SEPTEMBER 8, 1899. | 
film or the results of imperfect development. 
The fact that they are found only in the imme- 
diate vicinity of the bright flash is additional 
testimony in the same direction. These mark- 
ings are wholly different from any that I 
have seen, not having the form of branched 
flashes. Something in their resemblance to 
photographs of sound-waves started by a spark, 
which I have recently made (see Phil. Mag. for 
August) suggested to me that they might possi- 
bly be due to the illumination of the sound- 
wave due to a powerful discharge by a second 
discharge. Under ordinary conditions, that is 
with a uniformly illuminated background, such 
waves would, of course, be invisible, but condi- 
tions might possibly arise, due to the proximity 
of black clouds, under which they might show— 
a sort of ‘Schlieren Methode’ on a large scale. 
Ihave not attempted yet to plan an arrange- 
ment of clouds, which, by acting as screens to 
light coming from certain directions, might 
render visible a region of the air, in which the 
optical density underwent a rapid change. In 
Mr. Lumsden’s picture there are many dark 
clouds close to the flash. The idea of a photo- 
graph of a thunder-wave is a pleasing fancy at 
all events. 
It seems to me that it will be impossible to 
formulate even a reasonable guess as to the 
cause of these dark flashes until a good many 
pictures are gotten together for comparison, 
and as much testimony as possible secured as 
to the appearance of the flashes to the eye. 
Personally, I have seen very few of the pictures 
and never the original negative. 
My intention in writing this letter is not so 
much to advance theories accounting for the 
phenomenon of the dark-flash as to re-awaken 
an interest in the subject and bring out ideas 
from persons better qualified than I to treat the 
matter. R. W. Woop. 
MADISON, WIs. 
A REPLY. 
EpIToR oF SCIENCE: The review of my 
‘Elements of Practical Astronomy’ by G. C. 
C., in Scrence for June 16th, criticises ad- 
versely some eight or ten small points. In so 
far as the article expresses the reviewer’s indi- 
vidual opinions, there is no call for a reply, 
SCIENCE. 339 
since that is the prerogative in which a critic 
should be protected. But I venture to say that 
the reviewer’s zeal has led him unconsciously 
to make several erroneous statements. 
In answer to the remark : 
“Throughout his entire work the author ap- 
pears to have ignored the advantage offered 
by addition and subtraction logarithms,’’ I re- 
spectfully refer him to page 50, where both ad- 
dition and subtraction logarithms are employed, 
and to the statement, p. 243: ‘If two quanti- 
ties are given by their logarithms, and the log- 
arithm of their sum or difference is required, it 
should be found by means of addition and sub- 
traction logarithms.’’ This covers the whole 
case. 
The reviewer regrets that the book gives up 
‘4% to diurnal parallax as affected by the 
earth’s compression.’ Such is not the case. 
Less than 2% is devoted to this subject, and in 
reality only about 1%, if we deduct the space 
demanded for the substitute treatment of the 
earth regarded as a sphere. Besides, the in- 
clusion of this subject is imperative, unless, in- 
deed, we exclude observations of meteors, the 
moon and any other near-at-hand bodies. Is G. 
C. C. willing to send out students of Practical As- 
tronomy ignorant of the fact that there can be 
a parallax in azimuth?’ His criticism means 
just that. 
The formula expressing the rate of a chro- 
nometer, p. 160, criticised in all seriousness by 
G. C. C., will meet his requirements if we re- 
place the missing exponent 2 over the paren- 
thesis—the only omission of the slightest con- 
sequence yet brought to my notice in the more 
than 400 equations. This formula is as funda- 
mental in dealing with a chronometer as sin? +- 
cos?—1 isin Trigonometry, and should give a 
reviewer no trouble. 
The reviewer refers to a well-known method 
of computing the azimuth, p. 199, and curiously 
enough misses the whole point of the method. 
He suggests another method—also well known 
—which in practical use is actually longer, with 
the added disadvantage of requiring two kinds 
of logarithms in the same solution. It is true 
that one solution by the first method requires 21 
entries on the computation sheet (all the quan- 
tities being recorded), whereas the substitute 
reviewer's 
