FOB WATCH SPHEROMETER
 If you're a metrication aficionado this will greatly irritate. In my collection of antique scientific instruments is a fob watch 'lens measure' or 'lens clock', a lens maker's spherometer. I found it many years ago (early 1990's) at a London camera fair. The stall-holder had it on display amidst an assortment of similar sized fob watches, thought it was a broken fob watch, and sold it cheap. It is fairly valuable. It is invaluable to me for two reasons; it is useful, and it is very revealing when you investigate its history. Do not let appearances deceive, it is far older than it looks. Notice there are two scales, An inner scale marked "DIOPTRIES" and an outer scale marked "POUCES". The "DIOPTRIES" scale is an antiquated French form of 'DIOPTRE', which is the current measure of lens power. A simple thin lens with a power of 1 Dioptre has a focal length of 1 metre. Dioptres are used by spectacle lens makers because there is a direct relationship between the lens radii and its power. The Dioptre was introduced in 1872 A "POUCE" is the old French INCH. Yes, the French used to use "INCHES"! The original definition of the Pouce is the thumb or big toe upper digit. Pouce is French for thumb. (In other words the French used a similar system to the British). The thumb of the King was given to be 750/27,706 metre or 443.296 lignes. In 1799 Napoleon Bonaparte decreed that a Pouce was 1/36 of a meter Belgium optical glass manufacturers continued using Pouces or the French Inch long afterwards. When the French Huguenot glass workers came over to Birmingham in the early 1840's they brought their traditional ways with them to Chance Bros. Thomas Cooke's achromatic refractors, until his sons took over the business after his death, were all sized in French Inches. For example the 6-inch Cooke & Sons refractor at Rossall, c1870 is in fact 6 Pouces aperture or 6".5, which indicates the lens was made earlier than the mount, by several years. Now I said 1 Pouce = 1/36 metre. True, but, the original pre-metrication (1812) metre was shorter than the adopted Napoleonic (1840) metre. Napoleon decided the new metre would be 1/10,000,000 the distance from the equator to the pole along the Paris meridian. Hence it increasing from slightly over 36 Imperial inches to 39".7 Imperial inches. In terms of Imperial inches the Pouce was 1".065738, but in terms of the post 1840 metre it is 1".093613. The way this device works is curious, and at first glance you miss it. It looks to be off calibration. The pointer is on just under 1 Pouce convex when not measuring. But notice it can measure both convex and concave sagittal depths ±20 Dioptres. When you press it against a hard flat polished surface it reads '0' Dioptres. The scale has to be divided such that 1 Dioptre equates to a lens focal length of 1 metre. But which metre? Look at the 1 Dioptre scale line, note the equivalent radius in Pouces is between 36 & 42. It is to all intents and purposes half way in between, so it is not unreasonable to judge the reading to be 39 Pouces. Now take a close look at the 10 Dioptre scale line. The corresponding Pouce reading is just under 4. If you multiply the reading by 10 to get the Pouce equivalent of 1 Dioptre, you obtain about 39.7. So this lens measure is based on the Pouce being not 1/36th of a metre but 1/39.7th of a metre. (NB 1m = 39".37 so the scale is based on 1 Pouce = 1".0095) If you take the Lens Maker's Equation If you have the least enquiring mind you will find this fact curious indeed. Here we have a French or Belgium lens clock An interesting find with a hidden history. Incidentally there is a female threaded hole in the rim, opposite the spring loaded pin, to fasten the fob watch spherometer to a key chain. The face is labelled 'SPHÉROMÉTRE G.L. BTE S.G.D.G.' This is not a maker's identification. 'G.L. BTE S.G.D.G.' refers to the practice of the Second Republic (1848-52) and the Second Empire under Louis Napoléon Bonaparte (1852-71) to grant a patent without a government guarantee of quality. "Guarantie Limitación Sans Garantie de Gouvernment". ______________________________________________________________________________________________________ USING A LENS CLOCK
How do you use a lens clock? It measures the depth of the lens curvature between the outer pair of pins. It can measure concave and convex surfaces. To find the focal length of a thin crown glass lens all you have to do is measure the power of each surface in Dioptres. For example suppose you have a positive meniscus BK7 lens whose surfaces are 13.8D & -3.5D (concave surfaces have negative Dioptric powers) the net power would be 10.3D. But suppose the lens is thick, what do you do then? You need to measure the axial thickness or calculate it from the edge thickness and the radii of curvature derived from the Dioptre measures. However the Radii of curvature need to be corrected for refractive index. The Dioptre measurement is based on crown glass n = 1.523, BK7 n = 1.5168. Lens radius R = (n-1)/P where P = surface power in Dioptres. Calculate R based on n = 1.523, then substitute R into P' = (n'-1)/R where n' is the actual refractive index & P' is the actual Dioptric surface power. The alternative is to substitute the scale readings into Gullstrand's equation 
lens cross section - all dimension inches the surface powers and the axial thickness and glass refractive index can then be plugged into the Gullstrand calculator which calculates the focal length of the lens from the first principal plane, and also the front and back vertex focal lengths. 
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