VOL. LXXVIII.] PHILOSOPHICAL TRANSACTIONS. 501 



Cor. If some of the letters a, |3, y, J", &c. be substituted for others, and others 

 for them, the equations resulting will be just, and consequently many new equa- 

 tions may be deduced. If in the preceding equations for s be written s', and for 

 the sum of all the divisors of a certain quantity not divisible by a prime number 

 («, or (3, or 7, &c.) be written the sum of all the divisors of that quantity not di- 

 visible by the same prime number, but divisible by / ; the propositions resulting 

 will be true. These equations may be applied to the equations given in the pre- 

 ceding parts, and from thence many others be deduced. 



XXV. Experiments on the Production of Artijicial Cold. By Mr. Richard 

 Walker, Apothecary to the Radcliffe Infirmary at Oxford, p. 895. 



Mr. W's most powerful frigorific mixture is the following: Of strong fuming - 

 nitrous acid, diluted with water (rain or distilled water is best) in the proportion 

 of 2 parts of the former to 1 of the latter, each by weight, well mixed, and 

 cooled to the temperature of the air, 3 parts; of vitriolated natron (Glauber's 

 salt) 4 parts; of nitrated ammonia (nitrous ammoniac) 3-i- parts; each by weight, 

 reduced separately to fine powder: the powdered vitriolated natron is to be added 

 to the diluted acid, the mixture well stirred, and immediately afterward the 

 powdered nitrated ammonia, again stirring the mixture: to produce the greatest 

 effect, the salts should be procured as dry and transparent as possible, and used 

 freshly powdered. These seem to be the best proportions when the temperature 

 of the air and ingredients is -|- 50°; as the temperature at setting out is higher 

 or lower than this, the quantity of the diluted acid will evidently require to be 

 proportionably diminished or increased. This mixture is but little inferior to 

 one made by dissolving snow in nitrous acid, for it sunk the thermometer from 

 -f 32° to — 20°; perhaps it may be possible to reduce the salts to so tine a 

 powder as to make it equal. In this last experiment the diluted acid was equal 

 in quantity to the vitriolated natron, being 4 parts each, the nitrated ammonia 

 3-i- as before. A powder composed of muriated ammonia (crude sal ammoniac) 

 5 parts, nitrated kali (nitre) 4 parts, mixed, may be substituted in the stead of 

 nitrated ammonia, with nearly equal effect, and in the same proportion. 



Crystallized nitrated ammonia, reduced to very fine powder, sunk the ther- 

 mometer, during its solution in rain water, 48", from -|- 56°, the temperature 

 of the air and materials, to -f- 8°; and when evaporated gently to dryness, and 

 finely powdered, it sunk the thermometer 49°, to -f 7°j the temperature of the 

 air and materials being as before at -f- 06°: therefore, in this salt (which pro- 

 duces, as appears above, much greater cold during solution in water, than any 

 other hitherto known) the water of crystallization is not in the least conducive 

 to that effect. Mr. W. expected, that by diluting the strong nitrous acid to 

 the proper strength with snow, instead of water, by which its temperature 



