TRIGONOMETRICAL SURVEY OF INDIA. 



201 



through the whole breadth, and leaving 0-3 of an inch of the depth above 

 and below ; the parts wliich remain being perforated so as to admit a 

 conical pivot to work in the two concentrically. 



Now, if the two bars be placed parallel to each other and clamped 

 together as abovementioned, and if a flat tongue of iron 0--Io of an inch 

 thick, ri broad, and 2 long, with two pairs of pivots, each pair forming 

 an axis projecting perpendicularly to its plane, be applied horizontally to 

 the apertures abovementioned, the distances between the centres of the 

 two axes being 1*8 inch, it is plain that if one bar increase in length more 

 than the other, one extremity of the tongue may, by means of these axes, 

 revolve through a small arc round some point near the other extremity ; 

 and moreover, if there be such another tongue and apparatus at each end 

 of the compound bar, both tongues will have a similar tendency, so that 

 if the cause be the same of this increase in length, the one tongue will 

 revolve through an arc just as great as the other. 



In Colonel Colby's system, one of the two bars is of brass, the other 

 of iron. The tongue has one axis at O o of an inch from one extremity, 

 working into the aperture of the brass bar, and tiie other at 2-3 nearly 

 working into that of the iron bar, whilst the rest of the tongue projects 

 outwards. 



The expansions of brass and iron are variously stated by different 

 authors, but they are not far from the ratio of three to two.* Let us 

 suppose them to be exactly so, then since l o inch is the di-^tance between 

 the two axes, if double that distance, or 3-() inch were set oil" from the 



» Expansion of brass bar, 

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