4'0 



the use of imaginary characters in the summation of series, proceed- 

 ing according to the powers of the series and cosines of arcs in 

 arithmetical progression. He likewise shows, that according to his 

 mode of explanation, certain ambiguous expressions that occur in 

 analysis are perfectly intelligible, and that in the controversy con- 

 cerning the logarithms of negative quantities, carried on formerly 

 between Leibnitz, Bernoulli, Euler, and Dalembert, all paradox and 

 ambiguity may be made to disappear, by referring to the origin and 

 real import of the impossible exponential quantities. 



Although the principal object of this paper is to vindicate the in- 

 dubitable justness of the operation conducted with imaginary cha- 

 racters, yet in the latter part some arguments are likewise offered in 

 favour of the commodiousness of imaginary expressions for facilitating 

 calculations. And, lastly, it is contended, that in the present state of 

 analysis, these expressions are particularly useful in deducing certain 

 conclusions, which without their aid could not be obtained without 

 much difficulty. 



On the Production of Artificial Cold by Means of Muriate of Lime. 

 By Mr. Richard Walker. Communicated by Henry Cavendish, Esq. 

 F.R.S. Read January 22, 1801. [Phil. Trans. 1801, p. 120.] 



Mr. Walker, since his late communications to the Society on the 

 best means of producing artificial cold, received intelligence that 

 Mr. Lowitz, Professor of Chemistry at Petersburgh, had made some 

 experiments, in which a neutral salt different from those he had him- 

 self used, and which is but little known or attended to, produced 

 effects which exceeded his expectations. The salt is the muriated 

 lime; which, mixed with snow in the proportion of about 3 to 2, at the 

 temperature of +27, produced a refrigeration which sunk the ther- 

 mometer to 55 ; and with this mixture the Professor in one ex- 

 periment froze no less than 351bs of quicksilver. 



Mr. Walker repeated the experiment with success ; but finding 

 that it can only be made during a freezing atmosphere, he resolved 

 to try the effect of this salt, reduced to such a strength by evapora- 

 tion as to endure being kept in a solid state throughout the year. 

 After describing the expedients used for this purpose, he enumerates 

 the results of two sets of experiments ; the first made with the mu- 

 riated lime prepared so as to be used in winter only, that is, of the 

 specific strength of 1-450 ; and the other made with the salt prepared 

 so as to be kept for use at any time, the strength of which was T490. 

 The apparatus here used (though somewhat improved) is not unlike 

 that described in Mr. Walker's former communication, nor is the 

 process materially different. 



The paper concludes with a general view of the different frigorific 

 mixtures: 1st, those composed of chemical substances with ice; 

 and 2nd, those in which the use of ice is dispensed with. In a post- 

 script the author suggests a method of obtaining transparent ice, fit 

 for optical purposes, which is effected merely by immersing a vessel 



