January 21, 1897 | 
NATURE 
271 
Acceleration. 
In Nature, No. 1415, p. 125, Prof. Lodge asserts that the 
subject of acceleration is at the root of the perennial debate be- 
tween engineers and teachers of mechanics ; and he urges clear- 
ness of idea and accuracy of speech on all who deal with the 
junior student. Towards this end I would suggest that the too 
common phrase “acceleration of velocity’ should be aban- 
doned when the idea intended is ‘‘ velocity of velocity.” Vand 
V ought not to be confounded. Let the student be told that the 
time-rate of change of a particle’s speed in any given fixed 
direction at a given instant is called the acceleration of the Aar- 
ticle in the given direction at the given instant. If the direction 
of the particle’s motion at the given instant makes anangle @ with 
the given fixed direction L, and if the speed of the particle in its 
own direction at this instant is V, its speed in the direction L is 
Vcos @. The time-rate of change of this is called the accelera- 
tion of the fardéc/e in the direction L. It is [V cos @— V@ sin 0] 
units of speed per unit of time. If @= 0, L coincides with the 
line of motion, hence the acceleration of a particle along its line 
of motion is V units of speed per unit of time. If @ = 47, L 
coincides with a normal, hence the acceleration of the particle 
along a normal is V@, 2.e. it is the product of the linear speed 
and the angular speed. Linear speed is expressed in units of 
length per unit of time; angular speed is expressed in units of 
angle per unit of time, Acceleration is expressed in units of 
speed per unit of time. EDWARD GEOGHEGAN. 
Bardsea. 
Tus is simply kinematic, and well known ; but perhaps its | 
adduction at the present time is useful as emphasising the fact that 
acceleration in general is not a ludicrously simple and obvious 
idea. The term “ velocity ” is, however, hardly a good synonym 
for ‘‘rate of change” of everything: the term ‘‘ fluxion ” would 
be better; moreover, none, of the phrases about ‘‘units”’ are 
necessary. OL Yerue 
The Rydberg-Schuster Law of Elementary Spectra. 
THE interesting law of connection shown so clearly by Prof. 
Schuster in the recent pages of Narure (vol. lv. p. 200, and 
p- 223), to exist between the primary and secondary series of 
lines in the representations given by Kayser and Runge of the 
spectra of certain metallic elements, is a law which seems so 
suggestive of the musical phenomena termed in acoustics 
‘« difference-tones,’’as a possible explanation of its origin, that it 
may perhaps be of some use in seeking fora true account of the 
connection, to show heré how it may be held, if not quite 
perfectly and exactly; at least up to a certain point of great 
resemblance, to possess that aspect. 
The set of fundamental and over agitation-rates comprised in 
a Balmer-series, form a sort of chime of rays together, perhaps 
not very unlike the mixture of notes composing the almost 
vocal-sounding scream, or buzz, rather than a pure note, whicha 
humming-top emits. From combined actions of the proper mem- 
bers of this chime, sets of vibrations would no doubt arise, with 
oscillation-rates in a succcession of secondary series, equal to the 
surplus rates of all the succeeding proper members of the chime 
above the oscillation-rate of some starting member. In the case of 
=A ( Le ( =. Ny) the differential set 
Balmer’s series, 7 
nN 
for all the vibration-rates following the first, or fundamental 
Kate; (7t<— A(t ~ (2)); is represented generally by 
3 
=@))--O}--@)}} 
or 2, =) 4G - (3)). a slightly modified Balmer- 
series, of which the convergence frequency, 
(4 #4 4(+- 0) 
or the excess of the primary series’ convergence frequency, 4, 
above its fundamental rate of vibration, 4 (1 = (¢)) 3; the 
3 
' 
n'y 
NO. TSI VOL. 55 | 
law of dependence of the secondary on the primary series found 
to hold good ina number of line-spectra of the elements, by 
Prof. Schuster and Prof. Rydberg. But the form of the second 
series is a little different from that of the first, in that the 
coefficient of its second term is nine times instead of four times 
the fixed value of the firstterm. I regret that Iam not familiar 
enough with the measurements obtained, and with the very im- 
portant discussions that have been based upon them, to be able to 
say if any secondary series of this modified form, or of the similar 
2 subaA ee LNs on fats 
higher forms, as 7’, = (3) AQ ( 
W 
with in the ranks of lines found by Kayser and Runge to 
accompany the chief, or leading ranks in so many of the 
spectra of the elements. But as a supposition which seems 
thus to present itself most prominently and invitingly for trial 
and consideration, I would yet venture to suggest that real or 
actual productions of secondary rays by differences of rates of 
vibration among primary rays, may perhaps occur in molecules 
in some such way as that recently expounded by Prof. Everett ! 
to account for the corresponding phenomenon of audition of 
diflerence-tones in acoustics without excluding those tones as 
purely subjective existences from a real place in physics. If the 
possibility of such secondary, differential light rays’ origination 
from primary vibrations in molecules is admissible, then this 
present description of their long secondary, tertiary and other 
higher ranks or scales of vibration-rates, may perhaps prove. 
means (with some transformations very possibly not quite in- 
explicable, in the least complicated cases) of comprising all the 
secondary ranks’ array of vibration-lrequencies, and the sur- 
prisingly exact law of numerical dependence shown so very 
certainly and clearly by Prof. Schuster to hold between the 
primary and secondary ranks’ terminal oscillation-rates, in one 
view of physical relationship together. A. S. HERSCHEL. 
Observatory House, Slough, January 9. 
) ’ ), &c,, are met 
P.S.—The answer to this suggestion is, I see, supplied already 
by Prof. Schuster in his first letter on this newly-found relation- 
ship; for he has there noted (this vol., p. 201), that the 
above supposed successive differences, although their series, 
B 
yy is of the type A- —, only approach to, with- 
ae 
SG 
out exactly reproducing the set of frequencies of the subordinate 
If A= iB represents the lowest or ‘‘funda- 
3 
mental” rate of vibration, F, in all the primary line-series, and 
spectrum-series. 
et 18} ; ? : 
therefore = A - F the ‘‘conyergence frequency,” A’, common, 
2 i 
by the observed law. to both the line-series subordinate to such 
a primary one, then whatever values, near 4, B may have been 
found to have in the chief series, the first of the above ideal series 
AB! 
and this does not correspond more than approximately, except 
in rays of frequencies very near to the ‘‘ convergence-value.”” 
of differences may easily be seen to be always A i ( 
Sailing Flight. 
ALL students of aerodynamics must be sorry to learn of the 
death of Herr Lilienthal, on August rr last. His loss is serious, as 
he evidently had the courage necessary to put these exceptionally 
dangerous experiments to practical test, which few care to do, 
and had thereby gained a large experience. 
I have just secured a Cyrus (Gras antigonz), 5 feet 2 inches 
in height. It weighs 16 pounds, and has a spread of wings 
8 feet 8 inches. 
The primary feathers require 10 ounces each to bend them to 
the curve seen when the bird is soaring ; they are 17 inches 
long on the feathered portion, not all identical in size or 
strength, but their total comes so nearly to the weight of the 
bird, that it is obvious the primary feathers constitute the lifting 
mechanism. 
From the almost universal arrangement of the mode of sup- 
port in relation to the weight, as seen amongst birds, bats, and 
1 Proceedings of the Physical Society of London, vol. xiv. p. 93; and 
Philosophical Magazine, March 1896. 
