October 24, 1895] 



NATURE 



63: 



in all possible directions from the epicentre combined in a single 

 plane. If the velocity is different in different directions, in the 

 general figure these differences will be eliminated when the 

 number of observations is large enough, and the result will be a 

 curve free from local disturbances. 



Although the time has not yet come for us to determine the 

 definite form of an carthquake-hodograph, yet we know enough 

 from the best examined earthquakes to decide whether the 

 hodograph is an hyperbola or a curve with points of inflexion, 

 whether Hopkins" law is confirmed by the observations, or 

 an increase of velocity is noticeable in the outer zone of the 

 disturbed area. 



The best example for such an investigation is contained in 

 von Seebach and Minnigerode's discussion of the earthquake of 

 March 6, 1872, in Central Germany. An inspection of the 

 map of coseismals published by them is sufficient to show that 

 the horizontal coseismals are crowded together in a striking 

 manner near Giittingen and Leipzig, at a distance of sixteen 

 (German) miles from the epicentre. Accordingly, in drawing the 

 hodograph we see how badly the hyperbola suits the observa- 

 tions. Several points which are most valuable for the 

 determination of the epicentre, because they are nearest to it, 

 and which agree most perfectly with one another, must be 

 rejected in constructing the hyperbolic hodograph, in order that 

 the earthquake may not begin at the surface of the earth until 

 I J minutes after it was actually observed at five different places 

 at five to six miles distance from the epicentre. For sixteen miles 

 the hyperbola leaves all the best observations below it, after 

 which nearly all points remain above it until it ends at Breslau, 

 at a distance of fifty-seven miles from the epicentre. At this 

 place a magnetic needle was found swinging by Prof. Cialle at 

 4h. 5m. 25s., Berlin time, but the shock itself may have occurred 

 several minutes earlier. The hyperbola is made to pass exactly 

 through the point corresponding to this time, for otherwise its 

 vertex would have to be placed still higher than it is now, and 

 this would increa.se the already existing disagreement between 

 the calculated time of the beginning of the earthquake and the 

 actual observations. 



How well, on the contrary, are the observations represented by 

 a curve the vertex of which is a little below 3h. 55m., and, being 

 convex downwards, passes at a distance of seven to eight miles 

 between Jh. 55m. and 3h. 56m., reaches its points of inflexion 

 at about eleven miles distance with a slope corresponding to 

 2 "5 miles per minute, and then leaving some points on one side 

 and some on the other, passes through Tubingen (367 miles), 

 the last trustworthy point, until it reaches Breslau one minute 

 before the observed time, with a velocity of at least fifteen miles 

 a minute. 



The Herzogcnrath earthquake of October 22, 1873, leads to 

 somewhat similar results. In drawing the hyperbolic hodograph, 

 some of the best obser\'ations, those used for determining the 

 position of the epicentre, have to be rejected altogether, while 

 others must be supposed to err by as much as two or three 

 minutes. But a curved line, passing through the mean positions 

 of the points, is concave throughout on its lower side, with a 

 large curvature at the epicentre. The figure certainly differs 

 little from the form of the hodograph corresponding to a centre 

 at the surface, and the inner zone is a circle of not more than 

 four kilometres radius. 



Thus the best investigated earthquakes at our disposal show 

 that the observations agree much less closely with the older 

 theory of concentric earthquake-waves, straight rays and 

 hyperbolic hodograph, than they do with the new theory of a 

 velocity of propagation increasing with the depth, rays convex 

 downwards, and a hodograph with points of inflexion. 



The Determination of the Depth of the Centre. — If the law 

 connecting the velocity with the de])th were known, we should 

 be able to calculate the forms of the corresponding rays and 

 hodograph, and to find a relation between the depth of the 

 centre and the form of the hodograph. In Fig. 2 we have 

 started with the simplest assumption, and supposed the velocity 

 to vary as the depth. As this law is an entirely arbitrarj' one, the 

 figure can only give a nearer approach to the truth than the 

 theory represented in Fig. I. If, for instance, the modulus 

 of elasticity were to varj' as the depth, the velocity would change 

 much more rapidly near the earth's surface than far below it ; 

 and the fact that the perceptibility of earthquakes decrea.ses so 

 rapidly as the dejilh increa.ses, certainly indicates that a rapid 

 change in the velocity takes place immediately below the surface. 

 Consequently, in calculating the depth of the centre correspond- 



ing to our law, we should find too large a value. Other 

 difficulties in determining the depth of the centre are our 

 ignorance of the true superficial velocity, and the uncertainty as 

 to the form of the hodograph, especially the doubtful positicm of 

 its points of inflexion. But, in spite of all these difficulties, we 

 may consider it as a rule that the depth will increase with the 

 radius of the inner zone of the disturbed area, and that it will 

 certainly always be smaller than this radius. 



On the other hand, a minimum value of the depth may be 

 found by means of the tangent at the point of inflexion. This 

 tangent in F"ig. 2, like the asymptote in Fig. i, makes an angle 

 of 45' with the horizon, because in both figures the central 

 velocity («,) was taken as the time scale. While in Fig. i the 

 asymptote passes through the centre, in Fig. 2 the tangent at 

 the point of inflexion passes above it. Now, let us imagine the 

 depth of the centre in Fig. 2 to remain the same, as well as the 

 velocities h, at the centre, and u at the surface ; but let the in- 

 crease of velocity be no longer uniform as before, but be 

 principally restricted to the neighbourhood of the surface. The 

 consequence will be that the rays will differ little from straight 

 lines at first when they leave the centre, and that the principal 

 increase of curvature will be near the sTirface. The point of 

 emergence of that ray which leaves the centre horizontally, will 

 move to a greater and greater distance, and, as the same is the 

 case with the point of inflexion of the hodograph, its tangent at 

 that point will be displaced parallel to itself downwards ; and 

 when the whole change is imagined to take place in the surface 

 itself, the hodograph will coincide with Seebach's hyperbola, and 

 the tangent at the point of inflexion becomes an asymptote and 

 passes through the centre. 



Thus, with a hodograph adapted as well as possible to the 

 existing observations, we find a depth of more than five, and less 

 than ten, geographical miles for the earthquake in Central 

 Germany, and a depth of less than three kilometres for the 

 earthquake of Herzogenralh. Each of these earthquakes 

 represents a special type. Type I., with a very small depth of 

 centre and an approximate disappearance of the inner zone, is 

 represented by the earthquake of Hcrzogenrath ; Type II., in 

 which both zones are pretty equally distinct, and the depth is 

 rather considerable, by the earthquake of Central (jemiany. 

 There- may exist a Type III. with a very deej) centre, or with 

 small intensity and moderate depth, for which the point of 

 inflexion of the hodograph falls outside the region when the 

 earthquake is perceptible, and where, consequently, the hodo- 

 graph is convex throughout. .Amongst the earthquakes so far 

 studied, for which the mean velocity has been calculated, those 

 with small velocities, which generally have a merely local 

 character, may safely be regarded as belonging to the first t)'pe. 



THE TOTAL SOLAR ECLIPSE OF AUGUST 8, 

 1896.' 



T T having come to my know ledge that some doubts had 

 arisen as to the suitability of Norway as a post of observation 

 for the total eclipse of the sun in 1S96, and having had both 

 experience in total eclipse expeditions and of travelling in 

 Norway, I determined to make a special tour of observation 

 both to the west coast, and also to Finmarken, Lapland, and 

 the Russian frontier on the east coast. 



In selecting stations in such an exceptional country as Nonvay, 

 many points must be considered that do not apply to most 

 places ; thus it is not enough to know that A is twenty miles 

 from B without also knowing how many fjords lie between, how 

 many peaks three or four thousand feet in height, how many 

 glaciers, and how far they are crevassed, if the mountains are 

 passable, and if so w hat weight besides himself a man can carry 

 up. Those people who have visited Norway, and the more so 

 those who have travelled in the interior and north of the 

 country, are surprised at the almost impossibility of moving at all 

 except by the fjords and certain made roads. These generally 

 may be said to extend as far north as Trondhjem, latitude 

 63° 26' ; longitude 10° 30' about. After that, on the north and 

 north-east coast and Russian frontier, roads are the feeblest 

 tracks generally, and the fjord communication only of a sjjecial 

 character ; the population, except at such places as Tromso, 

 Hammerfest, Vardo, and \'adso, is very scanty, and chiefly con- 

 fined to the sea coast, and in the latter case subject to consider- 



1 Abridged from a paper read before ihe koyal .Astronomical Society*, by 

 Col. A. Burton-Brown (Montltly Notices, R.A.S., vol. Iv. No. 3). 



NO. 1356, VOL. 52] 



