466 
to war conditions the National Physical Labora- 
tory has been unable to issue published results of 
experiments with any machines other than a 
Blériot monoplane which was tested as an illus- 
tration of the general method before the war broke 
out. On the other hand, the paper deals largely 
with mathematical considerations, and on exam- 
ination there will be found to be scarcely a single 
feature for which chapter and verse cannot be 
found in the present reviewer’s “Stability in Avia- 
tion,” published five years ago. It scarcely ap- 
pears desirable, when so much further work 
remains to be done, that the resources of the 
Hodgkins Fund should be expended in duplicating 
what has previously been said and worked out in 
greater detail elsewhere. Furthermore, several 
changes that have been introduced into: the 
treatment are open to serious objections. We 
all regret the discrepancy between the co- 
ordinate axes of the National Physical Labora- 
tory papers and those used in the mathe- 
matical theories; unfortunately, as the result of 
mutual discussion, it is evidently impossible to 
break the continuity of the Teddington investiga- 
tions. But there is no justification for extending 
this lack of uniformity to an entirely new set of 
investigations started in America. The main 
reason for objecting to the system in question is 
that the notation is unfamiliar to English students, 
all of whom have acquired their knowledge of 
applied mathematics, in the first instance, from the 
study of two-dimensional problems, and after- 
wards extended it to three-dimensional space. 
This objection applies with special force to the 
problem of longitudinal stability, which is essen- 
tially two-dimensional, But Messrs. ‘‘ Hunsaker 
and others ” make further changes which are not 
only very confusing, but out of accord with 
the usage of both our mathematicians and our 
physicists. The most objectionable feature is the 
use of the letter D in two entirely. different mean- 
ings in the same equation with only a suffix to dis- 
tinguish them. The writers would have done well 
to study a little more carefully the long alphabet 
at the end of “Stability in Aviation.” 
The exclusive reference to Mr. Bairstow in con- 
nection with the splitting up of the two biquad- 
ratics is open to the objection that it would be 
quite impossible for anyone without exceptional 
mathematical ability and power of insight to 
deduce the formule in question by any method 
of factorisation or numerical substitution indi- 
cated in the advisory committee’s National 
Physical Report, Paper No. 77, and even verifi- 
cation by long multiplication is none too easy, 
whereas the proof in “Stability in Aviation” is 
perfectly straightforward and simple. 
The omission of references to methods of suc- 
cessive approximation is again unfortunate when 
the authors come to describe the character of the 
lateral motions. Why, for example, is one root 
of the biquadratic said to represent a “spiral 
dive’ and another pair to represent a “ Dutch° 
roll”? These things can be found partially ex- 
plained in “Stability in Aviation” (although the 
late Prof. Harper worked the subject out in 
NO. 2468, vot. 98] 
NATURE 
| 
[FEBRUARY 15, 1917 
greater detail in a paper he never published) andi 
| also in Mr. Bairstow’s National Physical Labora- 
tory researches, but a reader of this paper 
_ would think that the difference in the periods and 
logarithmic increments or decrements was the: 
only essential distinction. 
A still worse feature of the whole investigation. 
is that while acknowledging the influences of cir-: 
cular motion on stability, the writers completely 
ignore the “Harper effect.” The present re-- 
viewer hopes that a fitting recognition may be 
given to the work of his former assistant and col-: 
league, the late Lieut. E. H. Harper, M.A. (pro- 
fessor of mathematical physics in University 
College, Cork, and recently killed in action), by 
thus associating his name with his independent 
discovery that stability, both longitudinal and 
lateral, is greatly affected by even small changes 
in the inclination of the line of flight to the hori~ 
zon. An aeroplane fatality has recently been re-- 
ported which was clearly attributable to this cause. 
It was no intention of the author of “Stability 
in Aviation” to extend his criticisms to state— 
ments, conclusions, and expressions of opinion. 
which fall within the province of the physicist 
or engineer rather than within that of the 
mathematician. But apart from specific refer— 
ences to the two machines which formed the 
subject of the experiments, the similarity betweem 
the present treatment and that of the Science 
Monograph obtrudes itself on one’s notice in the — 
most unexpected quarters. It will be most in- 
teresting to learn whether Mr. 
better than did the present writer in appealing to: 
practical men to study stability with models rather 
than to rely on experiments in the open air. He 
states (p. 5) that he actually “knew a pilot” who 
nearly lost his life by trying a spiral dive in the 
air! But when “Stability in Aviation ” was in the 
press fatalities occurred daily, and killing off the 
pilots of unsafe machines was the only method that 
the practical man would have anything to do with. 
To invoke the assistance of a mathematician 
would have been an idea too terrible for words, 
and as for compensating him for his loss of time 
over the work, this might have cost 10ol., which 
would have been a preposterous waste of money ~ 
-when the same thing could be done by smashing — 
up ten machines costing 1000l. each. 
Mr. Hunsaker claims that laboratory experi- 
ments and calculations are superior to tests made — 
in the open air, and remarks that “weather con- — 
ditions, motor ‘troubles, personal peculiarities of 
pilots, etc., tend to add to the complexity of an 
otherwise very simple problem.” But exactly the 
same considerations were invoked in 1910 by the 
opponents of theoretical and physical methods as: 
proving that the latter methods were practically ~ 
The large number of mathematical in-— 
useless. 
vestigations (some of them in progress) that were 
bundled into the collection of “problems” at the 
end of “Stability in Aviation ” will give some idea 
of the amount of work which, as the result of 
this opposition, was suspended on the ground 
that no useful purpose would be served by its con- 
tinuance. 
Hunsaker fares. — 
