John Perry and Alwin Walther, two pioneers of engineering mathematics.
The teaching of mathematics to the engineering
community is a subject that is very dear to my heart and something that must
have been of considerable importance to the industrial nations. Two members of the senior professional
teaching fraternity made considerable contributions to the subject. Both men invented slide rules, one of which
went on to become the final extremely popular standard scale layout for
engineers, the Darmstadt standard.
In Professor Dr. John Perry's outstanding book
(1), The Calculus for Engineers a
statement from Lord Kelvin of Largs (2) is quoted in the Foreword: "…that there is no useful mathematical
weapon, which an engineer may not learn to use". Whether Lord Kelvin actually thought of the
slide rule we will never know, but Perry went on to design his slide rule.
Perry (1850 - 1920), Figure 1, was a Fellow of
the Royal Society (FRS), Professor of Mathematics at the Royal College of
Science in London, and an important advocate of mathematics in England. He reformed the teaching of mathematics in
the basic schools (3) and instigated a very successful series of lectures for
the working man, introducing them to mathematics (4). It is probable, but not proven, that he also
mentioned the slide rule. His greatest
achievement was that he imparted the basics of mathematics to engineers at that
time. His Obituary (5) gives a wonderful
quote from him: "When I am among
scientific men I pose as a professional man - and when I am among professional
people I pose as a scientific man - and when I find both professional and
scientific people together I try and hold my tongue". His work in imparting mathematics to
engineers is emphasised in the preface by two German Professors to the German
editions of his book (6)(7). Their
statement "Wir Deutsche waren eben
nicht so glücklich, wie z.B. unsere Nachbarn im Westen, führende Geister zu
besitzen, welche zugleich im Lager der Techniker, wie in dem der Mathematiker
die Anerkennung besaßen" - "We Germans were not so lucky as, for
example, our Western neighbours, to have leading spirits, being able to have
the same acceptance in both the camps of the technicians as well as the
mathematicians". This applied to
Perry, and he also went on to develop a slide rule layout which was named after
him (System Perry) which was the subject of a patent (no 23,236 of 1901) and
which was made and sold originally by Thornton (see Cajori (8)). The design was adopted by Nestler in about
1908 who continued to sell it as the No 25 until about 1937 when it was
replaced by the Darmstadt arrangement.
Figure 1: Dr. John Perry
The System Perry slide rules carried the basic
scale arrangement of A/B,C/D with the additional novelty for that time of a
continuous LL scale on the upper and lower edge of the front of the rule. The Thornton Perry slide rule is shown in
Figure 2, (taken from an A.G. Thornton advertisement in The Handbook of the Napier Tercentenary celebrations, published in
Figure 2: Thornton Perry Slide Rule
The Nestler version (taken from a Nestler
catalogue of 1911) has a scale length of 25cm, was made from Mahogany faced
with celluloid, and is shown in Figure 3. Differences that can be seen are minor, such
that one could believe that Thorton devices were made by Nestler, despite what
is implied by Cajori.
The Nestler (Perry) Model 25 has the following
scales from front top downwards: LL from 1.1 - 104, A/B,C/D, LL from
0.91 - 10-4, i.e. a two cycle positive and a two cycle negative
log-log scale. The log-log scales are
related to the A and B scales appropriately.
Perry developed the log-log scales to achieve the optimum (in his
opinion) range and accuracy. At that
time the use of e = 2.718 had not yet been selected as a base for the
arrangement of log-log scales, Perry took 2.51 as the base for his scales, 2.5110
= 104, and 2.510.1 = 1.097 respectively.
Figure 3: Nestler Perry Slide Rule
The reverse of the slide had the usual S and T
scales as on System Mannheim slide rules
Nestler extended the ideas of the Perry slide
rule design into an improvement of the original System Peter, Model No 35. This had two Log-log scales similar to those
of the Perry but with a base 2.2 and with the sin.cos and cos² scales for
tacheometric/stadia calculations on the rear of the slide (9). Upper LL scale: 2.210 = 2.65 x 103,
and 2.20.1 = 1.082 respectively; lower LL scale: 2.2-0.1
= 0.924. See Figure 4.
Figure 4: Nestler Peter Slide Rule
The development of log-log scales on slide rules
reached its peak some 30 years later in the development of the Darmstadt scales
by Alwin Walter.
Professor Dr. Walther, Figure 5, was Professor of
Applied Mathematics at the Technical University in Darmstadt, Germany, from
1928 to 1966. He was another strong
champion of mathematical teaching to all - mathematicians, natural scientists
but especially to engineers. He founded
the IPM (Institute for Practical Mathematics) making the link from
mathematics to information technology; and he was a leading developer of
computers in Germany.
Figure 5: Dr. Alwin Walther
However, in 1934 slide rules were still
completely relevant. Together with his
team, Prof. Walther developed the Darmstadt slide rule layout which was to
become one of the most popular standards for engineers lasting until about 1950
when it was replaced by Duplex slide rules with widely expanded ranges of
The Darmstadt system was a single sided design
with the following layout: L,K,A/B,CI,C/D,P,S,T on the front, but the usual
trigonometric scales on the reverse of the slide replaced with three log-log
scales (from 1.01 to 100,000). The
unusual placement of the log-log scales on the rear of the slide rather than
the more usual front of the rule caused no problems in practice, and the model
became very popular.
All three major German manufacturers,
Faber-Castell, Aristo - Dennert & Pape and Nestler, made Darmstadt
rules. Faber-Castell were the first to
manufacture a Darmstadt rule and became the leader of this design with 12.5cm,
25cm, and 50cm versions. The most
popular design was the Faber-Castell 1/54 (25cm) Darmstadt rule made of
pearwood with celluloid facings, see Figure 6.
Figure 6: Faber-Castell 1/54 Darmstadt Slide Rule
Notes in the slide rule instruction manual
referred to the authorship of Dr. Walther and his team and made his name and
"Darmstadt" well known. A
comprehensive contribution to dating Faber-Castell System Darmstadt slide rules
(1935 - 1976) was published some years ago (10). The Darmstadt arrangement was adopted by
European (including British) manufacturers and also by Sun-Hemmi in Japan, but
not any of the American manufacturers (11).
We can see how two very important mathematicians
acted very successfully in the same way, one in England at around the turn of
the century (Perry) to develop a log-log slide rule, and the other some 30
years later in Germany (Walther) to develop the final and most important log-log
scale layout, the Darmstadt. Both of
these men also contributed considerably to the training of engineers in that
most important of topics - the "Weapons of Mathematics".
and additional notes.
1. "Höhere Mathematik für Ingenieure" von Dr John Perry, FRS, Dritte Auflage, 1919, B.G. Teubner, Leipzig-Berlin, Vorwort zur ersten Auflage (1902) p viii. The original edition is "The Calculus for Engineers" by John Perry, 1st edition 1896 by E. Arnold, London.
2. Sir William Thomson, later Lord Kelvin of Largs, (1824 - 1907), English Physicist, one of the greatest natural scientists of the 19th century.
3. "Elementary Practical Mathematics, with numerous exercises for the use of Students", Prof. J. Perry, Macmillan & Co, London, 1913.
4. "Practical Mathematics, Summary of six lectures, delivered to working men" by Prof. John Perry at the Museum of Practical Geology, Jermin Street, February and March, 1899, with certain exercises supposed to be worked after every lecture. 1899.
5. "Obituary Notices of Fellows deceased" By H.H.T. in the Proceedings of the Royal Society, 1,1926, piii. "It is, fortunately, not necessary to discuss whether Perry's direct contribution to knowledge, or those which flowed from his own teaching and his influence on other teachers, are the most important. The obituary goes on to cite: A report by The Mathematics Association titled "Teaching of Mathematics to Evening Technical Students" opens in the following words: "Mathematics has long been recognised as an important element in the education of engineering and other technical students. Much thought has been devoted to the problem of presenting mathematical ideas in such a form that they can be assimilated and applied to technical problems. At one time the presentation was undoubtedly too abstract. This tendency has now disappeared, chiefly owing to the efforts of the late Prof. Perry. His methods have been adopted very widely. When they were first introduced, they aroused great enthusiasm, and it was hoped that henceforth no difficulty would be experienced in imparting a good working knowledge of mathematics to every student of average capacity. Subsequent experience has proved that these hopes were too sanguine. Some very good work has been done, both by teachers and students, and yet in the opinion of many, the results obtained are somewhat disappointing".
6. "Höhere Mathematik für Ingenieure" see (1). Preface to the 1st edition.
7. "Prof. Dr. Robert Fricke, o Prof. der Mathematik an der Technischen Hochschule zu Braunschweig, und Fritz Süchtig, o Prof. für Maschinenkunde und Elektrotechnik an der Bergakademie zu Clausthal".
8. Florian Cajori - "A History of the Logarithmic Slide Rule and Allied Instruments", mentions in the preface page iii "advanced mathematicians as Segner, Perry, Mannheim, Mehmke and the great Isaac Newton". He also lists the "Perry Slide Rule" at 1902, and "Perry's New Slide Rule" at 1908, placed on the market by A.G. Thornton.
9. Letter from Günther Kugel to the author about Nestler's Perry and Peter slide rules.
10. "Faber-Castell Rechenstäbe System Darmstadt" Dr.-Ing. E.h. Günther Kugel; Historische Bürowelt, 1997, No. 47 pp 25-30; No. 48 pp 27-30.
11. For example, the Unique Brighton slide rule, and the Sun-Hemmi No 130.
My thanks to Peter Hopp
for his help and advice.