Latitude and Temperature in Barometric Hypsometry, 145 



employ |y, as they also commonly use 1 4-^cos 2Lfor 1 ~ (1 — 2 cos 2L). 

 The values assigned to z by different writers vary considerably. La- 

 place makes 2= '002837, and M. Mathieu (Annuaire, I.e.) gives 

 -£'=•00265. I have thought it, therefore, advisable first to consult 

 the authorities who have calculated y directly from pendulum expe- 

 riments, next to calculate y from the compression deduced from 

 measurements of arcs *, and then, having determined z for each of 

 these values of y, to take the mean result to five places of decimals. 

 The pendulum reductions are taken from Baily (Mem. of Astron. 

 Soc. 1834, vol. vii. p. 94) ; the four first reductions are cited on the 

 authority of the Engl. Cyclop. A. fy S. vol. iv. col. 362, and the 

 fifth from the Proceedings of the Royal Society, vol. xiii. p. 2/0. 

 The following are the results. 



Pendulum Experiments. 



Baily, final result y= '005 1449 *= -0025659 



Sabine, -0051807 -0025837 



Airy, -0051330 -0025599 



Measurements of Arcs. 



Airy, y= '0053273 *= -0026566 



Bessel, -0053252 '0026555 



Everest, -0054530 '0027191 



Clarke, -0052750 -0026306 



Pratt, -0052816 '0026339 



Mean values y=-0052651 ^=-0026256 



Hence I adopt the value z='00263. This differs from Laplace's 

 value by '000207, and from that of M. Mathieu by -00002. Viewed 

 in relation to the possible errors which may arise from other sources 

 this correction is slight, but it should be made on the principle advo- 

 cated by Laplace, that it is assignable (Mec. Cel. vol. iv. p. 292). 

 Adopting this value of z and reducing the formula (a) to English feet 

 and Fahrenheit degrees, I have constructed Tables I. and II., which 

 give formulae and figures for calculating heights with every correc- 

 tion of Laplace, more readily than any other that I have seen. As 

 there is no necessity to interpolate, the Tables are even simpler to use 

 than M. Mathieu's (Annuaire, 1. c.) or Loomis's (Astronomy, p. 390), 

 and they are not only simpler but more complete than Baily' s 

 (Astronomical Tables, 1827, p. Ill), which do not give the cor- 

 rection for the variation of gravity on the vertical. They have the 

 further advantage of being applicable to both English and conti- 

 nental measures. The unavoidable uncertainties of the theory make 

 it useless to consider more minute quantities than a foot, or the hun- 

 dredth of a metre or of a toise. Hence only five-figure logarithms 

 are required. The following examples will show the use of these 

 Tables. 



Ex. 1. (Feet and Fahrenheit.) Part of Glaisher's Balloon Ascent, 

 5th Sept. 1862. (Report of British Association, 1862.) 



* I have vised Airy's formula y =■- '008668 — 1 -f- c, and not Biot's where the 

 constant is -00865, 1-f-c being the compression. 



Phil. May. S. 4. Vol. 30. No. 201. Aug. 1865. L 



