hat my outlook into the future was no better than his.

"One of the unfavorable results of the attempt to popularize science is
this: the reader of popular scientific books is very likely to think
that he understands the science itself, when he merely understands what
some writer says about science.

"Take, for example, the method of determining the distance of the moon
from the earth--one of the easiest problems in physical astronomy. The
method can be told in a few sentences; yet it took a hundred years to
determine it with any degree of accuracy--and a hundred years, not of
the average work of mankind in science, but a hundred years during which
able minds were bent to the problem.

"Still, with all the school-masters, and all the teaching, and all the
books, the ignorance of the unscientific world is enormous; they are
ignorant both ways--they underrate the scientific people and they
overrate them. There is, on the one hand, the Irish woman who is
disappointed because you cannot tell fortunes, and, on the other hand,
the cultivated woman who supposes that you must know _all_ science.

"I have a friend who wonders that I do not take my astronomical clock to
pieces. She supposes that because I am an astronomer, I must be able to
be a clock-maker, while I do not handle a tool if I can help it! She did
not expect to take her piano to pieces because she was musical! She was
as careful not to tinker it as I was not to tinker the clock, which only
an expert in clock-making was prepared to handle.

"... Only a few weeks since I received a letter from a lady who wished
to come to make me a visit, and to 'scan the heavens,' as she termed it.
Now, just as she wrote, the clock, which I was careful not to meddle
with, had been rapidly gaining time, and I was standing before it,
watching it from hour to hour, and slightly changing its rate by
dropping small weights upon its pendulum. Time is so important an
element with the astronomer, that all else is subordinate to it.

"Then, too, the uneducated assume the unvarying exactness of
mathematical results; while, in reality, mathematical results are often
only approximations. We say the sun is 91,000,000 miles from the earth,
plus or minus a probable error; that is, we are right, probably, within,
say, 100,000 miles; or, the sun is 91,000,000 minus 100,000 miles, or it
is 91,000,000 plus 100,000 miles off; and this probable error is only a
probability.

"If we make one more o