Mechanical Powers
   This compound lever demonstration apparatus was made by Harris and Co. of London. Five systems of levers are mounted on the stand, which is about 6o cm in height. 

   It was originally at Middlebury College, and in 1957 was transferred to the collection at the National Museum of American History of the Smithsonian Institution. 

   In the nineteenth century (and most of the twentieth), students carefully learned the three classes of levers. There must be something important in knowing which is which, for at the beginning of the twenty-first century the State of Ohio still thinks that fourth grade children should know the difference. 

   But, the basic physics is always the same: the ratio of the lever arms is always in inverse proportion to the loads.
 

   The compound lever has completely disappeared from the physics curriculum. The lower lever is pivoted on the right-hand column, and the upper lever on the left-hand column. The load is hung from one of the holes in the lower lever, and the balancing load is hung from the right-hand end of the upper lever. 

  The apparatus is in the collection of the National Museum of American History of the Smithsonian Institution. Most of the collection is not on display, and this rather appealing piece of apparatus is in storage.

  The incomplete apparatus at the left at Transylvania University in Lexington, Kentucky was intended to show the operation of the various classes of levers.

   At the right is a somewhat similar apparatus at Hampden-Sydney College in Virginia. 

   The two pieces of apparatus at the right are at Transylvania University. They are not marked with marker's names, but similar apparatus was made by most manufacturers in the 19th century. 

   The pulley frame at the left typically cost about $30, and was equipped with every useful arrangement, down to and including the Spanish windlass. The arrangement of strings shows how far the load and the force-applying mechanism will travel as the silk thread runs through the pulley systems, thus showing that the product of the displacement and the force is constant.

   The apparatus at the right had a large circular gear at the top with a worm gear running across its top. Also at the top is an arrangement of parallel wheels whose use is not known at present.

   Here is another piece of apparatus in the Smithsonian connection by W. Harris & Co. of 60 High Holborn, London. Note that this area had a number of apparatus makers in the early nineteenth century. The catalogue card for this apparatus notes that the apparatus was donated by Middlebury College, and was probably bought in the eighteen thirties. 

   In the nineteenth century there was a goodly amount of practical engineering mixed in with the Natural Philosophy course, and the study of pulley systems was important for a society which relied on human and horse muscles to shift heavy weights. 

   Today I look at the arrangement of pulleys on the right-hand side of the apparatus, and think of the lovely problem in Lagrangian mechanics which it poses.

   Students at Denison University probably made this mechanical powers apparatus in the eighteen-nineties as part of a second-year course in experimental physics. It is a combination of designs from the catalogues of commercial apparatus manufacturers, starting with the Differential Axle on the left-hand side. On the right-hand side is a Screw and Helix combination, and below that is a model of a windlass. The screw-eyes at the top suggest that pulleys might have been hung from them 
   This well-preserved Illustration of Gears and Belts appears  in the 1881 catalogue of E. S. Ritchie of Boston. It is in the collection of Amherst College, and dates no earlier than 1875. 

   According to the catalogue, it "consists of a mahogany base and pillars supporting a double metal bar, by which the frames of the systems of wheels are held, allowing them to be placed at all desired distances and positions.
   Three metal frames with screw pivots, holding steel axles, upon which the geared wheels or pulleys are arranged as desired. 
   Six brass geared wheels, with 72, 48, 48, 36, 24 and 12 teeth, and all of which have hubs with binding screws, and can be arranged in a great variety of combinations.
   A frame, with geared wheel of seventy-two teeth, and pulley for weight, and an endless screw [at the top of the apparatus], which engages in the gear, with pulley for power.
   A heavy balance-wheel, grooved for belt, with crank and treadle [at the lower part of the apparatus]...
   All the frames have square shoulders to fit the space between the plates of the upper bar, and brass screw nuts,...$40.00"

   When I saw this amazing multiple pulley block at HampdenSydney College in Virginia, I immediately started to look for its twin. Alas, it is all alone in the collection, and we can only calculate its immense mechanical advantage. There is no maker's mark.
   Browsing through the 1881 Ritchie catalogue showed that this piece of apparatus had been modified from its original use. In its original form, systems of pulleys were suspended from the arm, and it was described as "Illustrations of Pulleys, polished mahogany supports of the systems of pulleys and wheel and axle." With sets of fixed and movable pulleys, plus the wheel and axle system that attached to the top of the pillar in place of the curving iron bracket, this was a $35.00 piece of apparatus.

   At some later date someone at Middlebury College converted the system to serve as a piece of electrostatic apparatus. 
 

   This demonstration of pulleys, block and tackle is on display at the Garland Collection of Classical Physics Apparatus at Vanderbilt University.

   When this apparatus was purchased from Deleuil of Paris about 1875 the Natural Philosophy course had a good many topics directly applicable to everyday life. In an era when heavy objects were still lifted by human or horse muscles, it was important to learn the trade-off between force and the distance over which the force was applied. 

   The apparatus is approximately one meter in height, allowing measurements to be made. 

   This moment of force (or torque) demonstrator is at the University of Vermont. 

   The maker is the Société Génovoise pour la construction d'Instruments de Physique, Genéve. I have seen only four other pieces of apparatus by this firm in the United States: an optical bench at Bowdoin College, a heliostat at the United States Military Academy, a small spectrometer at Washington and Jefferson College, and a huge spectrometer I used as an undergraduate at Amherst College in the 1950s. 

   The apparatus at the right was designed to show the principle of the lever and allow measurements to be made of the forces exerted by pulleys. The bar across the top can be moved back and forth. In use, a cord connected to a point on the left-hand arm of the pivoted lower bar runs over the pulley and down to a suspended mass-hanger. Mass-hangers are also hung from points on either side of the pivoting bar. Amazingly, the three mass-hangers still exist after nearly 150 years.

   The demonstration was purchased from Lerebours et Secretan of Paris by Prof. Frederick A.P. Barnard of the University of Mississippi sometime between 1854 and 1860. It is listed in the 1853 L&S catalogue for 110 francs, a little over $20. 

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