Introduction

This rule is one of my specialised rules - that is, it is designed for one specific purpose. In this case it is for calculating the cost of producing steam and energy from coal fired boilers. The rule was produced for Vickers-Spearing Boiler Co. Ltd. of 20 Kingsway, London WC2. On the front of the rule is a notice "Copyright H.W.Healy, 1923". My guess is that it was produced around this time.  Below I give first a simple description of how to use the rule. Since some of the terms in the explanation might not be very meaningful to the non-initiated, I then give some more background information.

Use of the rule

Set the price of coal (in shillings per ton weight, upper left slide) against the calorific values of the coal (in British Thermal Units per pound weight, upper left stock). In the example shown the values of twenty shillings per ton and 10(thousand) B.T.U.s per pound are used. Set the cursor to the arrow against the 100% efficiency.

Move the slide so the boiler efficiency (bottom right slide) is against the cursor, in this case 90%. Read the cost of evaporating water in shillings per thousand gallons against the upward pointing arrow (9.55, upper right stock) and cost in pence per million BTUs against the 100% efficiency (11.9, lower stock).

In the above the expression "F & A 212°F" stands for "from and at 212°F" and therefore does not include the cost of heating the water from its initial temperature to boiling point nor in producing superheated steam at a temperature higher than 212 °F.

Pre-decimal currency and cost of coal

Before decimalisation (1971) the pound was divided into 20 shillings, each shilling of 12 pence and each penny of 4 farthings (largely obsolete by 1971) . If the price included pounds then, for example, 7 pounds 3 shillings and 4 pence was written £7 3s 4d (from the Latin "libra, solidus, denarius"). If pounds were not given then, for example, 3 shillings and 4 pence was written 3s 4d or 3/4. If there were no pence then, for example, 12 shillings was written 12/-.

I had assumed that it might be possible to date the rule by cost of coal at different times but was surprised that this was not the case. One source gives the cost of coal in 1833 in London (with an interesting breakdown of the components of cost) as 17s 9d, well within the range of values on the rule. Another source gives a range of prices in 1906 from 27/6 to 44/6 which goes past the range on the rule. Yet another source quotes the cost of coal in Australia in 1874 as 12/- per ton.

Calorific value of coal

Not all the solid matter of coal is combustible. The upper left of the stock has scales for % non-combustible and calorific value. The non-combustible proportion is made up of ash and water. These scales assume a fixed relationship between percentage non-combustible and calorific value. This ties in with other sources I have found. On the other hand the range of calorific values on the rule goes from 8000 to 13000 BTUs per pound weight of coal. Two of the sources I have found (one Australian and one US) quote values of 13 700 for the calorific value, which is off the scale. An Argentine source gives 11000, which is well within the range. The British Thermal Unit is widely used and I have even found references to it in a French web site! It is sometimes written BThU which complicated the web search as it seems that "Thu" is a very common name in Vietnam!. 1 BTU is equal to 0.252 kcal and is the heat required to raise the temperature of 1 pound of water by 1 degree Fahrenheit.

Basis of calculation

Both of the above calculations could be performed with a normal slide rule.

CpM = 1000* (Pr *12)  /(CV *2240 *(Eff/100))

where:
CpM = Cost per million BTUs in pence.
Pr  = Price of coal in shilling per ton. The factor 12 is to convert shillings to pence.
Efficiency = Boiler efficiency
CV = Calorific Value in 1000s BTU per pound weight. The factor 2240 is to convert (Imperial) tons to pounds.
The factor of 1000 is to convert the answer to pence per million BTUs.

The second example can also be performed with a normal slide rule.

CpG =Pr *  9700/ (CV*2240*(Eff/100))

where:

CpG = Cost per 1000 gallons of water evaporated in shillings
The factor 9700 is the latent heat of vaporisation in BTUs per (Imperial) gallon.

Summary

Working all this out has taught me several things:

1. Whilst specialised rules simplify specific calculations the downside is that assumptions made may not have general validity. For example, calorific values higher than the maximum on the scale were not unknown.
2. To fit the answers into a limited space the units of measurement have to be adapted accordingly. Why, for example, use pence for the cost per BTU produced and shillings for the cost of evaporation?

Searching the internet for information has also proved very fruitful and I was able to get explanations of all the factors in the calculation - including a tutorial on boiler design. I was also surprised how frequently coal was mentioned e.g. a political pamphlet by Engels, explanation for the fall of the German republic in 1938 (coal in Germany was twice the price of coal in England due to the system of land tenure) and a black coal miners' strike in South Africa in 1946. In short it's added a sociological/historical perspective to my slide-rule collecting.

References

The calorific value of coal during World War II in Australia.
    http://www.railpage.org.au/comrails/wthcr/html/w01.html

The calorific value of coal in Argentina
    http://www.rieles.com.ar/revista/ENERO-FEB/historia.htm

The calorific value of coal in the Pennsylvania Railroad
    http://www.cwrr.com/Lounge/Reference/baldwin/part03.html

Reference to the cost of coal
    http://www.abridgewater.freeserve.co.uk/Mining.htm

A tutorial on boiler design
    http://www.kewaneeboiler.com/tutor/bbd5.htm