70.S 



NATURE 



Ui.^L. 



1923 



Letters to the Editor. 



[ Tht Eilitor does not hold himself responsible Jot 

 opinions expressed by his correspondents. Neither 

 am he undertake to return., nor to correspond with 

 the writers of, rejected manuscripts interuied for 

 this or any other part of Naiukk. No notiie it 

 tahen 0/ anonymous communications.] 



Dutch Pendulum Observations In Submarines. 



Dr. F. a. Vkning Mkinksz, commissioned by the 

 Dutch Geotletic Committee to make pendulum 

 observations on board the Submarine K II of the 

 Royal Dutch Navy during the voyage from Holland 

 to "Java (see NATuaE of September ^5, p. 393), has 

 sent particulars of his observations from Gibraltar, 

 Tunis, and Alexandria. 



The beginning of the voyage was extremely dis- 

 appointing because of the bad weather. For the 

 first live days the sea was continually very rough. 

 The rolling of the ship amounted to 30° to each side, 

 and the pitching to 8 metres ; the nights had to be 

 spent strapped to the berths. It was a very rough 

 experience for the first stay on board a seagoing 

 vessel. 



After passing Portland Bill in the English Channel, 

 an attempt was made to take observations. Submerged 

 to a depth of 20 metres, the rolling still amounted to 

 }° to each side, which made observations impractic- 

 able. At length, off the Portuguese coast, the 

 weather cleared and it became calmer, but the long 

 swell continued. On September 24 an inquir>' was 

 made again into the movements of the submerged 

 ship. The greatest angle of inclination caused by 

 the pitching amounted at the sea-surface to 1°, the 

 rolling to 6° to each side. At a depth of 30 metres, 

 and while the vessel was going in the direction of the 

 swell, the inclination caused by the pitching was at 

 most 1°, which by the use of the horizontal rudder 

 could be reduced to less than J° ; but as the rolling 

 was still I J° to each side, observations were practically 

 impossible. 



Notwithstanding the considerable rolling of the 

 ship, the amplitudes of the pendulums appeared to 

 vary fairly regularly. The principal impediment was 

 the circurnstance that the rays from the electric lamp, 

 reflected by the mirrors of the pendulums, went 

 beyond the edge of the film. The actual trouble w^as 

 therefore of an incidental nature. This induced Dr. 

 Vening Meinesz to devise an arrangement for suspend- 

 ing the whole apparatus from a horizontal axis to be 

 placed lengthwise in the ship in order to neutralise 

 the rolling. He supposed that it would be possible 

 to get this constructed at the workshops of the 

 Royal Navy at Gibraltar. 



On September 26, between Cape St. Vincent and 

 Cadiz, the sea was very smooth, and for the first 

 time observations were crowned with success, as at 

 a depth of 25 metres the movements were very small. 

 The first observation was made in a place where the 

 sea was no metres deep, the second where it was 

 480 metres deep. During the second observation 

 the direction of the course was taken successively 

 W.E. and E.W., to test the effect of the speed of the 

 ship on the intensity of gravity, first mentioned by 

 Eotvos. 



On the afternoon of September 28, Gibraltar was 

 reached, and immediately Dr. Vening Meinesz took 

 steps for the construction of the suspension apparatus. 

 All the assistance desired was kindly given by the 

 British authorities. The time being very limited, 

 it was necessary to carry on the work daj' and night 

 without intermission. 



During the stay at Gibraltar the observations were 



NO. 2822, VOL. I 12] 



nd they proved to be very - 

 ics of the observations si 



worke<! 



The «! 



accura« > .■' .•< ^jr^-Mtfr than was expecte<; 



preliminary obs< i .I'vns at the Helder. 



• '.]' was clearly indicati . 



! I ould even Iw derivetl Iroi 



I <• of but I mile from the tm 



of the speed of t i 

 diagrams ; tht- 

 these with a did 

 value. 



On October 3, a few hours before leaving Gibraltar, 

 the suspension apparatus was fitted up on board the 

 submannc. I am glad to express thanks to th«- 

 British authorities at Gibraltar, who so t< 

 tributed to the realisation of Dr. Vening 

 project. 



During the passage between Gibraltar and Tunis, 

 the arrangement proved to be s.i* ' ' rv in every 

 respect. Although the rolling . to 2^ to 



each side, observations were eaMi\ |>t,i<..iicable. A 

 stay at Tunis, where the submarine arrived on 

 October 7, was again used by Dr. Venin;- v' — ""-' 

 for the preliminary computation of his ob 

 One of these gave the value of g for a sc . , 

 2500 metres with a difference of only 0-003 cm 

 from the theoretical value, which indicates con , 

 isostasy. 



Tunis was left on October 13,' and Alexandria was 

 reached on October 18 ; the sea being generally very 

 smooth, observations were made without any diffi- 

 culty. The Eotvos effect was tested again ; the 

 deduced speed of the ship differed only 0-3 mile from 

 the true value. 



It appears from the diagrams that the accuracy 

 of the deduced period of oscillation in favourable 

 circumstances may be about 1/1,000,000, and that in 

 a rough sea there is little fear of the divergences 

 exceeding 1/100,000. We must wait, however, for 

 the complete computations before a positive statement 

 will be possible. 



It should also be mentioned that the rate of the 

 chronometer was controlled by using the rhythmic 

 time-signals of the Eiffel Tower. 



On October 31 the squadron, consisting of the 

 mother ship Pelikaan and the three submarines, left 

 Suez ; it will touch at the ports of Aden, Colombo, 

 and Sabang, and arrive at Batavia about the middle of 

 December. Dr. Vening Meinesz will carry out observa- 

 tions in the Red Sea and the Indian Ocean, and will 

 ultimately determine, with the invar pendulums, the 

 intensity of gravity at a few stations in Java. 



From the results already obtained it may be con- 

 cluded that, by the method of Dr. Vening Meinesz, in- 

 vestigations of the intensity of gravity by pendulum 

 observations can be realised on the parts of the 

 earth covered by the ocean with almost the same 

 accuracy as on continents and islands. For the study 

 of isostasy, and of Wegener's hypothesis of floating 

 continents, observations in submarines, especially 

 between the coast and the deep sea, will be of the 

 greatest value. J. J. A. Muller. 



Zeist, November 7. 



The True Relation of Einstein's to Newton's 

 Equations of Motion. 



The equations of a space- time geodesic or Einstein's 

 general equations of motion of a free particle are, in 

 usual symbols, 



d^XK fa^\dx^ dxfi 

 ds^'^Xi i ds ds 

 In order to show their relation to Newton's equa- 

 tions of motion, which may be written 

 d%^'cii 



o. L = i, 2, 3, 4. 



I, 2. 3, 



(I) 



{N) 



