Physical property data and estimates are often fitted to equations for analysis and dissemination. These equations are stored in each section's equations table control. For example, some equations for calculating Bubble Point Temperatures are shown below.
Sections use the Equations Dialog to add and edit Equations. This dialog is activated by clicking the left mouse button on the section's equations table control or by selecting the Edit Values command from the section's equations table control commands menu.
Each equation entry displays the equation's name, form and parameters. The independent variable is denoted by the character "X". The dependent variable is not shown. (See below for additional documentation on equations.)
The Equations dialog provides controls for editing equations, sorting values, and calculating values.
1

Table Control: displays the current list of equations. Each row contains the equation's name, form, limits, and coefficients. Clicking the left mouse button on a table row selects that table row. Clicking and holding the left mouse button down and then dragging the mouse will select several table rows. Doubleclicking the left mouse button on a row selects the row and edits the contents of that row. 
2

Edit Button: activates the Equation dialog enabling you to enter the equation's name, form, limits, a parameters. See below for documentation. 
3

Commands Button: pressing the dialog's Commands button or clicking the right mouse button on the table control displays the commands menu. This menu provides standard commands for copying, pasting, and clearing phase equilibria equations. See the documentation on Common Menu Commands for details. 
4

Sort Button: the dialog's Sort button will be enabled if two or more rows are selected. Pressing the Sort button activates the Sort Attribute dialog. This dialog enables you to sort curve points in ascending or descending order by the selected attribute. 
5

Add Rows Button: pressing the Add Rows button will add rows to the bottom of the table control. 
6

Calculate Button: pressing the Calculate button activates the Equation Values dialog which enables you to calculate equation results for a series of inputs. See below for documentation. 
Clicking the right mouse button within the dialog's table control or pressing the dialog's Commands button displays the Equations Dialog's commands menu.
The menu's commands enable you to copy, cut and paste values to and from the table control. See Common Menu Commands for documentation on the commands commonly found on command menus.
In Cranium and Synapse, equations have four key parts: 1) a name; 2) a form, also called the righthandside; 3) applicability limits; 4) coefficient values. The following values shows these four key parts for a typical equation:
Jul 16, 2021 at 09:20:47Key Part  Value 

Equation Name  MKS035P101 
Equation Form  A + B*X + C*X^3 
Composition, minimum  2.0 
Composition, maximum  99.0 
Coefficient A  340.72±0.44 
Coefficient B  0.0984±0.014 
Coefficient C  1.839E05±1.3E06 
The equation's right hand side must one or more 'X' varaibles, coefficients, and mathematical operators. Multiplication operations must be written explicitly, i.e., you must write "A*X" and not "AX".
You made enter equation terms in any order and include any spacing you wish. However, keeping equations in a consistent format will make it easier to find and reuse equations.
Clicking the left mouse button on a row in the table control or selecting a row and pressing the Edit button, activates the Equation Edit Dialog. The dialog enables you to enter the equation's name, form, limits, parameters, and supporting information.
1

Equation Name Control: enables you to a short text string for the equation's name. (See below for additional documentation about equation names. 
2

Equation Form Control: enables you to enter the 'righthandside' of the equation. Note that the application will check the validity of the entered equation before saving the dialog's entries. (See above for additional documentation about equation forms. 
3

List Button: activates the Equations Dialog which enables you to select the equation's name and form from a list of current equations. An initial menu enables you to choose from a list of standard equations or a list of all equations present in the current document. (See below for additional documentation on the Equations Dialog. 
4

Temperature Limits Controls: enables you to enter the minimum and maximum temperatures between which the equation is valid. 
5

Pressure Limits Controls: enables you to enter the minimum and maximum pressures between which the equation is valid. 
6

Composition Limits Controls: enables you to enter the minimum and maximum compositions between which the equation is valid. 
7

Coefficient Controls: enables you to enter values for each of eight coefficients, labeled A through H. A coefficient can be any valid real number. 
8

Coefficient Accuracy Controls: enables you to enter the accuracy of each coefficient value. 
9

Comments Control: the Comments control enables you to enter general information to better describe the entered equation. Very often comments document the date of entry, the name of the person who entered the value, the units of the x and y variables, and the source of the equation. 
10

Date, Phrase, Set Buttons: these buttons provide standard operations to help you enter comments. Pressing the Date button inserts the current date and time into the comment control. Pressing the Phrase button inserts the stored 'common phrase' into the comment control. Pressing the Set button enables you to change the 'common phrase'. (See documentation on the Set Phrase dialog for details. 
Cranium and Synapse compiles two lists of equations: a list of standard equations; a list of all equations. These lists are available within various regression and editing dialogs. Pressing the Equation Dialog's List button enables you to access each list.
Standard equations are provide by MKS and are always available for selection and use. Some of these standard equations are shown in the table below.
Eqn Name  Equation Form (RHS) 

MKS001  A + B*X 
MKS002  A + B*X + C*X^2 
MKS003  A + B*X + C*X^2 + D*X^3 
MKS009  exp(A + B*X) 
MKS010  exp(A + B*X + C*X^2) 
If you select the All Equations menu command, the application compiles all equations used for the current physical property and adds these to the list of stanandard equations.
The compilation of standard equations or all equations is displayed in the Equations Dialog.
Standard equations all have names of the form 'MKSXXX' where each X represents a number from 0 to 9. Many of the regressed equations included in MKS knowledge bases use this form as the core of the name and then append a suffix, e.g., 'T298', that provides some additional information. For example, if the equation is the result of regressing data at 298K.
When using the Equations Dialog, selecting an equation and pressing the dialog's Calculate button activates the Equation Values Dialog. This dialog enables you to enter an x value and then have the equation calculated for this x value.
1

Comment Control: displays the comment associated with the current equation. The comment may contain important information about units and limits of applicability that could influence you selection of x values. 
2

Table Control: displays the input x values and the calculated y values. 
3

Edit Button: activates the X Value Edit Dialog which prompts you for an x input value and, if present, displays the calculated y value. 
4

X Series Button: activates the Equation Calculations Series Dialog that enables you to enter a minimum and maximum x value which the application will use to generate and assign a range of x values. The Series button is enabled if two or more table rows are selected. 
5

Calculate Button: instructs the application to use the current equation to calculate an output y value for each input x value. These output y values are then displayed in the table control's Y Value column. 
6

Commands Button: pressing the dialog's Commands button or clicking the right mouse button on the table control displays the commands menu. This menu provides standard commands for copying, pasting, and clearing phase equilibria data. See the documentation on Common Menu Commands for details. 
7

Sort Button: the dialog's Sort button will be enabled if two or more rows are selected. Pressing the Sort button activates the Sort Attribute dialog. This dialog enables you to sort x values or y values in ascending or descending order. 
8

Add Rows Button: pressing the Add Rows button will add rows to the bottom of the table control. 
The output values calculated for equations are very often used as curve points. (See documentation on a Curve Points Dialog such as Temperature Dependent Curves Dialog or Compsition/Temperature/Pressure Dependent Curves Dialog for additional discussion on curve points.) However, additional state variables may be needed to be added before these values can be pasted into MKS documents.
Pasting the x and y values calculated from an equation into the Scratch Pad Dialog can be very useful. The Scratch Pad Dialog gives you the ability to add constant columns, e.g., temperatures or pressure, and calculate columns, e.g., the composition of component 2 when given the composition of component 1.
1

X Atrribute: set to Pressure 
2

A Variable: set to Constant. 
3

B Variable: set to X. 
4

Regression Coefficients Controls Group: this controls group shows the values of the regressed coefficients and their associated standard error and confidence limits. The results shown in this example indicate that the selected equation fits the data with high confidence. 
5

RSquared Statistic: the Regression Statistics table shows various summary statistics to help you determine the accuracy of the fitted equation. The RSquared metric in this example is very close to 1 indicating a very good fit of the data. 
Click the left mouse button one the table controls matching row and press the OK button.
Topic  Description 

Getting Started using Synapse  provides a quick tour of Synapse's capabilities including examples of chemical product design. 
Getting Started using Cranium  provides a quick tour of Cranium's capabilities including a discussion of structure editing. 
Estimating Chemical Properties  a short video demonstrating how to estimate the physical properties of chemicals using either Synapse or Cranium. 
Estimating Mixture Properties  a short video demonstrating how to estimate the physical properties of mixtures using either Synapse or Cranium. 