42 
LANGLEY. 
observer, but even in his case it varies with the daily acci¬ 
dents of the human organism, and even with him it is pre¬ 
sumably constant only for the particular observation to 
which the experience applies. There is not even a pre¬ 
sumption, I think, that the personal equation belonging to 
an experienced transit observer would apply to the same 
person’s notation of the occultation or emergence of a star, 
and still less, if possible, to any phenomenon outside his 
ordinary professional experience; for we must, of course, 
recognize that we carry this fallibility with us in every act 
of life, and that it is just as present when we attempt to de¬ 
termine the instant at which a race-horse passes the winning 
post as when we seek to note the particular hundredth of a 
second at which a star passes the wire. 
The very words “ personal equation ” imply that the errors 
due to this fallibility can be ascertained and allowed for, and 
may lead us to think (if we think carelessly) that there is a 
personal equation always ascertainable; whereas, as we in 
fact know, it is only possible to apply the correction where 
long habit has settled the amount of error to be expected 
with regard to some one special phenomenon. 
The number of devices for obtaining and correcting the 
personal equation, even in the special case of meridian ob¬ 
servation, is, as those who have studied the subject know, 
surprisingly great. I think I have myself examined more 
than fifty such, and with hardly an exception they all ex¬ 
hibit variations on one idea—the idea, that is, that the error 
must have been committed first; the committing of the error 
being assumed to be an inevitable necessity, for which sub¬ 
sequent correction is to be made. 
I have thought, then, that it might be interesting if I were 
to ask you to consider with me what may seem at first the 
somewhat paradoxical suggestion, that means may be found 
by which any individual, skilled or ignorant, may make, 
not only meridian observations, but an observation of any 
sudden visible event of whatever nature, so accurately that 
we need apply no correction, because the precision may be, 
