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Stanley-Amsler double act

Like the previous post’s Amsler Type 6 with its added spikes for engine indicator diagrams, today’s planimeter is another general purpose instrument with a special trick up its sleeve. Patented in 1894 by William Ford Stanley and Alfred Amsler (son of Jakob, inventor of the polar planimeter), this compensating planimeter with vernier scale was devised to address a particular problem: the correction of errors due to the shrinkage of maps and drawings.

Stanley-Amsler patent planimeter

The Railway Times of 17 November 1894 reported on the new instrument:

“Mr. W. F. Stanley, Great Turnstile, Holborn, the well-known mathematical instrument maker, has brought out a new planimeter by Dr. A. Amsler (the son of the original inventor of the planimeter). The idea of the method was proposed by Mr. Stanley, and Dr. Amsler worked it out. It is really a most important addition to the instrument, as it renders all the ordnance maps measurable for area which could only be computed heretofore trigonometrically by means of a scale made specially to the shrunk scale of the map.”

Of particular interest here is the subdivision of labour, with Alfred Amsler apparently undertaking the technical work necessary to realise Stanley’s commercial concept. The shrunk scales to which the article refers had been sold by Stanley in boxwood and ivory since the 1870s and were based on the observation that Ordnance Survey plans tended to shrink by approximately the same amount as a result of the printing process. Stanley gives the value of “about a seventh of an inch to the foot” in his book. These scales are seldom encountered today, but are easily distinguished by the designation “SHRUNK”, as seen on this boxwood example.

WF Stanley shrunk scale in boxwood detail

Accordingly, the planimeter scales for which the patented vernier was offered were those most commonly used for Ordnance maps, as listed in The Surveyor of 22 November 1894:

“The four following scales have been worked out and a corresponding planimeter is kept in stock: 1-2,500, 1-500, 6 in. or 5 ft. to the mile, and 12 in. or 10 ft. to the mile.”

Several contemporary articles gave an account of the instrument’s operation, which was relatively straightforward whether dealing with uniform shrinkage or with different degrees of contraction horizontally and vertically. A more comprehensive explanation of the mathematics behind the adjustment scale can be found in the patent specification, which according to The Engineer was the work of Alfred Amsler.

Stanley-Amsler patent compensating planimeter drawing showing vernier scale window

The patent drawing shows a rounded window cut into the top of the tracing arm housing, with vernier scales along top and bottom edges. Each vernier was associated with a specific scale mark on the back and front of the tracing arm respectively. On my example, the front vernier relates to the Ordnance Survey 6 inches to the mile scale (1:10,560) and its related units, while the back vernier is keyed to the larger OS scales of 1:2500 (aka 25-inch) and 1:500 (used for the most detailed town plans of the 1850s to 1890s).

Stanley-Amsler patent planimeter front and back views

Inside the lid of the case is a handwritten label with six constants relating to different scales on the instrument. These were used to obtain the area when the pole arm was located within the figure being measured, rather than outside, a useful technique for tracing larger outlines.

Stanley-Amsler patent planimeter in case

Such constants were usually inscribed on the top of the tracer arm (or sometimes on the pole weight for fixed-scale models), but on the Stanley-Amsler design they are displaced to its underside in order to accommodate the shrinkage scales on top. However, the six numbers beneath the arm of my planimeter are different to those on the label, which suggests the latter were the result of user recalibration.

My example is marked in the usual place with serial number 21196, which dates it to 1895, the same year that the patent was granted.

Stanley-Amsler patent planimeter serial number detail

The pole arm is signed “Stanley Great Turnstile, Holborn, London”, with the additional labels “Agent” and “Patent No. 13567”.

Stanley-Amsler patent planimeter address detail

In keeping with other Amsler planimeters of this era, the index wheel is still metal, while the roller and vernier scales are made of celluloid. Stanley continued to sell planimeters with the patented shrinkage scale for several decades, as confirmed by his catalogues. I have seen later models with celluloid index wheels, which also differ in being marked simply “Patented” without the number. In addition, there are examples of both type 5 (pantograph) and type 6 (indicator diagram) models which feature shrinkage scales.

While the Stanley-Amsler instrument was probably the first to incorporate a dedicated compensation mechanism for paper shrinkage, the idea itself can be traced right back to the genesis of the polar planimeter. A communication from Jakob Amsler himself appeared in the Neue Zürcher Zeitung of 23 October 1855 to explain the benefits of his new planimeter, in which the inventor suggested that:

“Die Instrumente können so eingestellt werden, daß keine Reduktion wegen Eintrocknen der Planblätter, an die Maßangaben anzubringen ist.”

(The instruments can be adjusted so that there is no need to reduce the dimensions due to the plan sheets drying out.)

Amsler's communication to the Neue Zürcher Zeitung of 23 October 1855

Unfortunately, there is no explanation as to how this adjustment would be made, other than by trial and error. Nor does Amsler’s 1856 description of his new planimeter offer any further clues. The 1855 newspaper piece is also of interest for the revelation that Amsler had not yet begun to sell his new planimeter at this date: 

“Der Preis eines solchen Planimeters ist noch nicht genau festzustellen, wird aber, je nach der Einrichtung und Ausführung zwischen 30 und 60 Fr. betragen. Gegenwärtig ist eine größere Anzahl dieser Instrumente, unter meiner Leitung, in Konstruktlon begriffen.”

(The price of such a planimeter cannot yet be determined exactly, but will be between 30 and 60 Francs depending on the fittings and design. Currently a large number of these instruments are being constructed under my direction.)

This suggests that the polar planimeter was unlikely to have been available to purchase before 1856, much closer to the date that Amsler began to appoint international agents, and possibly coinciding with the publication of his theory.

Returning to the Stanley-Amsler collaboration of almost four decades later, there is a final twist to the story that deserves clarification. From my research, it would appear that their invention represented the first use of the term “compensating planimeter” in the English language. However, by what seems to be complete coincidence, 1894 was also the year in which the Lang-Coradi Compensations-Polarplanimeter was introduced (see Zeitschrift für Vermessungswesen, Heft 12, 15 June 1894, p. 353), an instrument whose name was likewise translated to English as “compensating planimeter”.

In Lang and Coradi’s case, the compensation was not for paper shrinkage, but instead referred to the ability to use the tracer arm on either side of the pole arm by means of a ball and socket joint. This configuration made it possible to compensate for errors due to non-parallelism in the axis of the roller and tracer arm, essentially by measuring the same area twice – once with the tracer arm on the left and once on the right – and averaging the results.

Coradi’s modification was to become the dominant form of polar planimeter in the 20th century, especially in the United States, and in consequence the term “compensating planimeter” now refers to this type of instrument alone. Somewhat confusingly, Stanley’s catalogues continued to refer to his own design as the Stanley-Amsler Patented Compensating Planimeter, even after the firm began to sell Coradi’s compensating planimeter alongside it.

Coradi's compensating polar planimeter listed in WF Stanley's 1931 catalogue

Any ambiguity was finally brought to an end with the introduction of Stanley’s new range of domestically-manufactured “Allbrit” planimeters in the early 1930s, at first sold alongside Amsler’s models, but eventually to supplant them. The Stanley revised price list of December 1938 reveals that the Stanley-Amsler Patented Compensating Planimeter P2338 had been discontinued, with a note in parentheses: “Special features embodied in P2334A”. This referred to the new Allbrit equivalent of Amsler’s type 4, described in the price list as “Stanley Pattern, British Made” and priced three shillings cheaper.

WF Stanley Allbrit planimeter instruction booklet cover

The great irony, however, is that Stanley’s Allbrit planimeter was not based on the Stanley-Amsler design it replaced, or even on Amsler’s original type 4. Instead, it was essentially a clone of – yes, you’ve guessed it – Coradi’s compensating planimeter!

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