DECEMBER 17, 1896, 
IEA TAC RE 
165 
a spirit-level depends not only on the bending of the surface of 
the earth, but also on the attraction exerted by the load, which 
slightly alters the direction of ‘‘ gravity.” He shows that if 
yw, is the alteration in level produced by the bending, and yp, 
the alteration in the direction of gravity, then the ratio W,/, 
depends only on the elastic constants of the earth, and is quite 
independent of the shape and size of the loaded area. In the 
case of a material having the elasticity of steel y,/, = 2, for 
brass Y,/) = 5, and for an incompressible material y,/. = 11. 
The author considers that this last value most truly represents 
what occurs in practice, and hence that the pressure effect is 
considerably larger than the gravitational effect. The pressure 
effect is worked out for the cases where the loaded area is a 
square, and a long narrow rectangle, and it is found that fora 
square of 100 metres side the effect, at a point one metre from 
one side, of loading the square with a layer of water one centi- 
metre thick, is to alter the level by o’oor2 second of arc. For 
the case of a tidal river 100 yards wide, and for arise of 5 
metres, the effect on an observatory at 100 yards from the bank 
would be to alter the level by o*1 second of arc. Hence the 
effect of an estuary or tidal river is likely to be much more marked 
than differential evaporation or rainfall. The author also considers 
the effects of the attraction of the sun and moon, producing as 
they must ‘‘ tides” in the solid crust of the earth, on the reading 
of a level and the measured altitude of a star as obtained with 
an artificial horizon. Finally the author considers the light the 
measurements on the velocity of propagation of earthquake dis- 
turbances throw on the credibility of the hypotheses he has 
made us to the elastic constants of the earth. He shows that 
the two observed velocities of 2°5 and 12°5 kilometres per second 
would lead to values for Young’s modulus, and the rigidity below 
those found in the case of iron; the bulk modulus, however, 
obtained is very high, and this he considers quite probable on 
account of the enormous pressure to which the earth’s deep- 
seated material is subjected. Prof. Perry said he had thought of 
taking up the subject from an experimental point of view, and 
trying the effect of loading a large block of indiarubber. He 
had not had time to refer to the author's paper, in which the 
reasons were given for taking the earth as incompressible. He 
(Prof. Perry), however, thought that this assumption led to 
results in contradiction to actual observed facts. Prof. Milne 
had obtained results which, for want of any other explanation, 
he had been compelled to attribute to meteorological causes. 
The reason Dr, Chree had obtained so small a value for the effect 
of loading by surface water might be because he had assumed 
erroneous values for the elastic constants. If he took a value 
for Poisson’s ratio such as we meet with in practice, the 
effects would be much larger. Prof. Darwin had also investi- 
gated the folding of the surface of the earth due to loading. 
The results obtained by the author with reference to the ve- 
locity of waves did not seem quite satisfactory. The small 
waves which were found, both at Berlin and the Isle of 
Wight, to precede the main waves coming from an earth- 
quake in Japan were not accounted for. The wave velocity in 
an infinite mass of steel (a very elastic material) was about 6 
kilometres per second, which was very different from 12°5 
kilometres per second. The author had assumed such values 
for the elasticity as would give the correct velocity. The 
author in reply said that in applying the equations of elas- 
ticity to the earth’s interior, unless the material were supposed 
nearly incompressible, one obtained values for the strains too 
large to be consistent with the fundamental mathematical hy- 
pothesis, that the square of strains are negligible. In the 
case of surface loading no such restriction was necessary, so far 
as the surface layers, at least, are concerned. The differences 
between the several numerical estimates for the ratio of the 
gravitational and pressure effects of a surface load were prin- 
cipally due to the differences in the hypothetical values ascribed 
to the rigidity. It was his wish to make it clear that the pres- 
sure and gravitational agencies treated in detail in the paper were 
not the only ones likely to affect the level; he had specially 
called attention to solar heating and possible direct influence of 
moisture on the foundations of buildings, &c. The reason why 
for the one wave velocity so much higher a value was obtained 
than that Prof. Perry calculated for steel, was solely the high 
value, 24: 1, found for the ratio of Thomson and Tait’s elastic 
constants 7 and 7. He knew Prof. Darwin had treated of the 
phenomena met with in loose earth in some cases, but could not 
say whether this was what Prof. Perry referred to. He had him- 
self once thought of attempting an application of what Prof. 
NO. 1416, VOL. 55] 
Karl Pearson termed the ‘‘ equations of pulverulence,” as treated 
in detail by Prof. Boussinesq, but had not done so, partly from a 
feeling of uncertainty as to their physical value. Supposing 
these equations satisfactory, they ought to give better results 
than the equations of elasticity when surface load was applied to 
a deep alluvial soil.—A paper on musical tubes, by Mr. R. T. 
Rudd, was, in the absence of the author, read by the Secretary. 
The author has examined a set of tubes ranging in length from 
95 inches to 12 inches, made out of ‘* 1-inch” gas-tube. Having 
tuned these to a diatonic scale, he found that there was a very 
marked difference in the character of the sound of the long, the 
middle, and the short tubes. Commencing with the long tubes, 
the first two octaves have a full rich tone very similar to that of a 
church bell. They range from D of 145 vibrations per sec. to D 
of 580 vibrations. At about this point the tone changes from 
that of a church bell to one peculiar to tubes, the note also falls 
back in the scale more than a fifth, viz. to F¥ (360), the san.e 
tube giving two notes, to either of which the attention can be 
directed. In order to distinguish these different classes of 
sound produced by tubes, the author calls the tone corresponding 
to that of a church bell the ‘‘low grade,” the next one the 
“middle grade,” and that produced by short tubes (27 in. and 
under) the ‘‘ high grade.” At the junction between the high 
and middle grade there is a fall in the note of about an octave 
anda half. The following formula may be used for calculating 
the pitch of the note given by a tube: V = DC/L’, where V = 
frequency, D = external diameter, L = length, and C is a 
constant which for iron tubes has the value 100 x 104, 62 x 104, 
or 22 x 10%, according as the note belongs to the low, the 
middle, or the high grade. The author explains the effects by 
a consideration of the partial tones present and their effect on 
the ear. Prof. Riicker said he thought it a great pity that in 
England such confusion of nomenclature existed, so that 
partials were often called over-tones. He considered that the 
author had made an extremely ingenious attempt to explain 
the differences of pitch observed, this explanation apparently 
resembling that given by Prof. Everett to account for combina- 
tion tones. The author explains the presence of a note of fre- 
quency 630, as being formed in the ear by the harmonies having 
frequencies of 1260, 1900, and 2600. He also explains the 
absence of lower partials having frequencies of 780, 390, and 140 
by the supposition that they are so far removed from the “‘ focus” 
as not toappreciably affect the ear. Another explanation of the 
presence of a note of frequency about 630 would, however, be 
the formation of a difference tone between the partials of fre- 
quency 780 and 140. Mr. Blaikley agreed with Prof. Riicker 
as to the vagueness of the terms often employed, and said that 
it appeared that in the ‘“‘high grade” the note was caused by 
the first proper tone, in the ‘‘ middle grade” by the second, 
and in the ‘‘low grade” by a difference tone produced by the 
fourth, fifth, and sixth proper tones. The distance of the 
nodes from the end of the tube was ‘224 of the length, and not 
‘25, as the author states, and in the case of a tube clamped at 
the node, this difference in the position of the clamp would have 
a marked effect on the tone. A great distance in the tone was 
also produced by varying the hardness of the hammer. _ Prof. 
Ayrton said he had once investigated the behaviour of some 
tubes by analysing the note given out by means of a Helmholtz 
analyser. In the case of the tubes that gave a good note, it 
was found that the components were few and well-marked, 
while in that of the tubes which gave 2 bad note, the com- 
ponents were numerous and sometimes very ill-defined. The 
relative length, diameter, and thickness of the tube had a great 
influence on the tone. 
Chemical Society, December 3.—Mr. A. G. Vernon 
Harcourt, President, in the chair.—The following papers were 
read: Constitution and colour, by A. G. Green. Colouring 
matters may be classified in two groups, viz. : (1) Colours whose 
leuco-compounds are not readily oxidised on exposure to air; 
(2) colours whose leuco-compounds aye rapidly oxidised on ex- 
posure to air. It is shown further that the members of class 1 
are all para-derivatives, whilst those of class 2 can all be repre- 
sented as ortho-compounds.—Derivatives of a-hydrindone, by 
C. Revis and F. S. Kipping. The authors have studied a- 
hydrindone in order to determine whether its reactions are 
analogous to those of camphor, which it resembles somewhat in 
constitution ; there is, however, a marked difference between 
the chemical behaviour of the two ketones.—Notes on 
nitration, by H. E. Armstrong.—3’-Bromo-f-naphthol, by 
