17 s Account of Dr. Jl'ollastmi's [Sew. 



rate the muriatic acid, would yield a precipitate of 2'3J muriate of 

 lead, and that there would then remain in solution nearly 116' 

 nitrate of soda. It may at the same time he seen, that the acid in 

 this quantity of salt would serve to make 232 corrosive sublimate 

 containing 185-5 red oxide of mercury, or would make Ulo mu- 

 riate of ammonia, composed of (> muriatic gas (or fvydromuriatic 

 acid) and 29*5 ammonia. The scale shows also, that for the pur- 

 pose of obtaining the whole of the acid in distillation the quantity 

 of oil of vitriol required is nearly 84, and that the residuum of this 

 distillation would be 1 2.' dry sulphate of soda, from winch might 

 be obtainedj by crystallization, 277 of Glauber salt containing 155 

 water of crystallization. These and many more such answers appear 

 at once by hare inspection, as soon as the weight of any substance 

 intended for examination is made by motion of the slider correctly 

 to correspond with its place in the adjacent column. 



" With respect to the method of laying down the divisions of this 

 scale, those who are accustomed to the use of other hiding-rules, 

 and are practically acquainted with their properties, will recognise 

 upon the slider itself the common Gunter's line of numbers (as it 

 is termer"!), and will be satisfied that the results which it gives are 

 the same that would be obtained by arithmetical computation. 



" '1 hose who are acquainted with the doctrine of ratios, and 

 with the use of logarithms as measures of ratio*, will understand 

 the principle on which this scale is founded, and will not need to 

 be told that all the divisions are logometric, and consequently thai 

 the mechanical addition and subtraction of ratios here performed by 

 juxta-rposition, corresponds in effect to the multiplication and divi- 

 sion of the numbers by which tho*e ratios are expres. ed in common 

 arithmetical notation. 



" To others who are not equally conversant with the nature of 

 logarithms, and consequently have not so correct a conception of 

 the magnitudes of ratios, tome further explanation of the mode in 

 which the scale of equivalents is constructed, will, I presume, be 

 acceptable. 



" They will observe, that the series of natural numbers are not 

 placed -at equal intervals on the scale; but that at all equal intervals 

 are found numbers which bear the same proportion to each other. 

 In fig. 3, some of the larger intervals alone are represented on v. 

 line similarly divided. The succession of intervals, marked/'. 

 C, D, E, are all equal, and at these points of division ere placed 

 numbers I, 2, 4, 8, |Cj, which increase progressively by the same 

 ratio. And since the series 3 : (i : 12: 121 increase in the same 

 ratio of I to 2, these intervals a, /■, c, a', e, are the same as the 

 former. At another succession of different yet equal intervals, 

 marked F, G, H, I, arc placed numbers ], 3, J), 27, which inciease 

 regularly by an equal rati.' of 1 to 3; and by means of a pair n( 

 compasses it would be found that the interval from 2 to 6, or from 

 6 to 18 (which are in the same ratio of 1 to 3), is exactly equal to 

 F G, the interval between 1 and 3. As any single space rcj icseuts- 



