Constants of Igneous Roch. 183 



13. Computation. — Lot the linear expansion of the platinum 

 fusion-tube be given by l = l (l +/(£)), where I and l are the 

 lengths at t degrees and at zero respectively. Let \ and X 

 be the depths of the meniscus below the plane of the top of 

 the fusion-tube, and v and v the volumes of the enclosed 

 molten magma at t and zero respectively. Then, if (1 +f(t) ) 3 

 is nearly enough l + 3/(i) ; if the expansion constants of the 

 fusion-tube and of the micrometer-tube be the same, and if 

 in consideration of the small motion of the latter and the 

 high temperature in the furnace, the air temperature outside 

 of it be nearly enough zero, since 



v i /v =(l -X)(l+/(t)y/(l -\ ), 



( w -» )/» =3/(<) + (A fl -A,)(l + 3/(t))/(4-Jlo). . (1) 



Here 3 f(t) is directly given at each observation, or may be 

 computed by some smoothing process from the data as a 

 whole. 



The equation, therefore, gives the actual expansion of the 

 rock, in terms of unit of volume of solid rock at zero Centi- 

 grade. If this be multiplied by the initial specific volume, 

 the absolute expansion is obtained. An inspection of (1) 

 shows that in the factor X — \, the micrometer value of the 

 length \ is to be inserted in both cases, supposing the contour 

 of the meniscus to remain similar to itself; whereas in l —\o 

 the value of X determined from bulk measurements of the space 

 at the top of the cold tube is suitable, since the tube is 

 flat-bottomed. 



I may add in passing that if 8H be the rise of a flat-bottomed 

 cylindrical float of platinum, submerged to a depth h in a 

 column of magma of height A, then nearly 



(v t -v )/v =Sf(t) + 8H./(A-h) (2) 



Since, therefore, the float shortens the efficient length of the 

 fusion-tube and there is difficulty in determining A in this 

 case, the above micrometric method is preferable quite aside 

 from flotation errors due to viscosity and capillarity, to the 

 easy welding of white hot platinum surfaces, to the tendency 

 of gas bubbles to accumulate on the surface of the float, to 

 the cessation of true flotation during the change from liquid 

 to solid, &c. 



14. Errors. — The change of temperature from top to 

 bottom of the fusion-tube is measured. The change of tem- 

 perature from circumference to axis of the fusion-tube is nil 



