4o8 



NA TURE 



[February 21, 1901 



"practical engineers or business men, thus bringing to bear on 

 their teaching, not only the general education gained at school 

 and their thorough knowledge of theoretical science, but also 

 their practical experience of the workshop and business life." 



These are but a few of the vital questions with which this 

 valuable report is concerned. We heartily commend the volume 

 to all who are interested in improving the home supply of 

 technical education until it is not only on a level with that of 

 Germany and Austria, but well in advance. 



When we turn to the second of the reports, that concerned 

 with the place in English secondary education of preparatory 

 schools for boys, we are confronted with another stage in the 

 preparation of the citizen for the duties of life. As every one 

 knows, probably, the preparatory school undertakes the educa- 

 tion, up to about fourteen, of the boy destined for our great 

 public schools. Generally, after some five years at the public 

 school, this fortunate son of well-to-do parents proceeds to 

 either Oxford or Cambridge to continue his education. It is 

 interesting to inquire as to the share science takes in the 

 work of a preparatory school. It may be stated parenthetically 

 that in a volume of 531 pp. only some sixteen pages are 

 devoted to the teaching of mathematics and natural science 

 together, though it is true nine of the sixteen are given to the 

 latter. 



It must be said at once that any science teaching at all in 

 preparatory schools is the exception rather than the rule. To 

 quote Mr. Archer Vassall, of Harrow, who deals with the sub- 

 ject in the official publication before us, " tentative efforts in 

 scientific instruction have been made, and are still in progress 

 at many of them " — and that is all that can be said. But there 

 is nothing surprising about this. Since the sole function of the 

 preparatory school is to prepare for the public school, those 

 subjects only which are in demand in the second will be taught 

 in the first, and, to quote Mr. Vassall again, " in public schools 

 the teaching of science has only recently begun to take reasonable 

 shape," a condition brought about by the regulations governing 

 the award of University scholarships. So that to ensure an 

 improved condition of things in the preparatory school men of 

 science must bend their efforts towards securing reforms at 

 Oxford and Cambridge. 



Mr. Vassall's short article is chiefly concerned with a sketch 

 of a suitable preparatory school course in natural science. In 

 common with modern ideas he insists upon the need of indi- 

 vidual practical work, and very properly urges that the study of 

 science might well begin with what he calls " kindergarten 

 physics." This mode of procedure has for some years been 

 followed in higher grade boards schools, and in those other 

 secondary schools which have adopted the syllabus of the 

 Headmasters' Association. But we think Mr. Vassall is wrong 

 in excluding chemistry from his preliminary course, for there are 

 many excellent exercises which are in no way dangerous. Any- 

 how, a beginning has been made with science in preparatory 

 schools, and if the masters will acquaint themselves with the 

 results of experience in schools of other grades, we shall soon 

 hear that science has gained for herself a more honourable place. 



A. T. Simmons. 



THE FIGURE OF THE EARTH.^ 



''PHE United States Coast and Geodetic Survey has just 

 published a quarto volume containing an account of the 

 transcontinental triangulations and measurements of an arc of 

 the parallel in latitude 39°. It also has ready for publication 

 the manuscript giving the result of an oblique arc in the eastern 

 part of the United States. Both are contributions of great 

 length and among the first of their kind in America. ,. 



Before entering upon the detail of the two arcs it may not be out 

 of place to state that in order to obtain a measure of the dimen- 

 sions of the earth, as represented by a spheroid, that is, by a 

 surface generated by the rotation of an ellipse about its minor 

 axis, it is essential that we should be in possession of at least 

 two arcs or of an equivalent thereof. For combinations of two 

 arcs of the meridian, their mean latitudes should differ widely ; 

 the same is true for the combination of two arcs of the parallel. 

 We may also obtain an arc of the meridian with one of the 

 parallel, but in every case the measures should be of considerable 



1 Abridged from a paper on recent contributions by the United States 

 Coast and Geodetic Survey to our knowledge of the earth's shape and size, 

 by Mr. C. A. Schott, in the National Geographic Magazine, New York. 



NO. 1634. VOL. 63] 



extent. Arcs of less than 5° (about 556 km., or 345 st. miles) 

 would now be regarded as short ones. It has been stated that 

 one of the arcs is an oblique arc, and as it possesses a great 

 range of latitude and also of longitude and is supplied with a 

 large number of astronoinical measures, it is of itself sufficient 

 for the deduction of values for the dimensions of the earth. 

 Furthermore, it may be remarked that for any relatively small 

 part of the earth's surface an osculating spheroid may be deter- 

 mined, as, for instance, was done for our oblique arc. Such a 

 spheroid has the property that its surface is in best accord, as 

 regards curvature, with the actual or physical one, the latter 

 considered as a mathematical surface of equilibrium and 

 generally known as geoid. 



The definition of an osculating spheroid thus implies that the 

 sum of the squares of the difference between the various astro- 

 nomic and geodetic measures be a minimum. The mathematical 

 treatment of the combination of the arc measures differs according 

 to their nature, whether they are extended in a certain direction 

 or whether large areas are covered, but in. its generality it is 

 necessarily laborious. 



The salient points of the two arcs measured by the U. S. 

 Coast and Geodetic Survey and the results reached may now be 

 briefly stated. First, the arc of the parallel in latitude 39°.^ 

 It extends from Cape May, N.J., on the Atlantic coast, to Point 

 Arena, Cal. , on the Pacific coast, and ranges over 48° 46'of longi- 

 tude, with a linear development of about 4225 kilometres, or 2625 

 St. miles. The triangulation is supported by ten base lines with an 

 aggregate length of 535 st. miles, the longest or Yolo base being 

 io'9 miles in length, one half of these lines having a smaller prob- 

 able error of measure than one part in a million. A characteristic 

 of the triangulation is its rigidity imparted to it by quadrilaterals 

 and other polygons. In crossing the Rocky Mountains, many of 

 its sides exceed one hundred miles in length, and there is one 

 side reaching to a length of 294 km., or 183 st. miles ; the 

 altitude of many of the stations is also considerable, reaching to 

 4300 metres, or 14 108 feet, in the case of Pike's Peak, and to 

 14,421 feet at Mount Elbert. All geometrical conditions sub- 

 sisting in the triangulation are satisfied by adjustment, inclusive 

 of the required accord of the base lines, so that the same length 

 for any given line is found no matter from what line one may 

 start. This involved much heavy work ; for instance, the tri- 

 angulation adjustment between the Salina and the El Paso base 

 demanded the simultaneous solution of ninety-nine normal 

 equations (with as many unknowns). In addition, the figures 

 required the evolution of a correction to each of the two hundred 

 and twenty-five observed directions. 



Coming to the astronomical measures, we have distributed over 

 or near the arc one hundred and nine latitude stations, occupied 

 almost exclusively with zenith telescopes ; there are, also, 

 seventy-three azimuth stations, various methods having been 

 used, and lastly we have twenty-nine telegraphically determined 

 longitudes. These, of course, are of paramount importance 

 for an arc of the parallel. There cannot be too many longitude 

 stations in consequence of that great stumbling-block in geodesy, 

 the local deflections of the vertical or plumb-line. These 

 deflections of the zenith from a normal direction have been 

 divided into two groups — those which are regional or manifest 

 themselves with marked common features over thousands of 

 square miles, and those which are quite local and greatly 

 depend upon the surface features immediately surrounding 

 them. 



These deflections, even in level countries, average about 2 '5" ; 

 but in mountainous regions this deflection is greatly surpassed. 

 Thus we find for deviation of the plumb-line at Patmos Head 

 station 12" to the north, at Colorado Springs 25" to the west, at 

 Salt Lake City about 17", and at Ogden about 15" to the east, at 

 Genoa Station, Nev., nearly 29" to the west, the quantities 

 depending to some extent on the spheroid of reference ; but their 

 amount and direction are obviously well accounted for by the 

 position of kno\*n attracting masses. In connection with this, 

 continental attraction may manifest itself and be recognised by 

 the astronomical artiplitude of the longitudes of extreme stations 

 of a long arc being in excess of the corresponding geodetic 

 amplitude. The matter cannot be further pursued here in detail, 

 but it may suffice to state that the average curvature of the 

 equipotential surface of the geoid along the parallel of 39° 



1 U. S. Coast and Geodetic Survey ; H. S. Pritchett, Superintendent. 

 The Transcontinental Triangulation and the American Arc of the Parallel. 

 By C. A. Schott, Assibtant, Coast and Geodetic Survey, Washington, D.C., 

 1900. 



