A Cooperative Stud// 
309 
wings. Fig. b is the only four-egg clutch observed. Plates V and VI show birds 
sitting, the camera being about 18 inches from the bird. 
The characters observed were identical Avith those of 1913, namely : 
1. Length (/>); 2. Breadth (B); 3. Longitudinal Girth ((?;); 4. Transverse 
Girth (G'i); 5. Tone or Ground Colour ; 6. Mottling; 7. Type of Nest. 
The tone or ground colour was in 1914, however, divided into browns and 
greens. The scale of browns was that of the (.'olour Value Scale of Plate VIII of 
the hrsl paper, and the green values were judged on a similar scale divided into 
corresponding classes a, h, c, d, e, f, g, h, i, k. These classes are distinguished by 
the subscripts 1 and 2 for brown and green values respectively. Two eggs only 
had to be excluded from these colour value observations; one was blue and the 
other slatey gray in ground colour. These reduced the total number of eggs avail- 
able for colour value reduction from 1110 to 1108. The classification of mottling 
follows Plate IX of the earlier paper. Types of Nest were divided into three 
categories, = no hole in the ground and no materials, t.2 = a, hole but no materials. 
= both hole and materials. As only one nest (with a three-egg clutch) occurred in 
type t-i, we have grouped with t.,, so that the distinction is I'eally of "inielaborated 
and elaborated nests. 
Of the characters dealt with, the transverse girth (Gn) was really taken as a 
check on the general accuracy of measurements. We should have 
TT = Mean Transverse Girth/Mean Breadth 
or rather tt is equal to this ratio multiplied by the factor (] — >',.^fj Va^Vjj + v^j-) 
where r^;^g is the correlation of the transverse girth with tlie breadth and Vq^^ and 
equal y^^y of the coeflficients of variation of transverse girth and breadth re- 
spectively. This factor was "99990 in the previous set of observations and is 
I'OOOOG now. Hence its influence on tt = G/JB is insensible for our purposes. 
We find TT = 3'207l against 3'2237 of the earlier series. Thus although the value 
of TT is bettered, we still find the transverse girth is somewhat e.xaggerated, i.e. 
TT is about 2 ' /o error when thus deduced. It might at first sight suggest itself 
that the transverse section of the egg may not be truly circular. Suppose it an 
ellipse of eccentricity e. Then if we agree that it is equally likely that the breadth 
of the egg may be measured in any meridian we find 
Transverse Girth _ /i , 4\ 
Mean Breadth " ^ + ti; O, 
if e be small. If, however, we put in the values found, i.e. Go/B = 3'207l, we have 
= -3320, 
leading to b = "GSlOa for the relation between the semi-axes of the ellipse — a 
quite impossible value. It may be suggested that our chance of taking every 
breadth is not equal and that we are most likely to take the wiinimuui breadth. 
In this case we should have 
Gj,IB = TT {I + {e% 
