84 
Proceedings of Royal Society of Edinburgh. [sess. 
measurements, are shown along with their corresponding longitudes 
in the following Table II. Here again, of course, the diurnal and 
lunar shifts have been duly accounted for. 
Table II. 
© 
Distance 
in t.m. 
© 
Distance 
in t.m. 
337 
0-3611 
o 
88 
0-3659 
0 
•3608 
93 
•3661 
8 
•3573 
95 
•3702 
24 
•3597 
103 
•3711 
48 
■3625 
120 
•3757 
61 
•3616 
151 
•3762 
65 
•3645 
170 
•3792 
70 
•3650 
176 
•3802 
73 
•3675 
183 
•3801 
77 
•3658 
197 
•3808 
81 
•3670 
201 
•3798 
83 
•3650 
214 
•3809 
If these values are represented by a simple harmonic of the form 
A + a sin (0 - a) 
and the values of A, a , and a are determined by the method of 
least squares, we find A = 0'3700, a= — 0’01048, and a=281°‘4, 
or, expressing a in km. per second : 
a= -0-4986 ± 0*0162 
a = 281°-4 ± l°-9 
Introducing in our formula 
27r. a e 
sin p. T J 1 _ e 2 
sin ( O - tt) 
the bestdaiown values of the constants, it assumes the numerical 
form : 
0-499 sin (O -281°-3) 
Accidentally the agreement is perfect ; the assigned probable 
errors may, however, give an approximate measure of the accuracy 
of the values for a and tt obtained from the observations. 
Let us now investigate how far the measurements are capable 
of showing the diurnal shift. We correct the original dis- 
