On aimospherical Refraction. 341 
In order to reduce the preceding measurements to the English 
national standard, we have to multiply the fathoms of the Indian 
degree by —*900018, and of the English by +°00007, to ob- 
tain the correction to be applied, with its proper sign, to the 
length of the degree. The French and Swedish degrees require 
no correction. 
We have then the following data for computation: 
4 Aat y 
By sections mt 9° 34 44 60471°74 fathoms. 
the Indian are 120 2 55 60486-47 
16 34 42 60511-69 
The French 47 30 46 60779 
English 52 2 20 60824°25 
Swedish 66 20 12 60955 
and the resulting compression 
1 1 ti 1 
| et aoa 
By the French 304-64 30555 31377 8" So7-09 
i l 1 1 1 
eS as mean ——— 
English 30567 30040 isso M8) sos-45 
: 1 1 1 1 
w —____  —__—_ —__._ mean ——— 
Swedish 304-44 305-01 309-09 by 307-55 
1 
and the mean of the three means = ———. 
307°55 
As it appears that the compression obtained by employing the 
length of the degree in lat. 16° 34’ 42” is uniformly in defect, 
whilst the results deduced from the other two sections are very 
nearly alike, it might perhaps be allowable to consider 354.57, 
the mean of these last results, as the true compression ; and this 
would agree very nearly with the deduction of M. Laplace, from 
the lunar irregularities ; with the result of Dr. Young’s interesting 
and nove) investigation, by a comparison of the mean, with the 
superficial density of the earth ; and with the conjecture | have 
hazarded from the compression given by the experiments on the 
length of the pendulum at Unst and Portsoy. 
August 3, 1820. 
LXXIHI. On Maygr’s Formula for the astronomical Refrac- 
tion. By James Ivory, M.A. F.R.S. 
Tus rule of Mayer for calculating the refraction of the stars 
was published with his Lunar Tables; but without demonstration, 
or any hint of the manner in which it was investigated. Since 
that time the formula has not been explained in a very satisfactory 
manner, and must still be considered as a problem to be solved*. 
* “La rdgle de Mayer, proposée sans démonstration dans ses Tables de 
la Lune, est encore aujourd'hui un probleme a résoudre, parce qu'il a laissé 
ignorer le chemin qui I'y a conduit.” —Knramp. Refractions Astron. p. 169. 
It 
