From Edward Sabine April 16. 1861 | midnight1
13 Ashley Place S. W. | April 16. 1861 | midnight.
Dear Tyndall,
The mean direction of the declination needle is the sum of 
equidistant observations of its direction in 24 hours, divided by 
.
The mean diurnal variation (in some definite period of time, say, a month) is the mean difference in the direction observed at every hour of the 24, from the mean direction as obtained above.
If there were no magnetic disturbances the diurnal variation at the same hour in each of the 30 days, would be a constant quantity: i.e. there would be a certain constant amount of diurnal variation (either to the east or to the west, according to the hour of the day,) in each of the 24 hours, we may call this the normal direction of the particular hour and month.
But by reason of the occurrence of magnetic disturbances, the actual direction of the needle does not always coincide with the mean or normal direction. Say for example that the normal variation at 8am is 10' of arc east of the mean direction in the day, (or of
); and that on a certain day the needle is seen at 8 am to point 15' instead of 10' to the east of the mean direction in the day; in such case we should say that there was a disturbance which amounted to 5' East; (an easterly deviation). Now suppose that on another day at the same hour, ie at 8 am, the direction were only 5' east of the mean direction of the day, in such case the needle points 5' west of its normal position at that hour—and this would be called a westerly disturbance; (or a westerly deviation, if you prefer the word).
The angle comprised between the extreme east & west directions in which the needle points by reason of diurnal variation would be called by me “the range of the diurnal variation”. The diurnal variation at any particular hour would be the difference between the monthly normal at that hour and the mean direction of the whole day; (i.e.
). Lamont2 would probably call the latter “horary variation”.
I will look out the references for the intensity in June & December & give them to you when we meet.
Sincerely yours | Edward Sabine
Wednesday morning
I have added this morning what may possibly make my meaning more clear—I returned late last night from the country.
The “decennial variation” in any particular year is the difference between what would be the direction if there were no decennial variation, and the actual direction, so far as the latter is influenced by the causes to which the decennial variation is owing.
The annual variation in any particular month, is the difference between what would be the direction if there was no annual variation, and the actual direction, so far as the latter is influenced by the causes to which the annual variation is owing.
The “solar diurnal variation” at any particular hour is the difference between what would be the direction if there were no solar diurnal variation, and the actual direction so far as the latter is influenced by the causes to which the solar diurnal variation is owing.
In the observations themselves all these and all other variations, from whatsoever causes they may proceed, are mixed up—To study any one of them correctly, you must eliminate the effects of the others.
In conformity with general usage, I call
Decennial variation, that variation whose period is ten years.
Annual variation, that variation whose period is a year.
Diurnal variation that variation whose period is a day.
The “range of the decennial variation” is measured by the extremes of direction in the decennial period, due to the causes to which the decennial variation is owing.
The “range of the annual variation” is measured by the extremes of direction which take place in the year, due to causes to which the annual variation is owing.
The “range of the solar diurnal variation” is measured by the extremes of direction which take place in the day, due to the causes to which the solar diurnal variation is owing.
You may call, if you please to do so, the decennial variation the annual variation: the annual, the monthly variation; and the solar diurnal, the horary variation. This is a mere substitution of one term for another; in which matter, I prefer and I believe the preference is very general, the terms decennial, annual, & solar diurnal. (The solar diurnal is so called to distinguish it from another diurnal variation due to the moon.)
But the real & substantial difference between Lamont & myself, apart from a difference in our modes of designation, is, I presume, that Lamont’s diurnal variation includes the effects of both solar diurnal variation & magnetic disturbances (which also have a diurnal period). In the crude observations these are mixed up together—By the process which I have adopted, each is eliminated when the other is studied. It is this process of separating the effects of different causes which in the crude observations are mixed up together, which constitutes the precautions of the methods which I have pursued, and which I believe to be the true way of analysing phenomena with a view to the discovery of their distinct causes & separate effects.
ES. | Ap[ril]. 17.
RI MS JT/1/S/22
RI MS JT/1/TYP/4/1317
17 April 1861: the letter was started on 16 April and finished on 17 April. See also letters 1760 and 1764.
Lamont: Johann von Lamont (1805–79), Scottish astronomer and physicist. Lamont spent much of his life in Bavaria, becoming assistant at the Royal Observatory at Bogenhausen near Munich in 1828. In 1835 he was appointed director of the observatory, and established it as a centre for meteorological research and measurements of the earth’s magnetic field. He lectured in practical astronomy at the University of Munich from 1837, before becoming Professor of Astronomy in 1852. His best-known work was in the field of terrestrial magnetism, in which he discovered the decennial periodicity in variations of the earth’s magnetic field (later the 11-year cycle), and the presence of earth currents. He became engaged in the global initiative to survey the earth’s magnetic field. In 1840, he built a magnetic observatory at Bogenhausen, and participated in the collection of data for the international project between 1841–5. He also undertook surveys outside Bavaria, in places such as Denmark, France, and Spain, and devised a number of new instruments which became widely used, including the chronometer in 1850.
Please cite as “Tyndall1777,” in Ɛpsilon: The John Tyndall Collection accessed on