172 Mr. Allan's Description of [March, 



which we are now going to describe, which may be put in place 

 of the other. We have supposed the tubes to be to one another 

 as 12 to 1, and have found that for every 12 parts the mercury 

 falls on the scale, the column of suspension is shortened 13. If 

 then an inch be divided into 13 parts, when the mercury in the 

 long tube falls through 12 of these, the column of suspension 

 will be shortened a full inch. Hence if a scale be made use of, 

 whose large divisions are equal to -ffths of an inch, instead of 

 real inches, these nominal inches and their subdivisions will 

 indicate with accuracy the number of true inches and correspond- 

 ing parts of inches, by which the column of suspension is 

 shortened . 



In order that altitudes may be found without logarithmic 

 tables, a scale of the kind we are going to describe, may be 

 attached to the other side of the barometer. This scale must 

 be so divided, as to show with accuracy the quantity of fall cor- 

 responding to certain determinate altitudes. The method of 

 finding the size of the spaces for the altitudes required is this. 

 Supposing that it is designed to make the large divisions of the 

 scale to correspond to 100 fathoms, and that we commence 

 the calculation from 30 inches of mercury downward, we seek 

 the logarithm of 30, the decimal part of which is 0*4771, from 

 this we subtract 100, and there remains 0'4671, which we find 

 to be the decimal part of the logarithm of 29"32, this we subtract 

 from 30, and there remains 0*68 of an inch for the size of the 

 first space. Next, from 0"4671 we subtract 100, and there 

 remains 0*4571, whose natural number is 28"63, which, when 

 subtracted from 29'32, leaves 0*67 of an inch for the size of the 

 second space. In this way are all the divisions and subdivisions 

 of the scale to be formed. 



In finding the spaces above, that I might be able to show the 

 method more simply, I have made use of logarithms of four 

 places of decimals only, and the size of the spaces is for that 

 reason not correct ; but, in calculating for the scale, tables 

 extending to eight or nine places of decimals will be required, as 

 the utmost accuracy is necessary in its construction. It must 

 be kept in view that the spaces are not to be taken off a scale of 

 real inches, but a scale of nominal inches, the same as is second 

 described. 



I come now to show the method of correcting for the tempe- 

 rature of the mercury, in making use of the above scales. If the 

 scale of real inches is used, this is done in the common way. If 

 the scale of nominal inches is used, one-thirteenth of itself is to 

 be added to the quantity that is to be taken from, or put to, the 

 length of the column of mercury, because each of the nominal 

 inches is one-thirteenth of an inch too little. If the scale that 

 is divided so as to indicate certain determinate altitudes, is used, 

 a sUde which is to extend across both scales is to be screwed 

 up or down to the place where the mercury should be if the 



