(^Astronomical Instrumcnls. 13 



If the divisions be upon a ring, supported by arms radiating 

 from the centre, the depression will in general be much greater 

 than in a solid circle, because the stress is not lessened in pro- 

 portion to the reduction of weight, and the power of resistance 

 may often be reduced in a greater ratio than the stress. Be- 

 sides, such circles are liable to be deranged from other causes, 

 which I shall now endeavour to explain. 



A circle with arms, as A D B C (fig. 2), wlien placed as 

 shown in the figure, is well adapted for explaining the cfiects 

 which I wish to be understood. 



In the first place, it may be observed that the weight of the 

 arc a b will tend to straighten it, and to spread ajiart its abut- 

 ments a, b. These effects will be increased by the support which 

 the arc must give to the arms, and to the arcs C, and D. 



The obvious remedy is to connect the parts a, b, by a straight 

 bar, as in fig. 4. This bar would form a direct tie, on which 

 the arc would be sustained as an arch by its abutments. It is 

 equally clear that a straight bar must be die most effectual 

 support to the weight of the other arcs and arms of the circle. 



Secondly. The effect of the weight of the arc dc (fig. 2), 

 will be to add to its curvature ; and this effect will be increased 

 by the support it must afford to the arms and arcs C, D. 



These pressures will also be most effectually counteracted 

 by a straight bar dc (fig. 4.) 



Thirdly. If the circle be put in die position shown by 

 fig. 3, it" will be found that the tendency of the arc A to 

 straighten, and of the arc C to curve, with the effect of both to 

 depress the arm a E, will be most effectually guarded against 

 by adding the straight bars indicated by the dotted lines. 



The arrangement to secure stiffiiess has only been consi- 

 dered for a circle with four arms ; but similar remarks apply 

 to one witii a greater number, as the reader will readily per- 

 ceive by fig. 5. And also in portions of arcs, as in fig. 6 ; par- 

 ticularly where a heavy telescope rests upon the graduated 

 arc. But it is not necessary to allow a telescope to depend 

 wholly on die arc for support; for by a simple extension of a 

 method sometimes employed by Mr. Troughton, the stress 

 from its weiglit may be thrown close to the bearings of the axis, 

 and the axis woukl be made very stiff" by the same means. 



On the whole it may be remarked, diat a system of triangle, 

 of which the sides are in jiroper directions for resisting die 

 stress they are to sustain, is most suited for any jiurjiose where 

 we wisii to be secure against the least change of form : for every 

 curved bar is less strong to resist tension or comi)ression than 

 a straiglit bar of the same bulk. Instruments arc lor the pur- 

 poses of science, and not to please the eye; and we ought not 



to 



