Mr. J. Brown on the Products of the Soda Manufacture. 15 



results he has recorded for his last observation. These two 

 different pressures accuse a corresponding difference of tem- 

 perature of 0°*63 F. ; a possible error, not so materially less 

 than what we have found as the maximum that can attach to 

 the formula. The Franklin Institute experiments, which cor- 

 respond closely with Ure's, I have omitted for a similar reason; 

 they do not profess even to read nearer than 0°*25 F. They 

 may, however, for illustration be compared with those of the 

 Academy, as under : — 



Academy pressure, 145" 15 inches; temp, observed, 305°'39 ; temp, calculated, 307°*51 

 Institute ... 154*28 ... ... ... 305 50 ; ... ... 311*73 



Diffbrences g*l3 0°*ll 4°*22 



Discounting the observed difference from the calculated one, 

 we have left 4°' 11 F. as the error of one or the other series; 

 an amount nearly four times that of the formula. 



It is manifest that the comparative error of the formula is 

 only approximate; because it is based in each case upon 

 only one observation instead of upon the combined mean of 

 all the observations, or, rather, the mean of the diff*erences at 

 every epoch observed. Also, it can only be called an error, 

 upon the assumption of the mean of all the experiments re- 

 sulting in absolute accuracy; an assumption by no means to 

 be made ; for in general the utmost that can be done for any 

 experimental series, is to determine the limits of its necessary 

 or accidental errors. Such a research and determination I 

 have thought the present formula of sufficient interest to war- 

 rant. The account, which is in fact the promised and proper 

 conclusion of the present paper, will appear in a future num- 

 ber of this journal. 



[On this subject, see the following papers in the Philosophical Magazine: 

 first series, Philip Taylor, vol. Ix. for 1822, p. 452, with engraved scale for 

 each degree of temperature from 212° to 320° Fahr. Mr. Ivory, vol. i. 

 second series, for 1827. Mr, Farey, S. 3. vol. xxx. for 1847. — Also the 

 papers by Holtzmann, Magnus,andRegnault, in Taylor's Scientific Memoirs, 

 vol. iv.] 



II. On the Products of the Soda Mamifacture. 

 By John Brown, Esq.* 



GLAUBER first showed in 1658 that common salt could 

 be decomposed by sulphuric acid. In the year 1736, Du 

 Hamel proved the base of common salt to be soda. Previous 

 to this, however, Cohausen, in 1717} had mentioned that salt 

 might possibly be decomposed by means of lime ; but as this 

 observation was associated with numerous errors, it was en- 

 tirely overlooked. In 1 737 Du Hamel succeeded in obtaining 



* Communicated to the Philosophical Society of Glasgow by Dr. R. 

 D. Thomson, and read April 12, 1848. 



