessary to complete forming of the cells from an interim point where the core sheet forming pressure and the die temperature are increased from interim levels to their final values is estimated by empirical analysis. A nomograph or single graph of the present invention then determines the gas mass flow rate necessary to safely and efficiently complete forming of the cells from the foregoing interim point. In both of the foregoing embodiments, the required gas mass flow rate, which is a target value, is maintained by regulating the forming pressure until the final forming pressure is reached.

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PROBLEM TO BE SOLVED: To provide an evaluation method of collapse risk of unstable rocks capable of preparing a nomograph related to the relation between a falling safety ratio of rocks on a slope and vibration characteristics and evaluating stability of each rock on the slope more in detail.SOLUTION: In the evaluation method of the collapse risk of unstable rocks, vibrations of the unstable rocks on the slope are measured on site, a rock sample of the unstable rocks or peripheral rocks of the same rock kind is acquired, rock physical properties (tensile strength, elastic coefficient) of the unstable rocks are recognized by an indoor test of the rock sample, collation is performed with a nomograph indicating the relation between a dominant frequency and the falling safety ratio for the respective rock physical properties (tensile strength, elastic coefficient), the falling safety ratio of the unstable rocks is obtained, and thus, the collapse risk of the unstable rocks is evaluated.

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The present invention is related to the metal-plate cutting technology for making tee tube, elbow, tapered tube and other parts made of metal-plate. On the basis of analyzing and summerizing the traditional lofting and metal-plate cutting technology using divider, relevant mathematical relations are utilized to provide an unfolding nomograph method for making metal-plate parts. The length of every line segment between equi-dividing points in view are calculated according to the relevant mathematical formulas, and the complex calculation formulas are deduced into corresponding nomographs so that the calculating time will be greatly shortened. The said method will not be restricted by environment, conditions and technical competence of relevant staff. It is free from the platen, oil paper and other auxiliary tools. The said method makes it possible to shorten the working period by 2-3 times and is an important innovation in metal-plate cutting technology.

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SUBSTANCE: invention relates to methods of studying water erosion of soil. Essence: determining average slope and potential of erosion resistance of underlying surface of analyzed key section on landscape slope of slope lands. Taking into account certain parameters, nomograph is used to establish degree of probable washing of soil of investigated key section. Appropriate soil treatment technology is selected.EFFECT: technical result is determination of degree of probable washing of soil on landscaping slopes of slope lands.

Apparatus and method for calculating vehicle movement parameters
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An apparatus and method of calculating a vehicle's elevation, speed, distance and time to arrive at a predetermined point. The apparatus includes a mechanical spring-driven clock mechanism having a rotating settable pointer passing adjacent a clock face for visually ascertaining time measurement during a specified time interval. The clock face has a prescribed set of indicia formed thereon defining a nomograph which correlates the vehicle's speed and distance to the predetermined point. An outer annular ring movable with respect to the clock face provides indicia showing the vehicle's elevation at specific time points. Tab elements which are slideably moveable on the annular ring provide visual guides to important elevation points. A central pointer on the clock is set at the selected vehicle speed and distance measurements on the nomograph and relates to a proper vehicle elevation mark on the annular ring. At a specific time designation, the clock pointer movement is initiated. The apparatus then provides a continuous display of elevation, speed, distance and time to arrival at the predetermined point.

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A nomograph type calculator which will use skinfold data and information relating to the actual body weight of a person to enable a person's ideal body weight to be determined. The nomograph comprises an elongated outer housing having open ends and a flat, translucent front face with a plurality of elongated, spaced, rectangular transparent windows therein. An indicator plate is slidable longitudinally within the housing adjacent the inner surface of the front face, the plate carrying a plurality of rows of indicia across a central portion thereof, each row of indicia adapted to be located and a portion thereof to be visible through a corresponding window. Two rows of indicia carry respectively calibrations representing a range of skinfold measurement values and a range of percent body fat values. These two rows of indicia and indicia markers associated with corresponding windows are arranged so that at any particular position of the plate in the housing the percentage body fat value is indicated through the one window for the skinfold measurement value indicated through the the other. Another row of indicia has calibrations representing a range of body weight values, these indicia being positioned and coordinated with a scale of percentage body fat indicia along the edge of the corresponding window so that positioning of the plate to align a value of percent body fat with a specific body weight value will give a visual indication of the ideal weight for that particular value of body weight and value of percentage body fat.

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FIELD: power industry.SUBSTANCE: method of work regulation of heat generating steam-turbine plant with steam-compression heat pump at heat generating mode, at set heating temperature of system water includes switching of access of main steam to the system water heater by closing of the diaphragm before low pressure section of the steam turbine, keeping part of steam flow though ventilation pass though LP section, as per nomograph of joint operation of LP section and hat pump unit the specific power of LP section is determined at steam pressure in the condenser with shutdown compressor of the heat pump unit and switched on compressor of the heat pump unit, as well as specific power of the heat pump unit switched on to maintain set heating of the system water, and according to the obtained power values the heat pump unit is controlled. EFFECT: improved efficiency of thermal power plant.

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SUBSTANCE: method involves performing nondestructive building beam testing to determine simple quality indexes by determination of geometrical steel beam dimensions and beam securing conditions; measuring normative working load applied to beam and intensity of normative stresses in weak metal beam sections; determining heat diffusion indexes of fire-protective material of the beam. Fire-protective beam resistance to heat applied from ordinary fire is given as function, which takes into consideration of normative force stresses intensity in beam cross-section caused by working normative load application and heat diffusion indexes of fire-protective material. Fire-resistance rating of fire-protected steel beams is determined from nomograph. EFFECT: increased test reliability and decreased test time.

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A device for the graphical solution of the simultaneous equations A = f (D, C, K), which equations can be represented by nomographs, e.g., Larson's Nomograph, having two spaced vertical axes bounding two families of curves. The device comprises a first straight line defining means (e.g., a transparent stick) having one end thereof presettable along the first vertical axis, a second straight line defining means (e.g., a second transparent stick) having one end thereof also presettable along the first vertical axis, their other ends intersecting at a common point on the second vertical axis, and means (e.g., a pin) disposed at the common point and movable along the second vertical axis.

Total environment decorating aid
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A coordination kit for choosing suitable fabrics, paints, wall coverings, window treatments, fabrics for chairs etcetera, rugs and other floor coverings to achieve a desired decorator effect. The kit includes at least two nomographs, mounted to a substrate, and numbering up to a number equal to the number of elements of the total decoration effect that the user desires to choose. Each nomograph (nomogram), includes a rotatable upper layer having at least two windows, which overlies a lower layer having viewable segments, each of which segments has a plurality of cells, all of which cells contain a set of predetermined generally accepted color spectrum specimens, from either the entire color spectrum or a portion thereof, which specimens are used in the selection of the coordinated decorator effect desired. The specimens may be from but not limited to actual or photographic representations of tile, fabric, paint, rugs and other aspects of a room's decor.

Improvements in stainless steels
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A predominantly austenitic chromium-nickel steel has the following composition: Cr 16-25 per cent; Ni 7-25 per cent; N up to 0.05 per cent; C up to 0.05 per cent; Fe together with residual deoxidizers such as Mn up to 3 per cent and Si up to 2 per cent forming the remainder, the maximum carbon content of a steel of selected chromium and nickel contents being ascertainable according to a formula set forth in the Specification. Within the above ranges alloy steels which are substantially 100 per cent austenitic after annealing at 1075 DEG C., air cooling, reheating to 650 DEG C. and air cooling, are selected by means of a nomograph accompanying the Specification. The alloy steels of the invention are substantially insusceptible to intergranular corrosion and may be used in the manufacture of welded articles and welding rods.

Method for calculating tide
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The present invention relates to a method for calculating tide. Said invented method includes: A. drawing tide calculation nomograph according to the following requirements: it has two scale coordinates of T1 and T2 for time of tide, their interspace is 90 deg., and has two scale coordinates of H1 and H2 for height of tide, those are perpendicular to T1 and T2 and their interspace is unit 1, and in the coordinate system frame formed from T1, T2 and H1 and H2 a Sin to the power 2 x curve using point of intersection of T1 and H1 as starting point is drawn; and B. calculating tide according to the invented method. Its advantage lies in that its calculation process is simple, convenient, visual, quick and accurate.

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SUBSTANCE: method of determining heat resistance of bentonite clay is characterised by that, a nomograph which reflects dependency of temperature of the second endothermal effect and heat resistance of bentonite clay from contained structural iron is constructed first. For this purpose samples of bentonite clay from known deposits are analysed. The samples are tested in a derivatograph. Derivatograms with differential thermo-weighted (DTW) and differential thermal (DT) curves are obtained, from which temperature of the second endothermal effect is determined depending on structural iron contained in the samples. Heat resistance of the samples is determined depending on structural iron contained in the samples. From the said two curves, the said nomogram is constructed, which is then used for subsequent determination of heat resistance of the analysed bentonite clay; a wet ground up sample is tested in a derivatograph by heating followed by drying. Derivatograms with differential thermo-weighted and differential thermal curves are obtained, from which temperature of the second endothermal effect is determined and heat resistance of the analysed bentonite clay is determined from the said nomogram. ^ EFFECT: cutting on time and simplification of the process of determining heat resistance.

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PURPOSE:To reduce planing trouble sharply by displaying a relationship between various planing variables necessary from the standpoint of train diagram planing graphically as a conditional judging chart, and forming, plotting and displaying a sample of the train diagram based on a variable value set on this chart. CONSTITUTION:A train diagram nomograph forming-plotting part 20 displays operating time for an operating interval featuring a train service, turn-back time for both terminal stations and the sum total on a display unit 14 by input out of a keyboard 12 via a man-machine interactive control part 11. A shuttle service period conditional judging type computing-plotting part 30 calculates a relationship between a shuttle service period and a train service time interval, while a turn-back time difference conditional judging type computing-plotting part 40 performs a calculation for avoiding any conflict of departure and arrival phenomena, and mutual relations of one-way service time of each speed classified train is calculated by a one-way time difference conditional judging type computing plotting part 50, displaying each of them, and on the basis of the judgment, a train diagram sample is displayed by a train diagram sample forming-plotting part 70. Thus, planing trouble is sharply reducible.

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SUBSTANCE: method provides for feed of massecuite to the agitators - crystallizers and measurement of the content of dry substances, purity and crystals in the massecuite, dry substances and purity of the mother liquor. The process of crystallization is carried out by cooling of the massecuite at agitation until the final preset values of temperature, content of crystals in the massecuite, dry substances and purity of the mother liquor are attained, they are determined by reference to a nomograph plotted beforehand. The scale of purity of the mother liquor is located in the lower part of the homograph, and the scale of the content of dry substances of the mother liquor of boiled massecuite before discharging is located its upper part. Located in the Y-axis of the homograph are the scales of the content of crystals in the massecuite, dry substances of the mother liquor of the massecuite at the end of cooling, final cooling temperature. Some of the curves of the homograph characterize the variation of the content of massecuite dry substances in the process of boiling, and the other curves have a section concerning the purity of the massecuite in the process of boiling, and a section characterizing the massecuite purity in the process of cooling. Depending on the found values of the content of crystals in the massecuite, dry substances and purity of the mother liquor, the content of dry substances and the purity of the massecuite before feeding of the massecuite to the mixers-crystallizers are corrected for attaining the final preset values of cooling temperature, content of crystals in the massecuite, dry substances and purity of the mother liquor. EFFECT: accelerated process of check of crystallization of the laser-strike massecuite, improved crystal structure of it and enhanced sugar output.

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FIELD: seismology. ^ SUBSTANCE: invention relates to the field of seismology and can be used for predicting tsunamis. Seismic signals are registered from earthquakes by seismographs, located in the peaks of equilateral triangles on bed rock. They determine the time the seismic signals were caused, the distance using triangulation. They measure the speed of the longitudinal and diametric waves in the volume of rock in the disposition of the triangle. The read the seismic signals from the earthquake. They measure the time of the delay. They determine using the two minimum times of the delay the azimuthal angles between the norm to the front of the seismic wave, occurring through the centre of the triangle, the epicenter of the earthquake, and the given initiating point of the report. The precise location of the epicenter of the earthquake, the magnitude of the temporal delay for the horizontal plain (surface of the earth), the angle of the location of the focus, the distance, the focus, the distance to the epicenter, the depth of the focus are calculated. At the seismic monitoring station with the aid of a computer the maximum magnitude of the observed underwater earthquake is calculated in microns or seismograms. The magnitude (M) is then calculated according to the Richter scale using a nomograph. If MëÑ7 then the conclusion is that a tsunami is possible. To confirm the accuracy of the information a check is carried out on the presence of tsunami waves with the help of information received by radio from a device for determining tsunami waves, located in the ocean in the proximity of contact between the lithosphere plates or the break in the earth's core. Furthermore, information is taken and analysed about the wave's movements from the surface to the seabed at a speed of 700-900 km/hour. The force of wave pressure is taken into account. The height of the tsunami wave is taken into account on its approach to the shore line. The time of the approach of the tsunami to the shoreline is calculated and the population informed. ^ EFFECT: increased responsiveness and accuracy in determining tsunamis.

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A calculating device comprising a flat generally oval-shaped card member having a perimeter defining somewhat semicircular sections interconnected by a central elongated section. The central section is formed of a generally straight periphery. A pair of indicating arms are rotatable about a pivot point on the member. The pivot point may be along the longitudinal axis of the card member, and offset from the center of the member. In addition, a scale may be printed on one side of the periphery of the member. Moreover, the semicircular sections can be identical in size, and a scale printed on the other side of the member and adjacent the periphery of the member may be the reciprocal of the scale on the first side. In addition, the calculating device may be used as a loan payment computer for determining the periodic payments due on a predetermined loan. By providing the card member with a plurality of interest rate curves which are juxtaposed with a plurality of loan duration curves, the scale may be representative of periodic payments. Thus, by positioning one of the indicia arms at the intersection of the desired interest rate and loan duration, the resultant position on the scale would be representative of the periodic payment for the intersecting interest rate and loan duration.

Nomograph or device for solving problems in spherical trigonometry
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Optical-mechanical nomograph
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SUBSTANCE: required magnitude of compression of stack may be determined by means of nomograph by actual magnitudes of working pressure in vessel, density of sealing graphite rings and height of stack of gland. Nomograph is plotted on basis of mathematical relationship of relative magnitude of compression of graphite rings versus their density and working pressure by the following formula:, where γis maximum density of rings made from thermally expanded graphite, g/; γ is density of rings, g/; P is working pressure of medium, MPa.\

SUBSTANCE: invention refers to medicine and represents a diagnostic technique for a primary-resistant form of a secreting extracranial germ cell tumor in children, involving determining an initial value of the alpha-fetoprotein (AFP) level in a patient with a morphologically verified germ cell tumour and AFP level with induction polychemotherapy, characterized by that the second AFP level is determined after two cycles of induction polychemotherapy on 40–43 days of treatment and use is made in Fig. 1 nomograph of the initial AFP level values matching and the AFP level after two cycles of induction polychemotherapy, constructed for a threshold half-elapse time of AFP of 6 days, an initial AFP level is found from the nomograph abscissa, ordinate - its value after two cycles of polychemotherapy, when these values cross the diagonal line of the nomograph, the primary-resistant form of the extracranial germ cell tumour is diagnosed.EFFECT: method enables diagnosing children with high accuracy, is simple and accessible in use.

SUBSTANCE: method involves determining structural features of crude material such as sugar content, titratable acidity, yield, selection of processing trend, degustation evaluation; measuring under different ecological cultivation conditions values of outside limiting factors at ontogeny phases of grape sort; designing, on the basis of data received, multiple regression models of association among structural features with outside limiting factors; selecting by parameters of model optimal harvesting time, cultivation zone, ecological conditions of which zone maximally correspond to genetic requirements of sort; building multiple regression models of association of degustation evaluation of grape wine with its structural features and, on the basis of data received, building nomograph; on the basis of said nomograph, judging kind and quality of wine by forming four quadrants defined by horizontal and vertical boundaries, first of which extends along line according to which wine has constant degustation evaluation regardless of level of titratable acidity and constant sugar content value, and second of which extends through point of intersection of all the lines on nomograph, with sugar content-acidity interval values lying on lines in left-hand and right-hand upper quadrants corresponding to higher-quality dry and special wines, correspondingly, and left-hand and right-hand lower quadrants corresponding to lower-quality special and dry wines. ^ EFFECT: provision for selecting grape sort or cultivation zone corresponding to genetic requirements of sort with predetermined quality and productivity factors, and defining optimal harvesting time owing to consideration of effect thereon of outside limiting environmental factors by ontogenesis phases to enable formation of quality and kind of wine.

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