16 National Geographic Magazme. 
ing the difference of the equations to be 0°.26. On May 1, one 
set gave 0%.32, and another 0°.29. On May 2, only one set was 
made giving 0°.36, a variation of 0°.07in two days. In June 1884, 
one year later, another series of observations of the same character 
was made at the Naval Observatory in Washington, and on the 
same nights the personal equation machine invented by Prof. 
Eastman, was used as a comparison. This is an instrument in 
which an artificial star is made to record its own transit over the 
wires of a reticle, while the observer records the same with a chro- 
nograph key. The difference is manifestly the personal error of 
the observer. This gives the absolute equation of the observers, 
and their difference is the relative equation, and should accord with 
that found by the method of alternate stars. Some of the results 
-were.as follows :—On June 4, the difference by machine of their 
personal errors was 0°.16 and by star observations 0°.24, on the 15th 
of June the machine gave 08.10 and the stars 0°.24, on the 16th, 
machine 0%.14, stars, 0°.13, a very close agreement, on the 17th, ma- 
chine gave 0*.07 and stars 08.18. The observer N. combined with 
another, C., who had not had as much experience in observing, 
gave still more discordant results. On June 20, the machine gave 
as their relative equation, 0°.08, while star observations gave 0°.27, 
on June 23, machine 0°.13, stars 0°.5t, and on June 28, machine, 
08.20, stars 0°.35. In the case of the first two observers a mean 
of the determinations amounting to about 0°.20 might have been 
applied to the measurements made by them, but as these were 
made under all conditions of climate, in latitudes varying from 
30° N. to 36° 8. and in different states of health and bodily com- 
fort, 1t was concluded not to introduce any correction at all rather 
than one that might be considerably in error. In all of the work 
it has been the custom as far as possible to place the observers 
alternately east and west of each other, so that the result of 
personal error in one measurement is neutralized to a greater or 
less extent in the next. Of course the method of exchanging 
stations and making two measurements of each meridian distance 
would afford the best solution of this problem, but except in 
certain favorable conditions, this is precluded by considerations 
of time and expense. In the measurement between Galveston 
and Vera Cruz mentioned above, it had been the intention to 
exchange stations, but by the time the first measurement was 
finished the season was rather far advanced, there was danger of 
yellow fever in Vera Cruz and an observer going there at that. 
