1830.]] 
Expansion of Solids* 
149 
tempts, in this way, not being quite successful, we had recourse to the follow- 
ing method. Into a tube of glass, 18 millimetres in diameter, (,7092 inch) and 
6 decimetres (23,64 inch) in length, closed at one of its extremities, we introduced 
a cylinder of soft iron, fixing it in the axis of the tube by four small pieces, 
the length of which was about equal to its diameter. After joining on to the ex- 
tremity of this tube, a second one, having a capillary bore, we filled it with mercury, 
which we subjected to ebullition during an interval sufficiently long to ensure the 
complete extrication of air and moisture. By afterwards exposing it to different 
temperatures, and determining the weight of the mercury driven out, it was easy 
to deduce the expansion of iron, the volume of the former being manifestly equal to 
the sum of the expansions of the mercury, and of the metal minus that of the glass. 
To calculate this result, however, we should know what the volumes of the three 
bodies would be at the freezing point. Now, that of iron is obtained by dividing 
its weight by its density at the freezing point, the volume of the glass is in the 
same manner deduced from the weight of the mercury, which it will hold at that 
temperature ; while that of the mercury is evidently the difference between the two. 
The arrangement we have just explained, may be applied in the case of other 
metals, by adopting the simple precaution of oxidating their surface, to prevent the 
dissolving effect of the mercury. We may easily satisfy ourselves that the layer 
of oxide is of too great tenuity to effect, in the slightest degree, the accuracy of the 
results. We have found this method, in fact, answer remarkably well in the case of 
brass, and we should have decided on employing it with other metals, if a wish to 
verify our results had not determined us to attempt a method something different. 
It is known that the complicated nature of the apparatus required for the mea- 
surement of expansion in solid bodies, is occasioned by the necessity of having 
part of it absolutely fixed and immoveable. But when the true expansion of 
any one substance is known, we may easily deduce that of others, by observing 
the changes in a pyrometer formed of two rods, firmly united together at one of 
their extremities : a conditiou easily fulfilled. 
Instruments of this kind have been employed by Borda and by Deluc. But the 
first having only observed the effect of low temperatures, (which was sufficient for 
the object he had in view,) we Can draw no conclusions as to the particular question 
we are here considering. As to the experiments of Deluc, they appear to us 
to include a source of error sufficient to occasion well founded doubts as to the 
accuracy of the results lie obtained. 
His apparatus was composed of two vertical rulers, the one of glass, the other 
of brass, firmly united by • their inferior extremities. The rods were of lengths 
reciprocally proportional to the respective expansibilities of the two substances. 
The longer, which was the glass rod, was fixed by its upper extremity ; but that 
of the brass rod was entirely free. It results, therefore, from the relation which 
the dimensions of the two rods bore to each other, that this end would not suf- 
fer any derangement, to whatever temperature the instrument be exposed, suppos- 
ing the expansions of the two substances to be proportional . Now, Deluc observed, 
that when the compensation for a certain change of temperature was once ad- 
justed, it remained unaffected by any further change, whether great or small. 
But it is not difficult to perceive that the water bath, in which the rods were 
immersed vertically, being of great depth, the inferior strata of the fluid must al- 
ways have been colder than those above, whatever care might be taken to agitate 
it. And as the brass rod occupied the lower half of the vessel, whilst 
that of glass was immersed through the whole depth, we may attribute the 
inrx*easing expansion which the glass manifested, to the circumstance of the brass 
rod being always at a lower temperature : this source of error increasing with the 
temperature. The error might, however, have been got rid of, by performing 
the experiments with the rods in a horizontal position ; or neutralised, by repeating 
them, and reversing the rods. But Deluc, not being aware of the objections we 
have stated, made no attempt whatever to verify his results. 
A compensation pyrometer, like that of Deluc, offering, as we thought, no 
particular advantages at low temperatures, while at high temperatures they are 
exceedingly difficult to manage, we found it requisite to adopt a different ar- 
rangement, which we shall now describe. 
The rulers which we used are all 12 decimetres (47,28 inches) iu length, 25 
millimetres (,985 inch) in breadth, and 4 millimetres (,1576 inch) in thickness. 
To compare their expansibilities, we have only to connect them in a perfectly 
secure manner at one extremity, by means of a cross piece, secured by strong 
screws. Each rod carries attached to its other extremity, a small stein ot brass, 
which rises, first vertically, and is then bent into a horizontal position. The 
horizontal branches of these two pieces are furnished, one with a scale. 
