52 



SCIENCE, 



[Vol. XII. No 287 



small, being only about one two-hundredth part of the whole ap- 

 propriation for the Survey. 



Another of the subordinate branches of the Coast Survey work 

 is the determination of the earth's density. The pendulum, being 

 an instrument which will swing faster or slower according as the 

 force of gravity is stronger or weaker, can be employed to measure 

 this force. All forms of pendulums will determine variations of 

 gravity, but different shapes are given it, depending upon the 

 particular object in view. That approaching nearest the ideal 

 mathematical pendulum would be a heavy ball suspended by a fine 

 string. This form was used by Borda, and a modification of it by 

 Bessel consisted of swinging the ball with strings of different 

 lengths. Kater employed a form known as the invariable one, — 

 meaning by the term ' invariable ' that none of the parts of the pen- 

 dulum are interchangeable, and that the instrument remains iden- 

 tical for experiments made at different stations. Kater's pattern is 

 generally preferred when the object is simply a determination of 

 the differences of the force of gravity for different places. The re- 

 versible pendulum is one having two points of suspension, which 

 are so placed that the times of oscillation are equal, or nearly so, 

 whether the instrument is hung in the direct or reversed position. 

 This form is used when the object is the determination of the ac- 

 tual force of gravity, or in other words, how far a body will actually 

 fall towards the earth in a given time. As the distance between 

 the two points of suspension is equal to the length of a simple pen- 

 dulum which would oscillate in the same time, the determination of 

 the force of gravity by this method becomes a comparatively sim- 

 ple matter as far as theory and principle are concerned. In the 

 practical e.\ecution of the work there are difficulties that make it 

 one of the highest precision, and at the same time one demanding 

 the greatest care and attention to details. 



In all pendulum experiments for the determination of gravity, 

 whether relative or absolute, it is evident that the pendulum must 

 swing under precisely the same circumstances, or the observations 

 must be reduced to what they would have been had they been made 

 under the same circumstances. The principal influences bearing 

 on the duration of an oscillation, and those which vary most from 

 one station to another, are the changes in the rate of the time- 

 keeper, those resulting from differences in amplitude of the oscilla- 

 tions, and those dependent on the temperature of the pendulum 

 and the pressure of the surrounding atmosphere. 



The first two are readily disposed of, as one is independent of 

 the pendulum and the other is a question of simple geometrical re- 

 lations. The influence of the temperature may be determined 

 either by swinging in great ranges of temperature and noting the" 

 changes in the period of oscillation for the two conditions, or by 

 measuring the increase of length of the pendulum for a given in- 

 crease of temperature and resorting to computation for the effect 

 of this increase of length on the time of an oscillation. The pres-* 

 sure correction, or at least as much of it as is dependent on the 

 buoyancy of the atmosphere, may likewise have two independent 

 determinations. A part of this correction comes from the influence 

 of the air that is set in motion, and depends on its viscosity. But 

 the whole atmospheric effect may be eliminated from the length 

 obtained for the seconds pendulum by using a reversible pendulum 

 whose external form is symmetrical with reference to the centre of 

 figure. The Coast and Geodetic Survey pendulums devised by 

 Assistant C. S. Peirce are so made. Two different lengths are 

 also used, one yard and several metre pendulums having been 

 made at the Coast Survey Office in 1881. These instruments have 

 been swung in many parts of the United States, from Boston in the 

 east to San Francisco in the west, and from Albany in the north to 

 Key West in the south. Besides these experiments, which were 

 nearly all made near the sea-level, comparatively speaking, many 

 determinations have been made at higher elevations in order to 

 study the effect of distance from the earth's centre, and the at- 

 tractions of mountains and table lands lying between the station 

 and the sea-level. 



In order to connect our series of pendulum observations with 

 similar work done in Europe and other parts of the world, several 

 of the principal pendulum stations in Europe were occupied with a 

 Repsold reversible pendulum, and the same was swung also at 

 some home stations. Also the Kater invariable pendulums. 



brought to this country by Captain Herschel, and which had been 

 swung in different parts of the world, were swung at several of our 

 stations as well as in New Zealand, Australia, the Malayan Penin- 

 sula, and Japan. The Coast and Geodetic Survey has thus 

 secured an intimate connection with pendulum research the world 

 over. 



Outside our own country the Peirce pendulums have been sent 

 to Lady Franklin Bay with the Greely expedition in 1882, to the 

 South Pacific Ocean with the solar eclipse expedition of 1883, and 

 to the Hawaiian Islands at the request of their government in 1887. 

 In this last voyage both a yard and metre pendulum were swung at 

 an elevation of ten thousand feet, and also at two stations at the 

 sea-level. All this foreign work was done either by an officer of 

 the Survey or by a trained observer following the most approved 

 home methods. 



The swaying of the stand on which the pendulum rests necessi- 

 tates another correction to the time of oscillation m the case of ab- 

 solute determinations. This source of error has been investigated 

 mathematically by Professor Peirce. The English have used a 

 small inverted pendulum attached to the stand for determining this- 

 correction. 



The determination of the figure of the earth is one of the objects 

 of pendulum observations. The force with which bodies at- 

 tract each other depends on the quantity of matter in them and 

 their distance apart. Places on the earth, therefore, which have an 

 excess of matter, either from the material being of greater volume, 

 or of greater density, will show a corresponding increase of the 

 force of gravity ; and places near the pole, from their being nearer 

 the centre of the earth, would be expected to show a variation in 

 the force of gravity in the same direction. Hence gravity deter- 

 minations made at different points, starting from the equator and 

 going towards the poles, will show the relative distances from the 

 centre, and from this, with the aid of Clairaut's theorem, the shape 

 of the earth. This would give a general figure for the sphere. 

 Besides this, the pendulum will determine irregularities in this 

 figure. In general, the result of pendulum observations thus far 

 seems to indicate that gravity is in excess at island stations and 

 coast-lines, and in defect on mountain tops ; but this last may be 

 partially due to the sea-Ievel being raised in the neighborhood of 

 continents by the attraction of the land, and the former is certainly 

 influenced by the attraction of the surrounding sea-water. At any 

 rate mountain observations point towards the conclusion that there 

 may be either immense subterranean caverns beneath, or that the 

 mass may be composed of lighter material than the earth's crust 

 generally ; and it may likewise be inferred that the stratum form- 

 ing the bottom of the ocean is composed of comparatively heavy 

 matter. 



There are shown in this exhibit two reversible pendulums which 

 have been used in the observations above described. One is a 

 Peirce reversible metre pendulum swung in the heavy wooden, 

 frame devised for it by Professor Peirce, who has found it neces- 

 sary to discard metallic stands. The other is the Repsold rever 

 sible metre pendulum referred to above. It is mounted now as it 

 was when used, except that certain parts not necessary for showing 

 the pendulum oscillations are omitted. 



ENGLISH RAILROAD SPEEDS. 



In a recent letter from Manchester, England, to the Railroad 

 Gazette of this city, Mr. W. H. Booth says that so important have 

 been the changes made in the passenger traffic of all the great En- 

 glish companies, and also so numerous, that ' Bradshavv," guide to 

 all British lines, did not appear until the 3d of July. The altera- 

 tions, of course, as usual, date from July i, and call for special 

 notice. ' Bradshaw ' is studied with especial zeal just now by old 

 established travellers, for the numerous changes have quite over- 

 thrown their knowledge. All the three companies which conduct 

 a traffic between London and Scotland have added new expresses 

 or increased the speed of existing trains, and the train service be- 

 tween the large towns has also been greatly improved and accele- 

 rated. For some time past American superintendents of motive 

 power, and master mechanics, have been priding themselves upon 

 running a good second to their English colleagues, and even ven- 



