590 MR J. A. BROUN ON THE 





Year. Dn Do VD = vDo gees | 
1854 0:594 0-199 0-330 — 0-028 
1855 0-562 0-168 0-340 — 0-018 
1856 0-570 0-137 0-385 + 0-027 
1857 0-613 0-187 0-351 — 0-007 
1858 0-723 0-237 0-363 + 0-005 
1859 0-826 0-305 0-356 — 0-002 
1860 0-824 0-257 0-401 + 0-043 
1861. 0-758 0-245 0-376 + 0-017 
1862 0-695 0-249 0-335 — 0-023 
1863 0-650 0-202 0-357 — 0-001 
1864 0-627 0.202 0-342 — 0:016 



(51.) It has been stated that the quantities D,, and D, are not the exact 
maxima and minima, but the differences from the mean shown in the last 
column (which are not systematic) are most probably due to another cause, if 
a perfect agreement with the equation should be expected. If the equation 
(50) be the expression of a law which relates the deviations from the 
normal positions and the forces producing them, it is obvious that it must 
refer to separate disturbances, and not to their means; and that if 2D re- 
present the sum of the deviations (their number being constant for each year), 
instead of employing “=D as has been done above, we should have taken 
=,/D. As the differences between these quantities will depend on the mode 
of distribution of the positive and negative deviations about the mean in each 
year, the nearness of the approximation obtained can be due only to the fact 
that the positive and negative disturbances are very similarly distributed at all 
hours. : 
(52.) As, in general, the hourly mean disturbance varies little near the hours 
of maximum and near the hours of minimum, I have sought the exact values 
for the hours 113 a.m., 03 and 14 p.m.. and for the hours 114 p.m, 124 and 
14 a.., in the curves for these hours showing the decennial variation (Plate XL.), — 
and have found for the former 0-847 and 0’527, corresponding to 1859'9 and 
1856°7 respectively ; and for the latter 0°335 and 0°141, corresponding to 
1860°2 and 1856°4 respectively. If D,, and D, be the maximum and minimum 
hourly mean disturbance in the maximum period, and d,,, d,, the corresponding 
quantities for the period of minimum disturbance, then by the equation, Art. 50, 
we may place 
f DE = DS Oa 
and : 
DJ ae = ./\), = / a 
we have from the values just given 
J/'847 — /'527 = 0194 
/°335 — /'141 = 0208 


