SCIENCE. 



457 



This problem was first solved by Alhazen, a learned 

 Arabian of the illh century, and published at Basle, in 

 Latin, in 1572. Since that time it has been studied by 

 several distinguished mathematicians and a variety of 

 solutions given. The paper presented contained a col- 

 lection of these solutions aiming to be complete. Eleven 

 solutions were contained in this collection, beginning with 

 Alhazen and ending with a solution by E. B. Seitz, in 

 1881. 



The first five solutions are by geometrical construc- 

 tions, in which the points sought are determined by the 

 intersections of a circle and hyperbola. The sixth solu- 

 tion, also a geometrical construction, is by means of the 

 intersection of a circle and parabola. The seventh, 

 eighth, ninth and eleventh solutions are by analytical or 

 algebraical methods, while the tenth is a trigonometrical 

 solution. 



Among the people who have studied and solved the 

 problem are Alhazen, Barrow, Hutton, Huyghens, Kaest- 

 ner, Leybourn, L'Hospital, Robins, Stitz, Sluse and 

 Wales. A complete list of bibliographical references 

 was appended to the paper. 



The paper contained further, an extension of the prob- 

 lem, first, to the surface of a sphere, and second, to an 

 ellipse. The first case was illustrated by the following 

 practical example : 



The great circle track between San Francisco, Cal., 

 and Yokohama, Japan, reaches nearly to latitude 52 N. 

 The Pacific mail steamers plying between these ports 

 usually avoid going north of latitude 45 N. Now, if the 

 45th parallel of latitude be designated as one north of 

 which the steamer is not to go, in what longitude must 

 this parallel be reached in order that the steamers' path 

 between the ports shall be the shortest possible ? The 

 extension of Alhazen's problem to the surface of the 

 sphere solves this problem and the longitude required is 

 168 W. from Greenwich. 



The extension of the problem to the case in which an 

 ellipse replaces the circle gives rise to a very complex 

 equation of no special value. 



Washington, D. C, Sept. 13, 1881. 



ROTATION OF REDUCING POWER, AS MEAS- 

 URED BY FEHLING'S SOLUTION TO THE 

 ROTATORY POWER OF COMMERCIAL 

 AMYLOSE (GLUCOSE AND GRAPE SUGAR). 



SECOND PAPER.* 



By Prof. H. W. Wiley, Lafayette, Ind. 



In a paper read at the Boston meeting of this Associ- 

 ation 1 I called attention to the fact that the reducing 

 power of Amylose, measured by Fehling's Sol., could be 

 readily determined by the polariscope. Since that time 

 I have extended the series of observation then reported, 

 and with such results as justify the conclusions at which 

 I arrived. 



In commercial Amyloses, whose specific gravities do 

 not vary much from 1.410, the reducing power is reliably 

 calculated from the reading of the polariscope. The 

 average percentage of water in these Amyloses is 

 nearly thirteen. If we allow one per cent for optically 

 inactive substances present, we may safely place the 

 optically active matter at 86 per cent. By prolonged 

 boiling with acids, even if they be quite concentrated, 

 only about 82 per cent of reducing matter is obtained. 2 

 Further boiling causes the mass to turn brown, and may 

 even cause a decrease in the amount of reducing matter 

 found. Since there is so much difference of opinion 

 respecting the reliability of Fehling's solution, and since 



*Read before A. A. A. S., Cincinnati, 1881, 



1 Proceedings of this Association, 1880, p. 308 ; Journal Am. Chem. 

 Soc, Vol. II., p. 387. 



2 Proceedings A. A. A. S., 1880, p. 320. Journal Am. Chem. Soc., 

 Vol. II., p. 399. 



there is no other reducing mixture that works as well, it 

 would, perhaps, be better to use the polariscope for the 

 determination of the amount of substances present in an 

 Amylose capable of reducing the various solutions used 

 for grape sugar measurements. 



In the following table the calculation of the reducing 

 power was made by the formulae, } which 1 have already 

 explained. Although, in a few cases, the specific gravity 

 varied by a few thousandths frcm 1.410, the difference 

 has not been of sufficient importance to make any correc- 

 tion 4 . 



Since the ordinary Amyloses, called grape sugars, of 

 commerce differ from those called glucoses only in hav- 

 ing the processes of conversion carried further, it is found 

 that the same rule applies to them also. In fact, I 

 believe it will be found true with all vatieties of Amylose 

 made by use of sulphuric acid, provided 8.6 grammes of 

 the anhydrous substance be used in each 100 c.c. of the 

 mixture to be examined. 



Following are the results of my observations : 



Table I. 



No. 



Sp. gravity. 



Reducing mat- 

 ter by Fehling's 

 Solution. 



Rotation of 10 g. 

 in 100 c. c. cone 

 sugar scale. 



Reducing matter 

 calcul tted from 

 Polariscope. 



Difference. 



Date of 

 Manufacture. 



















+ 







1880. 



1 . . . . 



I 



414 



52 



1 



53 °4 



52 -°5 







04 







September 15 



2 . . . . 



I 



419 



52 



2 



53.00 



53-00 



O 



08 







14 



3 .... 



I 



410 



S3 



8 



51.00 



55-05 



I 



07 







15 



4 .... 







53 



2 



55-o5 



49.09 





06 



3 



3 



October 12 



5 •••• 



I 



412 



5i 







54 01 



51 c6 











18 



6 .... 





413 



5i 



1 



S3- 02 



52-75 



I 



65 







19 





I 



417 



5i 



6 



53-45 



52-44 



O 



84 







19 







417 



49 



7 



55.02 



50-03 



O 



<6 







20 



9 .... 



I 



408 



49 







55-05 



49.09 



O 



09 







" 2t 



10 .... 



I 



413 



49 



5 



55-04 



50.00 



O 



05 







" 21 





I 



411 



48 



1 



56.06 



48.05 



O 



04 







17 



12 .... 



\ 



421 



48 



8 



56.04 



48.08 







00 











16 



13 • ■ • • 





417 



5° 







57.00 



48.00 







2 







16 



14 ... . 



I 



413 



46 



4 



56.07 



48.04 



2 



00 







14 



IS .... 



I 



417 



48 



1 



56.05 



48.06 



O 



°5 







14 



16 .... 



I 



418 



46. 



3 



58.02 



46.05 



O 



02 







13 



17 .... 



I 



412 



47- 



2 



57.00 



48 .00 



O 



08 







12 



18 .... 







72. 







37-03 



72.63 



O 



63 







Unknown. 



The above analyses were of samples sent by the man- 

 ufacturers, the Peoria Grape Sugar Company. They 

 represent the whole number of samples examined 

 and in the order in which the analyses were made. 

 Seventeen of them were of syrups, and the eighteenth 

 of a solid sugar. Only four out of the eighteen show 

 discordant results. In one of these the specific gravity 

 was not determined. It was my intention to make these 

 four analyses in duplicate, but a press of other business 

 prevented. In general, it appears that the results given 

 by the polariscope, by the above method of calculation, 

 are a little too high. If they were diminished by 5 the 

 agreement would be better. That the reducing power 

 of Amylose can be correctly calculated from its rotatory 

 power is certainly established from the thirty-eight un- 

 selected instances which have been presented. 



Electric Light for Lighthouses — The first of the 

 series of lighthouses round the French coast which are to be 

 henceforth illuminated by electricity, has, with all its neces- 

 sary machinery, been completed. It is called the " Phare 

 de Planier," and is situated at the mouth of the Rhone, 

 near Marseilles. 



3 Proceedings A. A. A. S., 1880, p. 313. Journal Am. Chem. Soc. 

 Vol. II., p. 393. 



* Proceedings A. A. A. S., 1880, p. 316. Journal Am. Chem. Soc , 

 Vol. II., p. 395. 



