118 Mr. J. J. Waterston on the Expansion 



It will be remarked that from 50° to 150° the second differ- 

 ences are sensibly uniform, their exact mean being 17*5. Now 

 the parabola being defined by the equation ax=y 2 , to find a we 

 have the differential equation 2 (dy) 12 = ad 2 x, in which dy = 5°, 

 d Q x = '000175, hence a = 285714; and since x=v — b and 

 y = t—c, in which v is the volume at t temperature, we have 

 285714(v — b) = (t — c 2 ), in which b and c may be computed from 

 two observations, or they may be computed from one observation 

 and its first difference. But the most exact method is to com- 

 pute a, b, and c directly from the volumes at 50°, 100°, and 

 150°; we thus obtain 



log« = 5-45196, 6 = -99710, and c= -14-4025. 



This parabola passes through the tabular volumes at 50°, 100°, 

 and 150° ; and at 75° the volume is smaller than the tabular 

 number by one-twelfth of a degree, and at 125° it is larger than 

 the tabular by one-sixteenth of a degree. Above 150° the para- 

 bola sensibly diverges from the tabular volumes; at 200° the 

 difference corresponds to 1°. But, as stated in Note E, these 

 higher observations were of inferior value. The tubes were 

 unfortunately of soft glass, which are corroded by steam under 

 200°. It was thus still an open question whether water expanded 

 in a parabola. The simplicity of the curve was inviting, although, 

 if confirmed at the higher temperatures, it would be fatal to the 

 generality of the law of expansion. I therefore endeavoured to 

 obtain observations at such high temperatures as would settle 

 the point. 



§ 3. This has proved a much more difficult task than was 

 anticipated, and has occupied several months. 



Below 200° it is comparatively easy to obtain good observa- 

 tions in tubes 20 inches long. In previous researches I employed 

 concentric boxes or hoods, in which a current of heated air, after 

 ascending on the outside of the inner one (which contained the 

 tubes and thermometers), was directed downwards upon the 

 tubes before escaping by the funnel, which also passed upwards 

 through the inner hood. Some attempts to follow this method 

 on a smaller scale having failed, I resorted to an open tube held 

 over Bunsen-flames, and after a good deal of labour and many 

 failures was at last successful in obtaining good observations up 

 to 335°, which afford distinct proof that the curve of expansion 

 above 200° conforms to the general law. 



To establish this decisively, requires observations above 300° ; 

 and unfortunately it is just at this temperature that difficulties 

 accumulate on all sides. To overcome these, required a kind of 

 apprenticeship to be served. 



I shall now describe the method finally adopted and employed 



