of Astronomical Instruments. 339 



come extended or compressed in a different degree, or that 

 which was extended in the first position becomes compressed 

 by the change, and the reverse. In many cases these changes 

 may be made sensible to the eye, and their effects may be 

 shown in all bodies, when their magnitude is sufficient for ap- 

 plying proper instruments. 



From these principles, then, which experience furnishes, we 

 may anticipate, tliat a change of fonn takes place in every new 

 position of an instrument ; and consequently that it should be 

 so constructed as to render the effect of these changes of form 

 msensible in making observations ; or, where that cannot be 

 accomplished, the effect of flexure should be estimated, and the 

 observations corrected accordingly. j . , , 



In the construction of instruments, it is therefore desirable 

 to inquire what fonn is adapted for any given purpose; and, 

 assuming that the flexure will have a sensible effect, it will be 

 of some advantage that the form be of the simplest kind, at 

 least as far as regards the calculation of its flexure. 



And here we may remark, that oeconomy of material is 

 of little if any importance, and therefore the forms of equal 

 strength should be abandoned, and those of the least flexure 

 substTtuted in their place. And since easy movement is not 

 so essential as accurate movement, that form of axis seems the 

 best which unites the greatest accuracy of form with that which 

 is least flexible. . , 



If an instrument be supported by a horizontal axis, and it 

 be put in motion, the centre will rotate in a circle of which the 

 radius is equal to the flexure of the axis at the point inter- 

 sected by the plane of the graduated arc or circle. 



Let us suppose the axis to be an uniform soUd cylinder of 

 which the radius is r, and the lengdi from centre of pressure 

 to centre of pressure /, W the weight of the moveable part 

 of the instrument, and M the weight of the modulus of elasti- 

 city of the substance to a base of unity; also let ]) be the cir- 

 cumference of a circle of which the radius is 1 or unity; then 



_^'— - = 8 or the deflexion in die middle*. (A). 

 If the axis be a tube or hollow cylinder of uniform diameter, 

 and r be the radius of the exterior part of die axis, and?/?- be 

 the radius of the hollow part; then 



w;3 



= 8, or the deflexion in the middlef. (B). 



iy/;MH(l -7i>) 



* Practical Essay on Cast-iron, &r. artt. 81, 87, and 100. Tlie expressiop 



— = M in tliis notation. The same equation may be derived from artt. 326 

 f 



and .3.39 B of Dr. Young's Natural Piiilosophy, vol.ii, 

 + Pract, Essay on Iron, artt. 8.3, HJ, and 100. 



U U 2 If 



