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Make Graphoplex, France
Model 645 Système Commercial
Notes

1. Although this rule was made in France, and the instructions are in French, it includes currency conversion for the pre-decimal British system, and for Imperial and US units of measure.
2. For those not familiar with it, before decimal currency currency was introduced in 1971, the British system had the pound as the basic unit which was divided in 20 shillings each of 12 pennies.
3. Despite having the conversion rates for non-metric units of measure, the measuring scale is calibrated in centimetres. The instructions are in French. It appears therefore to have been designed for a French person who had to work iwth Imperial or US units of measure.
4.The rule has the CF and DF scales folded at 360. This is common on commercial rules as it was normal commercial practice to treat the year as having 360 days for interest calculations. The cursor only has one hairline whereas other commercial rules have a small hairline allowing multiplication by 365.
5. The back of the rule has a series of diagrams showing in a simplified way how different commercial calculations can be performed and tables of conversion factors.
6. The back of the slide has log-log scales for interest calculations and a duplicate C scale. To use it the slide has to be removed and replaced with the log-log scales showing.

Front view
1089-graphoplex-645-01.jpg (26016 bytes)
Detail - front left
1089-graphoplex-645-02.jpg (39995 bytes)
Detail - front right
1089-graphoplex-645-03.jpg (25428 bytes)
Back view
1089-graphoplex-645-04.jpg (39855 bytes)
Detail - back left
1089-graphoplex-645-05.jpg (30569 bytes)
Manufacturing date c 1965
Length 10"
Material Plastic
Scales DF [CF, CI, C / LL3, LL2, Ll1, C] D, £, s/d
Cursor Plastic, single hairline.

Summary of Instructions

Introduction

Whilst the rule can be used for basic calculations it is very much aimed at commercial calculations.

Percentage increase or decrease

1089-graphoplex-645-06.jpg (23845 bytes) Example: Increase of 30% on 130 francs or 30% off 130 francs.
1. Align the 130 CF with the 0 DF.
2. Bring the cursor the the (black) +30% mark.
3. Read the answer (169 francs) on the CF scale.

For a reduction use the (red) -30% mark.

Percentage increase or decrease for a list of items.

1089-graphoplex-645-07.jpg (34865 bytes) To calculate a percentage increase or decrease for a list of items, it is better to put the 1 of the CF scale under the appropriate percentage reduction or increase, and the read the answers on the DF or D against the original value on the CF or C scale.

In the example shown the reduction is 25% and the diagram shows the reduction from 8 francs,6, from 12 francs, 8 and from 3 francs, 2.25.

Purchase and sale price for a given profit.

1089-graphoplex-645-08.jpg (40790 bytes)Align the 1 of the CF scale against the appropriate profit margin. Against the purchase price on the DF or D scale read the sale price on the CF or C scale.

In the example shown, for a profit of 30 1/3%, the purchase and sale price would 5 and 7.5 francs or 2 and 3 francs respectively.

Discount and simple interest

1089-graphoplex-645-10.jpg (30921 bytes)The formula for simple interest is:

Interest = Principal * Duration * Rate

The method is to align the interest (% per annum) on the CI scale against the principal on the DF scale. Read the interest on the D scale against the duration in days on the C scale. This calculation makes use of the fact that the scales (CF and DF) are folded (relative to the C and C scales) at 360, the nominal number of days in a year.

The example shows the calculation for a principal of 72 000 France and interest rate of 3.5% per annum. The interest of 2772 is read against the period of 396 days.

Compound interest

1089-graphoplex-645-11.jpg (23362 bytes)The formula is:

Payment = Capital * ( 1 + Rate / 100) Duration (years)

The calculation has to be performed in two stages. First you calculate:
x = ( 1 + Rate / 100) Duration (years)
Then you calculate:
Payment = Capital * x.

To perform the first calculation it is necessary to remove the slide and turn it round. You the set the the value of "1+rate/100" on the appropriate LL scale (usually the one labelled LL1 on this scale) against the 1 on the D scale. The you read the value of x on the appropriate LL scale against the number of years on the D scale.

For example what would be total payment on a mortgage of 1 200 00 France at 4% for 15 years. Set the 1.04 against the 1 on the D scale and read the value of x,  1.80, on the LL2 scale. Note that we have got the answer on the LL2 scale. If the period had been 1.5 years we would have got the answer on the LL1 scale.

Next multiply 1 200 000 by 1.8 and get the answer 2 160 000 francs.

Conversion from £.s.d. (pounds, shilling and pence) to decimals of a pound

1089-graphoplex-645-12.jpg (6741 bytes)The basic, pre-decimal currency, unit of currency was the pound, this was divided into 20 shillings each of which had twelve pence. The penny itself was could be divided into half-pennies, written ha'penny, and farthings, a quarter of a penny although this was no longer used by the time of conversion to decimal currency in 1971. The advantage of the duodecimal. (i.e. 12 based) system as opposed to the decimal (10 based system) was that many more factors were possible. For example 12 has the factors 2, 3, 4 and 6 whereas 10 has only two factors, 2 and 5.

The example on the right shows the conversion from 11s 6d to decimal £ 0.575.

Conversion of Imperial/ U.S. units to metric.

1089-graphoplex-645-13.jpg (38874 bytes)Along the bottom of the rule there are a number of gauge marks for conversion factors from/to metric and U.S. and Imperial units. Whilst in many cases the Imperial (i.e. British) and the U.S. systems are the same for other units, for example the hundredweight (abbreviated cwt) this is not the case.

The instructions also  show a quick and ingenious way of doing the calculation in one set of units and getting the answer in another.

The example shows 4" * 3" * 1.5" with the answers in cm3 .

1. Set the cursor line to the cu.in mark.
2. Align 4 on the CI scale with the cursor.
3. Align the cursor with 3 on the C scale.
4. Align 1.5 on the CI scale with the cursor.
5. Read the answer 295 cm3 against the on the D scale against the 10 on the C scale.