ybr Measuring the Expansions of Solids, ^c. 199 



detached from the part which is exposed to the fire, obviates 

 one important objection which has always been made to other 

 contrivances of the same nature, from the uncertain degree of 

 heat and expansion to which they are liable; while the sim- 

 plicity of that part of the arrangement which alone is subjected 

 to great heats, renders it little liable to injury ; and together 

 with the cheapness of the materials of which it is constructed, 

 occasions but a very trifling expense for replacing it when 

 injured. 



The calculation of the absolute expansion of the bar indi- 

 cated by the scale may be performed as follows : — As radius 

 to double the sineof half the arc read off, and found in a table 

 of natural sines, so will the radius B be to the chord of the 

 same arc ; and this divided by ten (the radius of B being ten 

 times the length of the radius_//z) will give the length required. 

 Suppose the arc read off upon the scale to be 4°, 



Radius. Sine of 2"". Indies. Inch. 



then 1-OOOOOCO : 0348995 X 2 : : 5 : -3489950 -i- 10 = 0348995. 



Now in working out this proportion it will be observed, 

 that the multiplication by 2 and by 5 being both constant 

 may, in conjunction with the division by 1*0, be omitted; and 

 leaving out also the final division by 10, the case resolves itself 

 into seeking the sine of half the arc, read off upon the scale, in 

 a table of natural sines, and reading it as the decimal of an inch. 



Moreover, the chords of small arcs are so nearly propor- 

 tional to their arcs that, the number of degrees measured upon 

 the scale never exceeding 10, they may be considered without 

 sensible error as denoting equal increments of expansion. The 

 following short Table of the value of a degree, and minutes 

 of a degree, may therefore be useful in practice. 



Table I. 



ft . Inch. 



The chord of ten degrees derived from this Table by mul- 

 tiplying -00872 by 10 would therefore be -0872, whereas it is 

 more accurately -0871 ; but the difference being only xu/ijijijdth 

 of an inch may, in most cases, be disregarded. 



[To be continued.'] 



XXVI. 0/1 



