558 



NATURE 



\Sept.i<^, 1878 



in the following manner by the method of triangulation. First 

 setting out from A (see Fig. i) in whatever direction the character 

 of the ground permits, a base-line A </ is measured with the 

 greatest possible accuracy. At the point A, the angle dKe, and 

 at the point d the angle A de are observed with a circular instru- 

 ment. Thus in the triangle Kde, the adjacent side A d and the 

 two other parts of the angles being known, the triangle can 

 be computed. Place now in the straight line connecting a 

 and B (in the same meridian) a point c, which can be seen 

 from the points d and e ; then we may, by means of the 

 theodolite, measure at d and e the angles Kdc and A e c} 

 Subtract now from these angles the previously observed angles 

 A de and Ked, and we have now found in the second triangle, 

 cde, the angles d and e. But then, also, the side de, 2& 

 belonging to the first triangle, is known, and thus also the 

 second triangle, and consequently its sides cd and Q.e are 

 known. But if the triangles hcd and Ked are known, so 

 are also the triangles Kdc and KeC; consequently, also, the 

 common side A c ; and thus a part of the distance is measured. 

 To obtain the length of the other part B c, a base B h will be 

 measured from B, and by operations similar to the above B c will 

 easily be found. As a test of the accuracy of the measurements, 

 we may connect the first operation, starting from ced towards 

 /and d, and going on to B, and obtain by means of the agree* 

 ment of the measured length B h with the calculated length of 

 B /^ as a side of the triangle B -^^ a proof of the accuracy of the 

 measurements of base and angles. Should the length A B be very 

 great and the intervening ground mountainous, a very great 

 number of small triangles may be required : in which case, 

 though the principle is exactly the same, yet in practice, on 

 account of the numerous measurements necessary imder such 

 circumstances, unavoidable errors and inaccuracies will certainly 

 accumulate. 



As we have already said, Snellius, in the year 1615, was the 

 first to measure a degree by the method of triangulation. He 

 measured a base line on the plain between Leyden and 

 Sonterwonde (316 Rhenish rods and 4 feet long), and by means 

 of connected triangles obtained an arc of the meridian (between 

 Alkmaarand Bergen-op-zoom) of 1° ll'3o". Although Snellius 

 was in possession of an improved instrument (Galileo had 

 already taught the use of the recently-discovered telescope* 

 for astronomical purposes), yet his measurements were so inac- 

 curate that he obtained far too small a result (5501 1 toises for a 

 degree). He soon became convinced of the erroneous nature 

 of his result, and seven years after repeated the operation, 

 measuring in the neighbourhood of Leyden a base-line in the 

 ice. Probably deterred by the multifarious and difficult numeri- 

 cal operations which were at that time conaected with the working 

 out of the calculation of this new measurement by means of 

 arithmetic, he did not carry this out, but his successor, Muschen- 

 broek, devoting himself to the execution of this work after 

 revising the triangulation, found 57033 toises as the length of a 

 degree in the Netherlands. 



Although the method of triangulation used by Snellius was 

 a great step in advance, yet it was a long time before it became 

 generally adopted ; for even in the years 1633 to 1635 a degree- 

 measurement was carried out by Norwood between London and 

 York after the old method. He used an improved instrument 

 (a five-foot sector) and obtained as the difference in latitude of 

 the two places 2° 28', and the length of a degree 57424 toises. 

 Newton, who shortly after began the elaboration of his theory 

 of universal gravitation, did not, at all events, know this 

 result, since he took as the basis of his researches the earlier 

 very inaccurate results as to the dimensions of the earth, and 

 since he found his calculations did not correspond with them he 

 abandoned for a time his theory. 



Soon after, Picard, at the instance of the Paris Academy 

 of Sciences, undertook anew a meridian measurement, and that 

 not only after the improved method of Snellius (since he 

 measured all three angles of each triangle, and computed the 

 length of the arc by pieces), but he also gave to the measuring 

 instruments a hitherto unattained accuracy by the addition of a 

 micrometer apparatus." He measured on the meridian of Paris an 

 arc of 1° 22' 55", and finding for the latitude of that place 49° 13', 



"• There is no necessity for the point c being taken in a line between A and 

 B, nor any advantage even if it could be done. The angles need not be 

 measured in the way here laid down. 



" This remark seems to imply that Snellius used a telescope in measuring 

 angles. The application of the telescope to circular instruments was a step 

 taken by Picard. 



3 Picard adapted to'his measuring instrument a telescope with cross-wires 

 in its focus ; this appears to be the only "micrometer apparatus." 



with the, as we now know, wonderfully accurate result of 57060 

 toises for the length of a degree. When Newton, in 1682, 

 learned the result of Picard's measurement, he resumed his 

 calculations in gravitation, and had the satisfaction, after 

 thoroughly revising his work, of seeing his theory of gravitation 

 established. A few years afterwards he gave to the world his 

 immortal work on the mechanics of the universe. For a short 

 time Picard's dimensions of the earth were accepted as correct 

 and were universally made use of. But while hitherto the measure- 

 ments had reference alone to the discovery of the size of the earth 

 — for its spherical form was taken as proved — there now began a 

 new epoch in the solution of the second part of the problem — 

 the true figure of the earth. Influenced by the fact that the 

 length of a degree measured at different places on the earth 

 always gave a different result — which could not in all cases be 

 ascribed to inaccurate measurement — Picard had already broached 

 the idea that the earth could not be a true sphere. Soon after, 

 Newton, in his great work, showed, on the supposition that the 

 earth existed originally in a fluid state, that on account of the 

 rotation round the polar axis, the supposed spherical form must be 

 more truly that of an elliptical spheroid, the polar diameter being 

 diminished and the equatorial diameter increased. Shortly after 

 Huyghens was led to the same result ; and while Newton by his 

 calculations found the polar diameter to be to the equatorial as 

 229 to 230, Huyghens, on the basis of less general theories, found 

 the proportion to be 577 to 578. Indeed, although differing 

 somewhat in magnitude (Newton's proportion was then accepted 

 as the more correct), yet, in principle, they both led to the same 

 result, viz., that the earth is flattened at the poles, so that the 

 length of a degree near the poles must be greater than in the 

 neighbourhood of the equator. Moreover, Newton had shown 

 experimentally the flattening at the pole, by rotating a soft clay 

 sphere quickly round its axis, by which it became flattened at its 

 poles. 



To this was now added another valuable proof. The French 

 astronomer Richer, in the prosecution of his observations at 

 Cayenne, found to his astonishment that his pendulum, which 

 beat seconds in Paris, vibrated too slowly in Cayenne ; he had to 

 shorten it by a line in order to make it again beat seconds accu- 

 rately. On his return to Paris he had to lengthen the pendulum 

 again by the same amount, since it now went too fast. Newton 

 perceived that this apparently insignificant fact was really of the 

 highest importance, for he recognised that these different rates of 

 oscillation were due in Paris to the less, and in Cayenne to the 

 greater, distance from the centre of the earth. Cassini's discovery 

 of the notable flattening of the planet Jupiter was an additional 

 proof of the truth of Newton's theory. Yet it was not until the: 

 middle of last century that Newton's theory was genefal!y 

 accepted as an irrefragable truth. 



{To be continued.) 



THE VARIOUS METHODS OF DETERMINING 

 THE VELOCITY OF SOUND 



nPHE propagation of sound is a question with many bearings 

 ■*■ in the province of physics, and the researches of physicists 

 in relation to it, though numerous, have left some points stilt 

 under discussion. It is useful in the view of further inquiry to 

 be furnished with a historical survey of what has been already 

 done, and this is the object of a recent memoir by Dr. II. 

 Benno-Mecklenburg, published in Berlin (a risume of which to 

 the following effect appears in the May number of the Journal 

 de Physique'). 



The author has adopted the following classification of the 

 methods that have been employed for measuring the velocity of 

 sound : — 



I. Methods requiring the measurement of a time and a course 

 traversed. 



1. Direct measurement of the velocity; the most ancient 

 measiu-ements of this kind were executed by P. Mersenne in 

 1657, by the Academicians of Florence in 1660,^ by Walker^ 

 (in England), in 1698 ; by Cassini and Huyghens (in France), 

 &c. 



2. Method of coincidences, indicated by Bosscha,* and em- 

 ployed by Koenig.* 



I Newton, "Philosophia Naturalis Principla Matheir.aticse," II., Prp. 

 XLVIII.-L. 

 " Laplace, " Mecanique Celeste," t. v. livre xii. p. iis- 



3 Tentamina, " Exper. Academ. del Cimento," 1738, xi. p. 116. 



4 Philosophical Transactions, 1698. 



