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The sense of verticality and its application to lighthouse work
THE SENSE
OF VERTICALITY TO LIGHTHOUSE
AND ITS APPLICATION WORK.*
BY
‘H. DE MIFFONIS. Senior
Assistant
Engineer,
Department
of Marine
and Fisheries,
Canada.
WHEREVER navigators have to lead boats through difficult waters, means to show the navigable channel have to be provided for. During the day, natural marks in the Iandscape have been for centuries, and are still, to a great extent, the only guides used by mariners acquainted with the locality. In much frequented waters, however, and at night, more reliable aids had to be installed. Floating bodies, moored at the proper place, are the usual means of marking a channel when the latter is at all crooked or exceedingly narrow; the design of buoys has been wonderfuIly improved in the last thirty years and to-day light buoys, bell buoys, whistling buoys, buoys with submarine signal attachment and others are used all over the world. But this method of marking navigable waters is expensive and when the channel is straight over a reasonable distance and is free from obstacles, it has been found cheaper, and most often more convenient, to mark its axis by means of two stations, generally high towers provided with powerful Iights and placed at one end. Boats follow the channel as long as they keep in line with the two marks. In practice, however, the mariners cannot use these marks as a surveyor would two rods to run a straight line; the latter conceals the farther rod with the nearer one and, from time to time, ascertains that he has both still in line by stepping on either side and thus “ opening ” the rods; the mariner, having no such freedom of motion, must at all times see both lights. To secure this result the back tower is considerably higher than the front one, their respective heights being calcuIated so that from the farthest point of visibility the two lights appear still as distinct, i.e., subtend an angle of not less than four minutes according to the most generally accepted rule. Then, of course, the problem facing the mariner is no more that of placing -_ -.. two rods in line * Communicated by the Author. VOL. 196, No.
1X71-7
89
90
H.
DE
~IIFFOSIS.
[J.F.
I.
with his eye, but to put two points on a same vertical; and to what extent our “ sense of verticality ” can be relied upon is still an open question. In 1864, L&once Reynaud, in his “ hlemoire sur 1’Eclairage et le Balisage des Cotes de France,” suggested as a limit for the possible error the quarter of the angular distance of both lights This rule errs obviously on the increased by four minutes. safe side and would necessitate very expensive ranges, the more FIG.
1.
so since L. Reynaud recommended at the same time a minimum angular distance of from eight to fifteen minutes, according to the power of the lights. In ~goz (Ann. P. C/z.), M. de Joly made a new study of the question and found the error in the estimation of verticality This, however, does not offer any safe rute “ nearly negligible.” for the calculation of the distance between the two lights of a range, and the usual practice among lighthouse engineers has been to take as the minimum of the distance of the two lights a set fraction of the useful length of the range-generally from onetenth to one-twel f th.
Juk
r9z3.1
THE SENSE OF VERTICALITY.
9’
This method is obviously unsatisfactory since it would lead to give the same sensitivity to two ranges used to mark, say, one a channel 400 feet wide, and the other, a pass half a mile large, if in both cases the point of maximum danger happened to be located at the same distance from the front light. Safe and reasonable results cannot be obtained unless the angular distance measuring the “ opening ” of the two lights at the edge of the channel is introduced in the calculation. This angular distance should be such that the non-verticality of the line passing through the two lights could then not be questioned. In order to ascertain what could be considered a safe limit beyond which the two lights should appear on two different verticals, the writer has endeavored to realize in the laboratory conditions somewhat similar to those of a range, and has measured the angular distance between the verticals passing through two very small lighted and movable points which observers had been requested to place on the same vertical line. The apparatus consisted essentially of two The Appnmtus.electric lamps in front of which were placed screens with pinbates, one each. The upper lamp was fixed, while the lower was mounted together with the screen on a carriage sliding between two parallel strips of wood and placed so that the two screens would be in the same plane. An endless string was fixed on the carriage, passed on idlers fixed to the table which carried the whole apparatus, and was attached to a drum placed in front of the observer; by this means, the later, who was some thirty feet distant from the screens, could move the Iower one to bring it to the position which, in his judgment, placed the two lighted pin-holes an the same vertical. The left end on the movable screen was abutting against a lever fitted with a needle which moved on a fixed dial, the latter having been empirically graduated to read small displacements (r/I50 of an inch j, and an assistant to the observer, placed on the light’s side of the screens, read the position each time theaobserver declared himself satisfied that he had both pin-holes “ in line.” The distance of the pin-holes was varied and, of course, it was found that the dificulty of correctly placing the lights increased after the anguIar distance passed a certain limfY. Later the experiment was repeated with a sector of paper on which a black line had been drawn; when the line was heavy enough to be
92
W. DE M~FFOIW.
If. F. I.
very readily seen, it seemed that the observer experienced much less difficulty in determining the vertical than he did with the first arrangement; the line, however, had to be comparatively long and subtended an angle of 2O. Results .-The most comprehensive series of tests was made with the pin-holes at an angular distance of 0~22’ which .corresponds for two range lights seen at a distance of two miles to a difference of levef of some 75 feet, a difference of height very FIG.
2.
.
rarely reached. The conditions in the rooms where the experiment was carried out made it advisable not to try a lesser angular distance and since other observations showed that the sensitiveness of the readings decreased when the angular distance of the lights increased, one would seem justified in considering the results obtained as erring on the safe side. In this series of tests, eleven observers, of very mixed training and ability, were requested to take readings, six for each observer. The results are given in Table I. Five .of the observers were obviously quite better than the others. Taking the average and the maxima in each case, we obtain the following results :
July.1923.1
TIIE
Average
SENSE
OF VERTIG\LITY.
03
of II observers
Average of 5 best observers -
Maximum of II observers
-I
Maximum of 5 best observers
Obseryers RE~I~RS I: : 4 f zi%
five
A
- 46/’ 56” I.
TABLE
B
C
_---
I
I)
---
-X8” - 8” -22” 30” 22’ 0
s$
-18” -32”
-"i"
26” 4” II”
-22"
-10"
X,$
_$"
-46”
-
*
* -
-
G -
1'14" I' 0"
"
8"
*
*
F
E
”
I’ I.$” 1’ 46”
”
8’ 36” - 1’14” 46”
I *
I 1 Ii
-‘-
--yll&
6"
1
Ii x
-;‘1x8”
-26” - 4” -30”
L
P
1’338” 32: 3:” 1'20" I* 6”
1’6” 56”
44” 8” -36” -x0"
-
-46” -56”
22" X2" 22"
b-
L
In all the above the error of verticality is expressed by the angular distance between the actual position of the lower light and the one it should occupy. As was to be expected, though the angular distance between the position of the lower light and that of the vertical passing FIG.
AXIS
of
3.
Channet
3 mites
through the upper light increases when the angular distance of the two lights increases, the angle between the fine joining the lights and the vertical decreases. Thus while this angle for the average error of the present series of tests was 2O, it was found to be half of that amount when the two lights subtended an angle of x030’.
94
H.
DE
MIFFONJS.
[J. F. 1.
Conclusion .-From the foregoing it would seem that an eye, trained as is that of the average mariner, should be able to detect readily for two lights a lack of verticality of less than I’, the angle being the angular distance between one of the lights and its proper position with respect to the other. In other words, the horizontal angle subtended by the verticals passing through the two lights seen from the edge of the safe channel should not be less than I’. Thus to mark a channel of 6oo feet by a range, the front light of which would be located three miles up the channel, the minimum distance of the back light should be calculated as follows: MPtan M&S - MF + FB
with Z&%X= verstan $c
or FPM - verstan 60.8 I 89” 3’2W M/sB = 89” 4’28” 3oo x 6x.90 - 18,240-d - say 330 feet
Distances thus obtained may still be somewhat empirical; they are, however, a nearer approximation to truth than those based on the old rule of a set fraction of the distance or similar ones, since they introduce in a rational way the main factor of the problem, tiz., the width of the channet at the distance where the danger is maximum. Etectrical Properties of a Flint Glass of Density 6.01. G. L. ADDENBROOKE. (Phil. Mug., March, rg23.)-The approximate cornposition of this glass is SiO, 22 per cent. ; PbO, 78 per cent. “ Judg-
ing by its density and composition, the density of natural silica being 2.61, fused silica 2.0, and lead x9.2 ( ?), it must contain over 30 per cent. by volume of metallic lead. It breaks easily, though hard. It softens and melts at a fairly low red-heat without showing any signs
of blackening. That such a composition should be perfectly transparent and a high-class insulator is remarkable enough in itself.” It has a refractive index for the D-line of 1.9201. When one forms Maxwell’s ratio of the dielectric c.onstant to the square of the refractive index the quotient comes out equal to 3.55. Other specimens of flint glass of different densities give for this ratio a series of values For the flint glass of density increasing as the density increases. 6.01 the dielectric constant is 13. “ So far as I am aware this is not only the highest dielectric const8nt yet found for any glass, but it is the highest found for any material not of abnormal character and not G. F. S. complicated by the effects of absorption.”
OF VERTICALITY TO LIGHTHOUSE
AND ITS APPLICATION WORK.*
BY
‘H. DE MIFFONIS. Senior
Assistant
Engineer,
Department
of Marine
and Fisheries,
Canada.
WHEREVER navigators have to lead boats through difficult waters, means to show the navigable channel have to be provided for. During the day, natural marks in the Iandscape have been for centuries, and are still, to a great extent, the only guides used by mariners acquainted with the locality. In much frequented waters, however, and at night, more reliable aids had to be installed. Floating bodies, moored at the proper place, are the usual means of marking a channel when the latter is at all crooked or exceedingly narrow; the design of buoys has been wonderfuIly improved in the last thirty years and to-day light buoys, bell buoys, whistling buoys, buoys with submarine signal attachment and others are used all over the world. But this method of marking navigable waters is expensive and when the channel is straight over a reasonable distance and is free from obstacles, it has been found cheaper, and most often more convenient, to mark its axis by means of two stations, generally high towers provided with powerful Iights and placed at one end. Boats follow the channel as long as they keep in line with the two marks. In practice, however, the mariners cannot use these marks as a surveyor would two rods to run a straight line; the latter conceals the farther rod with the nearer one and, from time to time, ascertains that he has both still in line by stepping on either side and thus “ opening ” the rods; the mariner, having no such freedom of motion, must at all times see both lights. To secure this result the back tower is considerably higher than the front one, their respective heights being calcuIated so that from the farthest point of visibility the two lights appear still as distinct, i.e., subtend an angle of not less than four minutes according to the most generally accepted rule. Then, of course, the problem facing the mariner is no more that of placing -_ -.. two rods in line * Communicated by the Author. VOL. 196, No.
1X71-7
89
90
H.
DE
~IIFFOSIS.
[J.F.
I.
with his eye, but to put two points on a same vertical; and to what extent our “ sense of verticality ” can be relied upon is still an open question. In 1864, L&once Reynaud, in his “ hlemoire sur 1’Eclairage et le Balisage des Cotes de France,” suggested as a limit for the possible error the quarter of the angular distance of both lights This rule errs obviously on the increased by four minutes. safe side and would necessitate very expensive ranges, the more FIG.
1.
so since L. Reynaud recommended at the same time a minimum angular distance of from eight to fifteen minutes, according to the power of the lights. In ~goz (Ann. P. C/z.), M. de Joly made a new study of the question and found the error in the estimation of verticality This, however, does not offer any safe rute “ nearly negligible.” for the calculation of the distance between the two lights of a range, and the usual practice among lighthouse engineers has been to take as the minimum of the distance of the two lights a set fraction of the useful length of the range-generally from onetenth to one-twel f th.
Juk
r9z3.1
THE SENSE OF VERTICALITY.
9’
This method is obviously unsatisfactory since it would lead to give the same sensitivity to two ranges used to mark, say, one a channel 400 feet wide, and the other, a pass half a mile large, if in both cases the point of maximum danger happened to be located at the same distance from the front light. Safe and reasonable results cannot be obtained unless the angular distance measuring the “ opening ” of the two lights at the edge of the channel is introduced in the calculation. This angular distance should be such that the non-verticality of the line passing through the two lights could then not be questioned. In order to ascertain what could be considered a safe limit beyond which the two lights should appear on two different verticals, the writer has endeavored to realize in the laboratory conditions somewhat similar to those of a range, and has measured the angular distance between the verticals passing through two very small lighted and movable points which observers had been requested to place on the same vertical line. The apparatus consisted essentially of two The Appnmtus.electric lamps in front of which were placed screens with pinbates, one each. The upper lamp was fixed, while the lower was mounted together with the screen on a carriage sliding between two parallel strips of wood and placed so that the two screens would be in the same plane. An endless string was fixed on the carriage, passed on idlers fixed to the table which carried the whole apparatus, and was attached to a drum placed in front of the observer; by this means, the later, who was some thirty feet distant from the screens, could move the Iower one to bring it to the position which, in his judgment, placed the two lighted pin-holes an the same vertical. The left end on the movable screen was abutting against a lever fitted with a needle which moved on a fixed dial, the latter having been empirically graduated to read small displacements (r/I50 of an inch j, and an assistant to the observer, placed on the light’s side of the screens, read the position each time theaobserver declared himself satisfied that he had both pin-holes “ in line.” The distance of the pin-holes was varied and, of course, it was found that the dificulty of correctly placing the lights increased after the anguIar distance passed a certain limfY. Later the experiment was repeated with a sector of paper on which a black line had been drawn; when the line was heavy enough to be
92
W. DE M~FFOIW.
If. F. I.
very readily seen, it seemed that the observer experienced much less difficulty in determining the vertical than he did with the first arrangement; the line, however, had to be comparatively long and subtended an angle of 2O. Results .-The most comprehensive series of tests was made with the pin-holes at an angular distance of 0~22’ which .corresponds for two range lights seen at a distance of two miles to a difference of levef of some 75 feet, a difference of height very FIG.
2.
.
rarely reached. The conditions in the rooms where the experiment was carried out made it advisable not to try a lesser angular distance and since other observations showed that the sensitiveness of the readings decreased when the angular distance of the lights increased, one would seem justified in considering the results obtained as erring on the safe side. In this series of tests, eleven observers, of very mixed training and ability, were requested to take readings, six for each observer. The results are given in Table I. Five .of the observers were obviously quite better than the others. Taking the average and the maxima in each case, we obtain the following results :
July.1923.1
TIIE
Average
SENSE
OF VERTIG\LITY.
03
of II observers
Average of 5 best observers -
Maximum of II observers
-I
Maximum of 5 best observers
Obseryers RE~I~RS I: : 4 f zi%
five
A
- 46/’ 56” I.
TABLE
B
C
_---
I
I)
---
-X8” - 8” -22” 30” 22’ 0
s$
-18” -32”
-"i"
26” 4” II”
-22"
-10"
X,$
_$"
-46”
-
*
* -
-
G -
1'14" I' 0"
"
8"
*
*
F
E
”
I’ I.$” 1’ 46”
”
8’ 36” - 1’14” 46”
I *
I 1 Ii
-‘-
--yll&
6"
1
Ii x
-;‘1x8”
-26” - 4” -30”
L
P
1’338” 32: 3:” 1'20" I* 6”
1’6” 56”
44” 8” -36” -x0"
-
-46” -56”
22" X2" 22"
b-
L
In all the above the error of verticality is expressed by the angular distance between the actual position of the lower light and the one it should occupy. As was to be expected, though the angular distance between the position of the lower light and that of the vertical passing FIG.
AXIS
of
3.
Channet
3 mites
through the upper light increases when the angular distance of the two lights increases, the angle between the fine joining the lights and the vertical decreases. Thus while this angle for the average error of the present series of tests was 2O, it was found to be half of that amount when the two lights subtended an angle of x030’.
94
H.
DE
MIFFONJS.
[J. F. 1.
Conclusion .-From the foregoing it would seem that an eye, trained as is that of the average mariner, should be able to detect readily for two lights a lack of verticality of less than I’, the angle being the angular distance between one of the lights and its proper position with respect to the other. In other words, the horizontal angle subtended by the verticals passing through the two lights seen from the edge of the safe channel should not be less than I’. Thus to mark a channel of 6oo feet by a range, the front light of which would be located three miles up the channel, the minimum distance of the back light should be calculated as follows: MPtan M&S - MF + FB
with Z&%X= verstan $c
or FPM - verstan 60.8 I 89” 3’2W M/sB = 89” 4’28” 3oo x 6x.90 - 18,240-d - say 330 feet
Distances thus obtained may still be somewhat empirical; they are, however, a nearer approximation to truth than those based on the old rule of a set fraction of the distance or similar ones, since they introduce in a rational way the main factor of the problem, tiz., the width of the channet at the distance where the danger is maximum. Etectrical Properties of a Flint Glass of Density 6.01. G. L. ADDENBROOKE. (Phil. Mug., March, rg23.)-The approximate cornposition of this glass is SiO, 22 per cent. ; PbO, 78 per cent. “ Judg-
ing by its density and composition, the density of natural silica being 2.61, fused silica 2.0, and lead x9.2 ( ?), it must contain over 30 per cent. by volume of metallic lead. It breaks easily, though hard. It softens and melts at a fairly low red-heat without showing any signs
of blackening. That such a composition should be perfectly transparent and a high-class insulator is remarkable enough in itself.” It has a refractive index for the D-line of 1.9201. When one forms Maxwell’s ratio of the dielectric c.onstant to the square of the refractive index the quotient comes out equal to 3.55. Other specimens of flint glass of different densities give for this ratio a series of values For the flint glass of density increasing as the density increases. 6.01 the dielectric constant is 13. “ So far as I am aware this is not only the highest dielectric const8nt yet found for any glass, but it is the highest found for any material not of abnormal character and not G. F. S. complicated by the effects of absorption.”