SEPTEMBER 29, 1899. ] 
The average range of the 24 adult per- 
sons represented in the Table is 1°.45 for 
horizontal settings and 1°.56 for vertical 
settings. The corresponding ranges of so 
many of these persons as were distinctly 
astigmatic were 1°.48 and 1°.56 respec- 
tively. The average deviation of the hori- 
zontal settings of the astigmatic adults is 
0°.46 and of the other adults 0°.35. The 
corresponding average deviations of the 
vertical settings were 0°.82 and 0°.54. I. 
have partial records for a good many other 
persons but the numbers given in the Table 
are fairly representative. 
Taking into account all the results, and 
calling the mean of a great number of read- 
ings of settings made by any person, his 
‘ deviation,’ we may say, that persons en- 
tirely untrained in making measurements, 
generally set the line rather carelessly, as 
children do, and have large ranges, though 
their deviations are not especially large. 
Trained observers have smaller ranges than 
other people, but their deviations are not 
noticeably small. Astigmatism, so severe 
as to require the constant use of spectacles, 
does not seem to affect the readings much. 
‘Only one person in ten is likely to have a 
deviation as great as 1° for horizontal set- 
tings, while one person in five may be ex- 
pected to have a deviation of 1° or more 
for vertical settings. A deviation as great 
as 1°.6 is very unusual, but many persons 
may be found whose deviations both from 
horizontality and verticality are less than 
0°.1. The average deviation is about 0°.4 
for horizontal settings, and about 0°.5 for 
vertical settings. 
If the platform upon which the observer 
stands be inclined (sidewise) to the horizon, 
he becomes ill at ease and his deviations 
are generally altered. Whether the plat- 
form is tipped downward towards the left 
or towards the right, however, seems in 
many cases not to affect the signs of the 
mew deviations, which are sometimes, if 
SCIENCE. 
429 
not usually, mere exaggerations of those 
obtained when the platform is level. A 
certain skillful mechanician, for instance, 
had deviations from horizontality and 
verticality of + 0°.5 and — 0°.8, respec- 
tively, with platform inclined 5° downward 
to the right, and corresponding deviations 
of +0°.6and — 0°.6 with platform inclined 
to the left. His horizontal and vertical 
deviations when the platform was level, 
were positive and negative respectively, but 
not greater than 0°.1 in either case. 
If the observer stood on a level platform, 
squarely facing ina direction at right angles 
to the axis of the tube, and then looked over 
his shoulder, using both eyes and turning 
only the head and neck, he was still able 
to set the line horizontal or vertical with 
some accuracy. The horizontal deviations 
of two observers while standing in the way 
just described and looking over their right 
shoulders were = 0°.0 and —1°.0. Their 
vertical deviations were — 0°.2 and — 1°.0. 
Table V. gives the results of some set- 
tings taken when the observer, using only 
one eye, stood at his ease in front of his in- 
strument. 
TABLE VY. 
S | Means of horizontal settings| Means of vertical settings 
z made with made with 
ic} 
4 the right | the left | both |the left|the right) both 
4 eye. eye. eyes eye. eye. eyes. 
1 | —0°.4 | —0°.1 | 09.0] +0°.0) —0°.1 | +0°.0 
2) +1 .4 | —0O.7 |+41 .4 +1 .3) +0 .2 |+0 .8 
3 | +0.1] +0 .8 | +0 .0|/—O .4) +0 .0 |-++0 ol 
It should be said that the first two of 
th ese observers when asked to point quickly 
at a distant object, always indicate a line 
passing midway between the eyes, and not 
a line passing through one eye, as many 
people do. 
Two persons successively took observa- 
tions by standing on a shelf with back 
squarely turned to the tube and trying to 
set the line horizontal while looking back- 
wards between the legs with head inverted. 
