1888. ] Observations of Supernumerary Rainbows. 287 
The following table relates to (D), taking the first set of obser- 
vations. 
Number Deviation Number Deviation 
of Bar Calculated Observed of Bar Calculated Observed 
1 ed laa? (og 1° 46’ WB) TP ay ay 
Ze 8) TONS a 8 AR ae co 12 24 
Seales Ama 16) Sale} 158) 
Ae con Gi BEG 16 13 44 13 33 
De On LOG. 6 10 Wf LS 14 6 
Orel on) Loe eA ait 14 38 
7 7 48 7 AT 1). 5) as 15 10 
3) eB By) 8 31 AX) AS) Bye} 15 43 
eee 9 14 Pale AUG) 340) 1 oy 
LOS 9 58 9 56 DORAL re meal 16 41 
iy 10 385 10 33 Dan wlyiarss Ih AG 
el yl 2o Ll 3 
The agreement is not so good as in (OC), as might be expected 
from the greater values of the deviation. 
Both (C) and (D) seem to show effects of temperance differences 
in the stream of water as evidenced by nearly constant differences in 
the readings in parallel columns persisting for a considerable time. 
Thus in the primary, a variation of 6°C. in the temperature of the 
cylinder will alter the position of the geometrical bow by 11-4. 
The index was observed before and after the experiments; but the 
error might not thus be revealed, as the index was found by means 
of still water in a hollow prism which might be filled from another 
source of more steady temperature. 
The series (B), which corresponds to (A) for the primary bow, 
is not sufficiently consistent to be of much value. The light was 
not very homogeneous. The observations of the first three dark 
bars give a displacement of 528 for the principal bow, as compared 
with 518 given by the theory. 
The first dark bars in the series (F), which corresponds to (E) 
for the primary bow, yield a value 64’ for the displacement of the 
principal bow, which agrees very well with that given by the 
theory, viz. 648 calculated from the first and sixth dark bars, and 
65°5 from the first and third. 
(3) On impulsive stress in shafting, and on repeated loading 
(Wohler’s laws). By Professor KARL PEARSON. 
(4) Application of the Energy Test to the Collapse of a long 
thin pipe under external pressure. By G. H. Bryan, B.A, 
Peterhouse. 
The energy criterion of stability lends itself very readily to 
the treatment of those thin flexible structures of elastic material 
which collapse through instability of equilibrium rather than 
21—2 
