350 



that, after having been constantly occupied, for nearly two years, in 

 making chemical investigations by means of polarized light, he might 

 venture to speak with some confidence upon these matters, without 

 being guilty of immodesty. 



Wilh reference to the objection, that the mathematical calculations 

 are troublesome, he observed, that they are perfectly simple, and 

 may be performed by mere arithmetical multiplication, division, &c. ; 

 that logarithms facilitate them; and that, by varying only the sub- 

 stance, all other circumstances being constant, the calculations of a 

 series of optical results become as short and as easy as those of quan- 

 titative analysis made by the ordinary dry and humid methods with 

 the common balance. 



As the result of the experience of Mr. Reynolds and himself, after 

 many hundred analyses, he stated, that five or six independent and 

 complete analyses may be made in a day by a single person, and 

 that by introducing method into all the manipulations, even a larger 

 number may readily be performed. He, therefore, believed that no 

 objection of time can be urged against such analyses; nor would any 

 one familiar with the manipulations of modern analytical chemistry 

 find just cause to complain of those of optical examinations after a 

 few days practice. 



Of the accuracy of quantitative determinations by circular polariza- 

 tion, he observed that the theory of the method is based upon rigid 

 mathematical deduction, and is, therefore, perfectly exact; all possi- 

 ble errors are consequently those of observations only. The mean 

 error of reading an angle of rotation, with the apparatus he had em- 

 ployed, does not exceed one-tenth of a degree, which for solutions of 

 sugar corresponds to 0.00:2, or two-tenths of a per cent. The most 

 exact assays of gold or of silver, by the humid method of Gay Lus- 

 sac, made by experienced assayers at the mint of the United States, 

 with balances far more delicate than those employed by analytical 

 chemists, are aflfected with a probable error of 0.0002, plus or minus. 

 Hence optical determinations compare advantageously with the re- 

 sults of ordinary analysis. That such determinations are fully en- 

 titled to confidence, is also proved by checking them with other 

 methods, and especially that of applying them to known synthetical 

 mixtures. 



In conclusion, Mr. M'Culloh remarked, that he had for some time 

 been prevented, by official and other duties, from completing a series 

 of experimental researches with reference to the effects of temperature 

 upon the phenomena of circular polarization, and also concerning the 



