106 Af. Ramond^s Instructions for the Application of [Aug. 



the observations being prepared, as in all possible methods they 

 must be, there are literally only two operations to perform ; a 

 subtraction and an addition; for surely no one will consider 

 worthy the name of an operation the slight trouble of searching 

 in the tables for numbers already calculated. 



It remains for me to point out the resources which these 

 tables present in those cases, assuredly very rare, where an 

 observation may be made in circumstances not included within 

 the hmits of the tables. 



We should not be surprised, for instance, if the prodigious 

 height to which M. Gay-Lussac was elevated in his aerial 

 voyage, should not be comprehended in the table for the vertical 

 diminution of gravity ; but it is easy to provide for such a case 

 by means of the differences placed at the bottom of the column. 

 I obtain the logarithm belonging to the logarithmic diflference 

 0*36 in the column + 40, by adding ten times the mean differ- 

 ence 129-7, or 1297, to the logarithm 0-0014658, which belongs 

 to the difference 0*26 in the table. 



In the same way, when we measure very small heights, the 

 double sum of the thermometers may sometimes exceed the 

 limits of the table. Thus, for example, if the double sum be 

 107, and the logarithmic difference O'OOo, I extend the series 

 corresponding to that difference to the column of 110^ which is 

 wanting in the table, by addina; the mean difference 108*9 to the 

 logarithm 0*0012003 in the column of 100°. This difference 

 must be subtracted if we wanted a number in the column of 

 — 20 ; but this excess of precision in small heights will readily 

 appear useless. We may confine ourselves to the logarithm in 

 tne nearest column to that which is wanting. 



The observation of Gay-Lussac makes the first table for the 

 temperature of the instrument equally insufficient. But with 

 what tables, if we except the logarithmic, will not this, in such 

 cases, happen. The difference of the thermometers was 40*3° ; 

 the table only extends to 30°. We may supply the deficiency 

 without sensible error by adding to the logarithm answering to 

 30° that which answers to 10*3°. But it would be both as expe- 

 ditious and more convenient to correct directly the height of the 

 colder barometer by means of table No. 4, which gives the aug- 

 mentation corresponding to a difference of temperature from 1° 

 to 10°: in many cases this may probably be the preferable 

 method. 



It has also another advantage. M. Daubuisson has recently 

 proposed to add to the correction for the temperature of mercury 

 a second correction for the dilatation of brass, when we employ 

 barometers whose mounting is made of this metal. This correc- 

 tion is very small, for the dilatation of brass is only about the 



tenth part of that of mercury ; namely, nearly — ^ for 1°. But 

 for the sake of exactness nothing should be neglected, and the 



