42 



NATURE 



[November 13, 1902 



As in ihe case of aqueous solutions, the solubility of the 

 precipitate is diminished by adding excess of the precipitant. 

 When dry hydrogen sulphide is passed into benzene solutions 

 of the oleate of copper, nickel or cobalt, the sulphides of the 

 metals are at once thrown down. If these solutions are first 

 saturated with hydrochloric acid so as to precipitate the chlorides 

 and then saturated with dry hydrogen sulphide, the sulphides 

 do not form. Stannic chloride dissolved in benzene was treated 

 with dry hydrogen sulphide in large excess without any visible 

 formation of sulphide ; but on standing overnight there was 

 a copious precipitate. Arsenic trichloride in benzene showed 

 a similar reluctance to form sulphide, but when petroleum 

 ether was used as a solvent the formation was almost instan- 

 taneous. 



Hughes has found that dry hydrochloric acid will not react 

 with dry ammonia, a fact which the author has confirmed. Yet 

 when anhydrous benzene is treated with hydrochloric acid dried 

 over sulphuric acid and phosphorus pentoxide, and then 

 ammonia (evolved by heating lime mixed with ammonium 

 chloride and dried by passing through a tower of lime and one 

 of dry pumice covered with phosphorus pentoxide) is passed 

 into the solution, a white, bulky precipitate of ammonium 

 chloride at once forms ; the benzene vapours are enough to 

 cause the reaction to take place. Neither of the solutions, nor 

 the mixture, conduct better than benzene itself, nor is there any 

 change of conductivity at the instant of mixing. Similarly, 

 when anhydrous pyridine is mixed with benzene, the solution is 

 a non-conductor. But when such a solution is mixed with a 

 solution of hydrochloric acid in benzene there is at once formed 

 a heavy precipitate of the hydrochloride. 



We must therefore conclude that instantaneous chemical re- 

 actions are possible with non-conducting solutions as well as 

 with electrolytes. W. R. C. 



A MEDIEVAL TREATISE ON SURVEYING. 

 pROF. HAMMER, of Stuttgart, who has from time to time 

 published interesting contributions to the history of geodesy 

 and of surveying instruments, has given in a recent number of 

 the Zeils'chrift fur Vcrmcssungswesen a detailed account of 

 Reinhold's treatise on surveying and mine surveying, a little- 

 known work that enjoyed great popularity in Germany in the 

 Middle Ages. In the bibliography appended to Brough's 

 "Mine Surveying" (ninth edition, 1902, p. 360), Reinhold's 

 book appears as the earliest independent treatise on the subject. 

 In view of the far-reaching influence exercised by the work, 

 a brief analysis of the contents may not be without interest. 



The title of the book is " Griindlicher und warer Bericht vom 

 Feldmessen " It was published at Saalfeld in 1574 by his son, 

 Erasmus Reinhold. Reinhold senior was born at Saalfeld in 1 5 1 1 

 and died there of the plague in 1553. From 1536 until his death 

 he was professor at Wittenberg. The main contents of the book 

 would appear, therefore, to have been written in the middle of the 

 sixteenth century. The] preface, written by Erasmus Reinhold 

 junior, a physician, gives examples of errors made in surveying. 

 Thus, a large forest was measured thrice ; the first determination 

 gave an area of 26,000 acres, the second 36,000 acres, and the 

 last 27,000 acres. The author divides his " Bericht " on survey- 

 ing into five sections. The first deals with the four rules of 

 arithmetic, the extraction of square roots, &c. ; the second 

 deals with the calculation of areas ; the third with the dividing 

 up of land ; the fourth shows how the rules given may be applied 

 in districts where other measures of area are in use ; and, lastly, 

 the fifth section enumerates the rules of surveying so as to 

 enable, as the author puts it, a common man of sufficient intelli- 

 gence to carry out his own measurements without further great 

 ado. The second part of the work is devoted to an account of 

 the quadrants and of the compass, and to a treatise in nineteen 

 chapters on mine surveying. 



In the first part of his book Reinhold complains that it is rare 

 to find a town which uses the same names and sizes for field 

 surveying as its neighbours. Morgen, Juchart, Tagwerk, 

 Mannsmahd, Hufe, Hufacker, Artacker, &c, are among the 

 units of area met with. He therefore carefully enumerates his 

 measures of length and area,' with the symbols used for them 

 throughout the book. The unit of length is the rod (Ktd/te) 

 of 16 feet {Werkschuh), each of which is again divided into 

 16 finger-breadths {Fingerbreit). The unit of area is the acre 

 {Acker) of 1 50 square rods (gevierdt Ruthen). The Werkschuh, 



NO. 1/24, v OL. 67] 



on which his whole system of measures is based, is dealt with 

 by Reinhold in a peculiar manner, very characteristic of the 

 period. He says in effect : how long, however, a Werkschuh is, 

 is known to everyone, or can easily be ascertained from any car- 

 penter, mason or cabinet-maker. Later on in the volume he 

 gives a woodcut showing the length of a third of this foot, from 

 which it is evident that the Werkschuh was 281 millimetres long, 

 and consequently the Ruthe was 4*50 metres long, which is in 

 close accord with the old Brunswick rod of 16 feet (4'566 

 metres). A square rod would represent 2oi square metres, and 

 the unit of area, the Acker, would contain about 3040 square 

 metres, which is in fair accord with several of the Morgen in 

 use in Germany before the introduction of the metric system. 

 For the measurement of lengths, Reinhold advocates the use of 

 a cord or rods. A wire cord is preferred to a hemp one, as not 

 being affected by weather or by varying tension. For setting 

 out a right angle the author makes use of the right-angled 

 triangle with the sides 3, 4 and 5. He also recommends the 

 numbers 20, 21 and 29, as well as the approximation with the 

 numbers 12, 12 and 17 (I2 2 + 12 2 = 288, whereas 17-= 289). 

 In reference to the latter method, he reminds the reader that he 

 writes for the common man who does not require everything to 

 be weighed on a gold-balance. Areas are calculated by means 

 of rectangles, trapezoids and triangles, attention being given to 

 the measurement of lakes and woods and other polygonal figures 

 in which diagonals cannot be measured. For the measurement 

 of angles the compass is used. It is graduated into single degrees, 

 each 5 degrees being numbered consecutively from o to 360'. 

 The direction of the pointer in the illustration given represents 

 a westerly declination of about 6 U . Lastly, the trigonometrical 

 solution of triangles by the aid of a table of natural sines is ex- 

 plained. The next section of the work deals exhaustively with 

 the division of land. Errors, it is pointed out, frequently occur 

 which a good surveyor could easily prevent. Every prince and 

 town, therefore, should, as the author quaintly puts it, have a 

 licensed, but nevertheless competent, surveyor. The second 

 division of the whole work is devoted to mine surveying. The 

 instruments described include the compass, a good quadrant, a 

 water-level and a hanging clinometer. The unit of length in, 

 mine measurements was the Lachter (fathom) of 6 shoes, and 

 the technical terms then used were much the same as those now 

 in vogue in German mines. 



Such in brief are the contents of this remarkable treatise 

 written 350 years ago. Comparing it with some of the most 

 recently published text-books on surveying, it is depressing to 

 find how little is the progress that has been made in the instruc- 

 tion in this important branch of engineering. In a large treatise 

 on the subject published this year the statement is made that a 

 slight knowledge of geometry is necessary, and consequently a 

 chapter is inserted in the middle of the book dealing with 

 geometry, trigonometry and logarithms. The development of 

 the theory of measurements and the mathematical principles on 

 which it is based are neglected, and the author confines himself 

 to enunciating mechanical rules for the testing of surveying instru- 

 ments and for carrying out surveys. This rule-of-thumb method 

 of education was not enough for Reinhold in 1550, whilst in 

 17S2 Prof. Lempe, in his lectures at the Freiberg School of 

 Mines and in his text-book, went still further by urging the 

 necessity of learning and applying arithmetic, geometry, plane 

 and spherical trigonometry, and even analytical geometry and 

 the elements of the differential and integral calculus, as the surest 

 basis of a successful study of mine surveying. B. H. B. 



DYNAMIC INTERPRETATION OF CELL- 

 DIVISION.^ 



TTHE author came to the study of biology possessing, as a civil 

 engineer, an equipment rare among the disciples of this 

 science. Some years ago he interpreted the phenomena of cell- 

 division and karyokinesis as due to the play of Newtonian forces 

 of equal potential but opposite sign, rather than to the gross 

 actions of pull or push performed by ordinary mechanical forces ; 

 and was able to reproduce the spindle-figure and centrosomes by 

 a trough full of spirits of turpentine in which were suspended 

 crystals of sulphate of quinine, and into which were introduced 

 a pair of wires joined to the poles of an electric machine. After 

 continued study under such masters as Giard, he now develops 



1 " Interpretacion Dinamica de la division Cellular." By A. Gallardo. 

 Pp. 101. (Buenos Aires, 1902 ) 



