The Sillcocks Miller Crichlow Artillery Rule

This remarkable 12 inches diameter circular rule was patented in 1936 by the US Army Captain Robert William Crichlow, by that time instructor at the Coast Artillery School at Fort Monroe, Virginia. Antiaircraft artillery requires trigonometry to solve triangulation problems, and Captain Crichlow designed this rule as a calculation aide, when, for instance, the Law of Sines was used to solve oblique triangles.  

The Crichlow Artillery rule was produced in the United States by The Sillcocks-Miller Company,  specialist in high quality, precision-made plastics,  seated in Maplewood N.J. There is little information about this company in the WEB, so the production years  cannot be determined with precision, but this rule was first described in a 1940 Antiaircraft Artillery Field Manual [1]. The Crichlow rule also appeared in a subsequent 1942 field manual, and in a 1943 artillery textbook [2], so can assume as production years 1936-1945 (?).

This binary (two cursors) circular rule was fabricated with thick plastic where scales were printed, coated with a protective transparent plastic sheet, and two movable transparent plastic arms screwed at the rule's center. The first design of this rule has differences with the model M1 in this collection [1]. I have not seen physically one of those first designs but only a print in the FM 4-110 Coast Artillery Field Manual. Antiaircraft Artillery. Gunnery, Fire Control, and Position Finding, Antiaircraft Guns. Edited by the US War Department in 1942. Originally it had six scales, labeled from inner to outer: F, E, D, C, B, and A.  From all these scales, E was a standard one cycle logarithmic scale (1-10), F was a double cycle logarithmic scale (squares), while the other were trigonometric scales not divided in degrees but in mils, the unit used to measure angles in artillery (45o  = 800 mils).  

In the redesigned Crichlow M1 model, referred in 1940's documents, two scales were removed: the protractor scale  F  (0o-360o  or  0 mils- 6400 mils), and the  trigonometric scale A  used to compute the Cosecant function (1/Sine) for angles 105 mils - 1500 mils (5.9o -  84.4o).  The remaining four scales were redesigned and redistributed. 

The Crichlow M1 has the scales, from outer to inner: D,E, B, and C. The scale D, a three cycles scales, is used to compute the function Cosecant (1/Sine) for angles  10 mils - 3100 mils (0.56o -  174.4o), the scale B is use to compute the function Secant (1/Cosine) for angles 100 mils - 1497 mils (0.564o - 84.2o), and the double scale C is used to compute the functions Cotangent for angles 105 mils - 800 mils (5.9o - 45o),  and Tangent for angles 800 mils - 1495 mils (45o - 84.09o). The explanation and examples of how to use this scales to solve oblique triangles it is out of the scope of this introduction, but it will be soon (I hope) in a separate document attached to this page

Only one of the items in this collection has an engraved serial number, but there is no reference to verify the fabrication year. The other rule had a printed label with possibly a serial number but this label faded with the years. But according with the documents making reference to the Crichlow M1, it possible to conclude that these items were fabricated in the lapse 1939-1945 and were used by the US Army in WWII, 

But comparing the designs and some of the materials used, the most recent is the one with the brass head:

There was also in this collection a version of the Crichlow rule made with a thick card-stock. I have not found any reference of this specimens fabricated with card-stock, I assume that this was a prototype of the second version with four scales,  possibly fabricated by 1938-1939. I made this conclusion based on the post stamp on the envelope this rule was sent to its user: First Lieutenant Emil F. Gehri. The post stamp is a John Tyler 10 cents issued in 1938.  Next are picture of this card-stock model compared with plastic one. 

References: 

[1]  Borchers, Brian: The Crichlow Slide Rule. Journal of the Oughtred Society. http://euler.nmt.edu/~brian/crichlow.pdf  

[2]  Levy, Sophia Hazel: Introductory Artillery Mathematics and Antiaircraft Mathematics. University of California Press. 1943

[3]  The Generals of WWII. General of the USA. https://generals.dk/general/Crichlow/Robert_William_Jr./USA.html