1865.] and Temperature in Barometric Hypsometry, c. 275 



pole, the coefficient z=y-r(2 + y')*, for which most writers employ |y, as 

 they also commonly use 1 -f^cos 2 L for 1 4-(l z cos 2 L). The values 

 assigned to z by different writers vary considerably. Laplace makes 

 ,?= -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 experiments, next to calculate y from 

 the compression deduced from measurements of arcsf, 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. 270. The 

 following are the results. 



Pendulum Experiments. 



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



Sabine, -0051807 '0025837 



Airy, -0051330 -0025599 



Airy, 



Bessel, 



Everest, 



Clarke, 



Pratt, 



Mean values y= -0052651 .?= -0026256 



Hence I adopt the value = -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 advocated 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 calcula- 

 ting heights with every correction 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 (Astro- 

 nomy, p. 390), and they are not only simpler but more complete than 

 Baily's (Astronomical Tables, 1827, p. HI), which do not give the cor- 



* The term 1 g cos 2 L represents the ratio of the gravity at latitude L, to the gra- 

 vity at latitude 45, which on the spheroidal theory of the earth's shape is 



[1+y. (sin L)]-5. (1-Hr), 

 and this gives the above value of z. 



t I have used Airy's formula y '008668 l-=-c, and not Biot's where the constant 

 is -00865, 1 -7-c being the compression. 



