266 M. Ramond's Instructions for the Application of [Oct. 



On the Tables. 



It may be useful here to subjoin a brief account of the con- 

 struction of the tables. 



In order to reduce the upper barometer to the same tempera- 

 ture as the lower, the formula, transformed into logarithms, is, 



log. H = log. h' + log. [l + (^')]. 



Table, No. I. expresses the values of this last term, which 



becomes = log. [ '''";,,; —] == log. (5412 + (r - r')) - 



log. 5412. 



In the formula, this correction is'applied to the iipjyer barome- 

 ter, and it is obvious that, according as the first log. is greater 

 or less than the second, (that is, according as T is greater or 

 less than T'), the correction will Ije + or — . 



By attending to these circumstances, it may be applied to 

 the lower barometer, and will in this case be — or -f, according 

 as the difference of the thermometers is + or — . 



M. Ramond adopts the method of correcting the lower baro- 

 meter, and to facilitate this, he has given Table I. a double 

 form, according as the difference of the thermometers is + or 

 — ; the one series of numbers being the arithmetical complements 

 of the others, by v/hich means the operation is always addition. 



Table No. 2 is constructed from the part of the formula log. 

 {1 + N (log. -0028371 + log. cos. 2 4^)}, N being the number 

 answering to the logarithm included in the parenthesis. 



The last factor in the formula when altered according to the 

 suggestion of M. Oltmans, becomes, 



[log. ^ + 0-868589) . 60158.39 



(in feet), 1 + ^o^sm^i ; 



Then according to M. Ramond's improvement, introducing 

 the correction for temperature, and transforming it into loga- 

 rithms, it becomes, (adopting the former notation), 



log. [l + N(log. ^log. g 4- 0-868589^ + log. 60158 + log. 



From this part of the formula, Table No. III. is constructed. 



Table No. V. is taken from one given by Laplace in the 

 " Connaisance des Temps," for 1812. It supposes the interior 

 diameter of the tube to be accurately known. 



Table No. VI. is described p. 105. 



Logarithms of the constant Coefficients. 



Log. 60158-39 = 4-7792962 

 Log. 60345-40 = 4-7806442 



The last value is to be used in cases where the less exact 

 method is thought sufficient; and in this case Table III. is dis- 

 pensed with. 



