102 M, Ramond's Listructions for the Application of [Aug. 



so expeditious a nature, that quickness may be regarded as a 

 suitable condition in the calculation. 



I have determined, therefore, to make a slight sacrifice of 

 rigorous exactness in order to afford philosophers the advantage 

 of knowing the result of an observation in less time than would 

 otherwise have been required. My mode of proceeding consists 

 in regarding as constant the fourth factor of the above formula, 

 by giving it the value which it would have at an elevation of 

 aoout 9842 feet, at lat. 45°, and at a mean temperature of 15° 

 centigrade. For this purpose it will only be necessary to replace 

 the factor in question by an augmentation in the coefficient cal- 

 culated according to the supposition just made. The formula 

 will then become, 



z = log. (^) 60345-4 feet . (1 + -0028371 . cos. 2 ^^) 



/ lOOO +9{t - t') \ 

 \ 1000 J* 



> This formula without doubt is not rigorously exact ; it exag- 

 gerates a little lesser heights, and diminishes a little those which 

 exceed 9842 feet. We have only to inq\»iie into the extent of 

 this inaccuracy. For most elevations it will be much under 

 3 feet ; and we must go to the equatfer, and ascend Chimborazo 

 to find 8 feet difference between the results of the approximate 

 and exact calculation; and 8 feet are, relatively to the height of 

 Chimborazo what about half a foot is to most ordinary elevations ; 

 a quaytity too small to be indicated by the instruments, and 

 covered in the uncertainty of observation,;- I, therefore, see no 

 reason for abandoning a mode of proceeding so convenient, and 

 I have never employed any other to arrive at results whose 

 exactness has been proved by the test of geometrical measure- 

 ment ; but what above all recommends it is, that M. de Laplace 

 himself has not disdained adopting it in the third edition of his 

 " Systeme du Monde," and that M. Biot has made it the basis 

 of his barometrical tables, by deducing my coefficient 60348*4 

 from his own 60136, by a mode of analysis peculiar to himself. 

 When, however, we possess a formula of such an order as that 

 which we owe to the author of the " Mccanique Celeste," we 

 always regret the want of being able to represent in calculation 

 the lesser quantities. M. Oltmanns has been unwilling to neg- 

 lect those which I have, and he has improved my suggestion by 



taking into account the variations ofr^, but neglecting as I do 



the small products which refer to the variation of the latitude, 

 and that of the temperature. His method is as follows : we 

 have allowed that in the last factor of the formula, the value of z 

 might be represented by the second member of the equation 

 without this factor. In this expression, the constant coefficient 

 being reduced into toises, and a mean value being given to the 



