"What do you do when you record av.lb. and av.oz. of babies say in an Excel spreadsheet, to later access the total weight, average weight, the variation, trends, and so forth?"
For the answer, I'll quote "Mathematics in Theory & Practice" published March 1946 in Liverpool, South Britain, United Kingdom of North Britain (Scotland), West Britain (Ireland), Britain (Wales), & South Britain (England).
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DECIMALS AND CALCULATING MACHINES
As we mentioned elsewhere, many calculations are today performed by ordinary calculating machines.
Decimals are particularly suitable for ordinary calculating machines because decimals are based on grouping by tens, just like ordinary numbers. This is just the same system as ten units making ten, ten tens making a hundred, ten hundreds making a thousand, and so forth.
As a result of the two systems being based on the same idea, it is possible to use an ordinary calculating machine to do sums with decimals.
But you cannot use an ordinary calculating machine to do sums with av.oz., av.lb., av.st., av. tods, av.cwt., and long tons, because in this system of weights the carrying over is based on all kinds of different numbers: 16 av.oz. making 1 av.lb., 14 av.lb. making 1 av.st., 2 av.st. making 1 av. tod, 4 av. tods making 1 av.cwt., and 20 av.cwt. making 1 long ton.
To do such work a special calculating machine would have to be built.
Nevertheless the ordinary calculating machine can be used to calculate sums of the above avoirdupois weights, just as it is now used in most modern offices to calculate sums of money.
Of course, like avoirdupois weight, the present money system is not at all suitable for an ordinary calculating machine, with 4 farthings to the penny, 12 pence to the shilling, and 20 shillings to the pound sterling. In order to get round this, girls who work calculating machines have to learn what is really a new money system: every amount of money is expressed in pounds sterling and decimals of pound sterling.
At the beginning each girl is given a printed table from which she can read off any sum of money as a decimal of £1. The table has 959 entries for the decimal values of every sum of money from 1/4d. to 19s. 11 3/4d. Although the abbreviated table below can be used, it will often be found that an extra calculation, or sometimes two extra calculations, will have to be done on the ordinary calculating machine (or in the mind) to obtain the final answer. With the full 959 entry table, no such extra calculation is necessary.
Thus the decimal equivalent of:
10'- is .5 of £1
2'- is .1 of £1
7'5 3/4 is .3 739 583 333 of £1
Thus, if a girl had to find the cost of 1,760 articles at
£2 7'5 3/4 each, she would set the machine for multiplying
1 760 .000 000 by 2 .373 958 After the machine had worked out the answer to this question, the table would again be used to turn the result back into pounds sterling, shillings, pence, and farthings.
With some practice, the girls get to know by heart the value of each sum of money as a decimal, and no longer refer to the table.
For such work it is not necessary for a girl to do long calculations in ordinary arithmetic, since the ordinary calculating machine does these. So it is an advantage to know the general idea of what a decimal is.
This point seems worth mentioning, as it is not widely realized that money sums are now done by decimals on an ordinary calculating machine, rather than by the method used in the older text-books.
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On reviewing the above quotation, I am not satisfied with it.
Firstly, it does not directly answer how to calculate avoirdupois weights.
Secondly, it chose money as an indirect example of how to calculate avoirdupois weights. Nothing wrong in principle with an indirect example, but money was the wrong indirect example.
That is because every street corner store in England & foreign parts, had a special calculating machine for money. It was called a
£ s. d. f. cash register. And I saw them in their packing boxes in Dayton, Ohio, before they were shipped out to sundry locations in the British & Indian Empires.
I do not doubt the truthfulness of the book's answer, but it does not make it clear to me why girls handling large amounts of money found it just as easy to use the ordinary calculating machine, as it was to use the
£ s. d. f. special calculating machine. Maybe it was because the ordinary calculating machine could be used for anything with the proper table, whereas the
£ s. d. f. special calculating machine could only be used for money, and therefore the expense of two different calculating machines could not be justified.
But what about banks and savings & loan associations: all they would handle was money and therefore presumably they would just have
£ s. d. f. special calculating machines. Well, not according to the book quotation above.
There are many models of £ s. d. f. cash registers and many models of
£ s. d. f. calculating machines. Clearly you had to use the
£ s. d. f. cash register in the store. But why the ordinary calculating machine in decimals was more popular for
£ s. d. f., than the special calculating machine in
£ s. d. f., is not clear to me.
Whatever my thoughts, it is obvious that the ordinary calculating machine using decimals presents no difficulty in calculating
£ s. d. f., or calculating avoirdupois weights, or calculating common linear measures.
I have seen special calculating machines for avoirdupois weights, but never used one.
I have briefly used special calculating machines for common linear measures.
So Ralph, in order to answer your question more directly, I am going to answer it myself.
The Egypt/Arabic number system is unique in that it is based on one number only: ten. That is, ten units make ten, ten tens make a hundred, ten hundreds make a thousand, ten thousands make ten thousand, and so forth. The advantages & disadvantages are obvious. It is a system that is easy to count with but difficult to measure with.
The ordinary calculating machine uses exactly the same system as the Egypt/Arabic number system, up to 9,999,999,999 Larger machines that can calculate larger numbers are exactly the same, they simply have more columns to calculate tens with.
The ordinary calculating machine can also be used to calculate decimals, either on its' own or in combination with the Egypt/Arabic number system. That is because decimals operate on the same system as the Egypt/Arabic number system and the ordinary calculating machine. Ten tenths make one, ten hundredths make one tenth, ten thousandths make one hundredth, ten ten thousandths make one thousandth, and so forth.
The Common Weights & Measures system continues on with the system that the Egypt/Arabic number system originated from. Usually there are at least two numbers used, and often more than that. On those rare occasions when only one number is used, it is never ten as ten is so difficult to measure with. An example of the later is 16 av.dp. making an av.oz., and 16 av.oz. making an av.lb.
So let's run through some of those numbers.
6.4.60.60.4 = common time measure
6.60.60.60.4 = common sexagesimal measure
9.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.3.20.4 = old avoirdupois weight
20.2.2.2.2.7.16.16.30.4 = new avoirdupois weight
60.88.12 = statute common linear measure
2.3.12 = short common linear measure
8.40.4 = common superficial measure
9.2.2.2.2.2.2.2.2.2 = common dry measure
2.2.63.2.2.2.2.2.2.2.2.2.2.3.20.4 = common fluid measure
6.60 = common temperature measure
20.12.4 = £ s. d. f. currency
The use of the ordinary calculating machine for decimal parts of £1 seems reasonable. (Although the above book quotation has not made it clear to me the advantage it has over the
£ s. d. f. special calculating machine.) A complete table of 959 entries could easily be made up by an individual in an hour, for permanent use by everyone forever and a day. Furthermore everyone in business not only uses money, but all denominations of that money, so such a table has universal use.
The use of the ordinary calculating machine for decimal parts of a merchant last, does not seem reasonable. A complete table would require 41,287,679 entries. I have no idea how long it would take to construct such a table, but it would be considerable. My guess is that it would be more practical to just use the ordinary calculating machine for a specific merchant last calculation, if it was thought the machine might be useful on that specific occasion. Furthermore, not every business uses old avoirdupois weights, and of those that do, most do not use the merchant last denomination of the avoirdupois weight. So that if such a mammoth table was ever constructed, it would have very limited use to absolutely no use.
What about the pages and pages of various mathematical tables, logarithms, and trigonometric functions. I am sure someone somewhere can come up with a reason for them all, but I don't think anyone can do the same for 41,287,679 entries for the merchant last.
However Ralph, you asked how midwives and maternity ward nurses could enter avoirdupois lb. & avoirdupois oz. baby weights on Excel sheets.
On the very first day of their 52 year career, every midwife and every maternity ward nurse takes a minute or so to construct a table of 15 entries, which she then keeps in her pocket or in a book for the rest of her career. She probably never refers to the table as it is so simple, she invariably memorizes all 15 entries.
In case you ever become a midwife with Excel sheets, I have taken 31 1/2 (00.00.31.2 sexagesimal or 31.5 decimal) seconds out of my day to construct such a table for you and your babies below.
P.S.
Ralph,
If you don't have 31 1/2 seconds to spare out of your 52 year dream career, just enter your fraction of an av.lb. into the Excel cell and it will convert it into a decimal. Excel will also convert your decimals back into fractions. Come to think of it, Excel is no different from those 1946 Liverpool, South Britain, "modern office" 15 year old girls. Excel is just slower & cheaper.
Hmm, I agree that those girls then were faster doing calculations in their head than the average person today, I kind of doubt though that any of those girls could do 5 Gigaflops.
BTW, you might want to consider adding Flops and Mips to your webpage, they are quit common measurements.
If you don't know what a Flop is, look it up.