640 Lieutenant Rennt on the Constants of 



Table IV., so that although the Table of Horary Corrections meet not our 

 wishes, nor even our expectations, it diminishes (by one half) the errors 

 of the other formulas. Therefore, let us not despond, — all we desire has 

 not been realized, but considerable improvement has been made, and by dili- 

 gence and zeal more may hereafter be done. The defect of the formula which 

 now remains to be remedied is brought within small compass, and is simply the 

 error occasioned by assuming an incorrect value of the real mean temperature 

 of the atmospheric column between the stations of observations. Time only 

 can tell if any considerable improvement be possible in reference to mean tem- 

 perature errors, but these, if not removable by positive improvements in the for- 

 mula itself, may be rendered for practical purposes comparatively innoxious, by 

 sound tables of local horary correction ; and in the formation of such tables the 

 new formula, with new constants, will give, I believe, very important assistance. 



I have now to bring forward the new formulas contrasted with the old 

 ones, as applied to the joint labours of M. A. Morlott and myself, near Mon- 

 treux, the same appearing in four small Tables: — 



Table V. shows the dates of observations, the calculated heights according 

 to four principal formulse, and the true height by actual spirit-levellings ; these 

 heights in Table V. have not as yet received the horary corrections. 



Table VI. gives the calculated heights after the application of horary correc- 

 tion, as given by my large Table. 



Table VII. gives the errors of heights as calculated by the four formula, 

 after the application of horary corrections. And — 



Table VIII. gives the influence of vapour of water of the atmosphere in 

 increasing the height, such as may be obtained by employing a formula suited 

 to a hypothetic atmosphere of dry air. 



As the four heights, for which there are five observations (one of them 

 being determined by a double set of observations) are unknown to the Academy, 

 I shall designate them by the characters A, B, C, and D. 



