ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 429 



the following quantities can be easily calculated : — (a) Horse-power of an 

 engine, (6) the necessary size of an engine for any desired power, (c) pis- 

 ton speed, (d) the mean pressure of a simple or compound engine, (e) 

 ratio of compound cylinders. 



3, Professor Fuller's spiral calculating rule is specially described by 

 both Culmann and Favaro, and consists of a cylinder that can be moved 

 up and down upon and turned round an axis, which is held by a handle. 

 Upon this cylinder is wound in a spiral a single logarithmic scale. Fixed 

 to the handle is an index. Two other indices, whose distance apart is the 

 axial length of the complete spiral, are fixed to the cylinder. This 

 cylinder slides in like a telescope tube, and thus enables the operator to 

 place these indices in any required position relative to the cylinder. Two 

 scales are provided, one on the piece carrying the movable indices, the 

 other on the cylinder. The inventor remarks that it must be remembered 

 that all calculations founded on measurements of length, weight, and 

 time can only be approximate, as the data for them are so. Except, 

 therefore, with the most refined measurements, it is a waste of time to 

 carry results beyond the fourth figure. The new rule possesses advan- 

 tages over the old form besides that of increased length of scale. The 

 setting and reading are performed by indices, and not by scale against 

 scale, and this is very much less troublesome. Also, multiplications and 

 divisions containing a series of factors can be worked with the greatest 

 facility, and as the logarithms of numbers by the use of scales are easily 

 read, the powers and roots of numbers are within the capacity of the 

 instrument. 



4. Thacher's cylindrical slide rule. The ordinary sliding rule in use is 

 12 inches long, with radii of 11 and 5^ inches, the divisions of which are 

 cut by hand, copying from a machine-divided plate. In Thacher's instru- 

 ment the radii are 60 and 30 feet, the divisions of which are printed 

 directly from machine- divided plates. These plates contain over 33,000 

 divisions, calculated to seven places of decimals from Babbage's tables by 

 using a common multiplier, every line being subjected to coi-rection for 

 error of screw and temperature variation, so that possibly every line- 

 centre is within -0001 inch of its true place. The plates contain ovci- 

 17,000 engraved figures. The scales, being of great length, will give 

 results correctly to four, and usually to five, places of figures. 



The instrument consists of a cylindrical slide provided with a knob at 

 each end, and which admits of both rotary and longitudinal movement 

 within an open framework or envelope of equidistant bars of triangular 

 section. The bars are connected to rings at their ends, which admit of 

 rotation within standards attached to the base. The surface of the slide 

 is exposed in the openings between the bars, the lower edges of which 

 are in contact with it. 



The scales for this instrument have a length forty times as great 

 as for an ordinary slide rule of the same length, and more than sixty-five 

 times as great as for the ordinary slide rule in use. 



With this instrument directions are given for not only performing 

 the ordinary arithmetic operations, but for the conversion of foreign 

 weights and measures, calculations and action with money matters, 

 mechanics, specific gravity, timber mensuration, gauging, railway woik, 

 weights of metal, calculations for plate girder bridges, truss bridges, &c. 



6. Gravet's calculating rule, by which calculations involving squares, 



