A Book Review – slide-rules at the ready

[Nigel Graham 2Participant @nigelgraham2]

Constructing a tank of maximum volume from a given sheet…

“A piece of lead 10 feet by 8 feet is to be made into a tank by cutting four equal square pieces from each corner and bending up the sides…”

We are to calculate the size of the squares to give the maximum volume, by graphical means: the algebra builds to Volume y = ???? * I expect you had already derived the equation from the above but I give it below rather than here so you can treat it as a little puzzle!

This is the first arithemtic and mathematics text book that does not give a worked example then a long exercise. Instead it is all worked examples, with explanations.

Not sure if Reeves or M-Machine sell sheets of lead that big, and you’d need a handy-sized pan-folder, but whence this gem? A worked example in a book I had inherited from my father. It is:

Harrison H.H., Engineering Mathematics Simply Explained, 3rd edition, 1/6 Net. Date not stated but my Dad was a student in the 1930s, I think.

Other titles advertised in various appendices?

No.2 The Slide Valve simply explained.

No. 6 Model Boiler Making.

No. 10. Small Dynamos and Motors: How to make and use them.

No.25: The Beginner’s Guide To The Lathe.

No.36 Windmills and Wind Motors: How to build & use them. So now you can have your very own green-power workshop, from Nos. 10 and 36, with 2 and 6 to help with the Base Load plant.

These monographs were not cheap, at 6d net each, or 7d post-free.

Over the page, and we find advertisements for ….

  …. The Model Engineer & Electrician (pub. weekly, 2d. net or 3d. post-free)

and of The Engineer In Charge and Works Manager (monthly, 2d. from all newsagents, or 3-1/2d post free).

“This Journal”, the text begs to inform us, “is devoted exclusively to the Installation, Management and Repair of Engineering and Manufacturing Plant, and in this respect differs from all other engineering journals”.

Plant no doubt including pan-folders capable of forming our sheet-lead tank, all L X W X D feet deep of it**. That were when them in charge of Engineering Tradespeople, were Engineers!

And if you have not already guessed, the publisher of this book and its advertised literature was Percival Marshall & Co, 26-29 Poppin’s Court, Fleet Street, London. The professional journal was edited by Percival Marshall, A.I.Mech.E., himself so one might excuse a little puffery in the advertising!

What, I wonder, would our present publishers make of producing such a library?

……

* Volume y = 80x – 36x^2 + 4x^3.

Plot y against x values from 1 to 2 feet, at intervals of 0.2

**Ans: 7 X 5 X 1.5 feet.

The book goes on to demonstrate Calculus.

 

 

 

 

[noel shelleyParticipant @noelshelley55608]

Forgive me Nigel but was the question to calculate the size of the squares not the size of the tank?  1.5′ x 1.5′ ? Set level and full of water to weigh  3280Lb, almost 1.5 tons. Lead gauge not stated ! Noel.

[noel shelley]

On noel shelley Said:

Forgive me Nigel but was the question to calculate the size of the squares not the size of the tank?  1.5′ x 1.5′ ? Set level and full of water to weigh  3280Lb, almost 1.5 tons. Lead gauge not stated ! Noel.

Haha.  Not even that, if taken another step further.🙂  The size of each square would be 2.25 ft^2, so 9 square feet in total.

The gauge of the lead would depend on more than the depth (pressure, which acts in all directions in a fluid increases with depth.  All the weight of the water would bear on the bottom only but the hydrostatic pressure would increase as the depth increases.

Look up Pascal’s Blaising Barrel on youtube.  It’s all about exploding a 25l glass carboy just using a litre of water.

[Nigel Graham 2Participant @nigelgraham2]

The question was a bit ambiguous. It needed you find the maximum volume but finding the squares’ size does seems a bit like circular reasoning.

The problem was purely of volume, not wall strength. We could assume the lead is a liner for wooden or concrete walls!

The pressure is not part of it either, but at 1′ 6″ would be <1 psi at the bottom, decreasing to 0psi at the surface.

 

My A-Level Maths text-book used as one example, making a dog-food tin of a certain volume with minimum material: we not expected to suggest the food, or design the label.

Come on, the book is called Engineering Mathematics Simply Explained so we may safely assume its readers would be perfectly well aware of what they are dealing with! 🙂

√ √ √ √ √

I have others of my Dad’s degree-course text-books on Even Harder Engineering Sums Complified, in very advanced areas of algebra, equations, calculus, series, etc. indeed. Impossible for me. (He was a BSc., Chartered Electrical Engineer, Senior Scientific Officer in the Civil Service, so very highly numerate. And very practical. Unfortunately, numeracy is not genetic!)

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