🚀 go-pugleaf

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I like to read older books in elementary physics, just to see what
things in the ed-biz change and which remain the same. I'll share
with you some problems from one of the older books in my
collection:
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Deschanel, A. Privat. Elementary Treatise on Natural Philosophy.
Translated and edited, with extensive additions, by J. D. Everett.
Appleton and Company, 1873. Earliest edition was published in 1868.
1068 pages.
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From=20the translator's preface:
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"[Deschanel's book] though only published in 1868, has already
obtained a high reputation in France, and has been adopted by the
Minister of Instruction as the text-book for Government Schools."
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"The treatise of Professor Deschanel is remarkable for the vigour
of its style, which specially commends it as a book for private
reading [self-study]. But its leading excellence, as compared with
the best works at present in use, is the thoroughly rational
character of the information which it presents. There is great
danger in the present day lest science-teaching should degenerate
into the accumulation of disconnected facts and unexplained
formulae, which burden the memory without cultivating the
understanding. Professor Deschanel has been eminently successful
in exhibiting facts in their mutual connection; and his
applications of algebra are always judicious."
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Does this concern about `disconnected facts and unexplained
formulae' sound familiar (and modern)? In the back of the book are
75 problems, illustrative of the sort of questions the student
should be able to answer upon completing the book. All these
problems are strictly verbal, with no illustrative pictures. (The
book itself does, however, have many pictures: very clear,
professionally rendered engravings.) Notice that the questions
seldom are simply "plug numbers into one formula and grind out an
answer". Note especially the conceptual difficulty of answering No.
6, and the mathematical care required for No. 15 (unless there's
a sneaky, insightful method which I haven't discovered). How would
today's students do on these questions?
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PROBLEMS {Selected, mostly without change, except for No. 9 which
was edited for clarity.}
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6. Explain the well-known fact that a straight stick, loaded with
lead at one end, van be more easily balanced vertically on the
finger when the loaded end is upwards than when it is downwards.
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7. Find the centre of gravity of a sphere 1 decimetre in radius,
having in its interior a spherical excavation whose centre is at
a distance of 5 centimetres from the centre of the large sphere
[and whose radius is 4 centimetres].
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9. A uniformly round table is suspended from its centre. At what
points of its circumference must weights of 4, 5, and 6 kilog. be
placed, that the resultant force may act at its centre?
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13. Two liquids are mixed. The total volume is 3 litres, with a sp.
gr. of 9.9. The sp. gr. of the first liquid is 1.3, of the second
0.7. Find their volumes.
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15. A frustrum of a cone of cork, the radii of its ends being 2 and
1 decim. respectively, and its height 1 decim., floats freely in
water, with its axis vertical. Find how much of its axis is
immersed, the sp. gr. of cork being 0.24.
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18. A sphere of cork, 3 cm. in radius, is weighted with a sphere
of gold. What must be the radius of the latter that the system may
barely float in alcohol?
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20. Given the weight of a body in air, and in water at maximum
density; deduce its weight in vacuo.
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29. A cylindrical test-tube, 1 decim. long, is plunged, mouth
downwards, into mercury. How deep must it be plunged that the
volume of the inclosed air may be diminished by one-half?
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37. A brass tube contains mercury, with a piece of platinum
immersed in it; and the level of the liquid is marked by a scratch
on the inside of the tube. On applying heat, it is found that the
liquid still stands at this mark. Deduce the ratio of the weight
of the platinum to that of the mercury.
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56. The specific gravity of platinum being taken as 22, and that
if iron as 7.8, what must be the ratio of the lengths of two wires,
one of platinum and the other of iron, both of the same section,
that they may vibrate in unison when stretched with equal forces?
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58. A pipe gives a note of 100 vibrations per second at the
temperature 10=F8 C. What must be the temperature of the air that the
same pipe may yield a note higher by a major fifth?
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64. A pencil of parallel rays fall upon a sphere of glass of 1
metre radius. Find the principal focus of rays near the axis, the
index of refraction of glass being 1.5.
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[End of Deschanel excerpts.]