Intelligence and Miscellaneous Articles^ 239 



various speeds . From those results I deduced a general formula for 

 the resistance of ships having such figures as usually occur m steamr 

 ers, which on the 23rd of December, 1857, I communicated to the 

 owner of the experimental data ; and he has since applied it to prac- 

 tice with complete success. 



As the experimental data were given to me in confidence, I am 



for the present bound in honour not to disclose the formula which I 



deduced from them ; but as I am desirous not to delay longer the 



placing- it upon record, I have recourse to the old fashion of sending 



it to you in the form of an anagram, in which the letters that occur 



in its verbal statement are arranged in alphabetical order, and the 



number of times that each letter occurs is expressed by figures. 



20 A. 4 B. 6 C. 9 D. 33 E. 8 F. 4 G. 16 H. 10 I. : 



5 L. 3 M. 15 N. 14 O. 4 P. 3 Q. 14 R. 13 S. 25 T. 



4 U. 2 V. 2 W. IX. 4 Y. (219 letters in all.) 



I hope I may soon be released from my present obligation to 



secrecy. 



I am. Gentlemen, 



Your most obedient Servant, 

 Glasgow, August 26, 1858. W. J. Macquorn Rankine. 



OBSERVATIONS ON THE NATIVE PHOSPHATES OF COPPER. 

 BY PROF. BEBGEMANN. 



I have been led by my late investigations of Ehlite to make some 

 experiments upon other compounds of oxide of copper with phos- 

 phoric acid and water, in order to ascertain whether these might not 

 al«o contain vanadic acid. And although I have not again found 

 this acid the experiments yielded unexpected results, inasmuch as 1 

 detected arsenic acid in all the minerals belonging to the phosphate 

 of copijer group, and often in considerable quantities. I was sur- 

 prised at finding this acid, for all the researches on these minerals 



mention no trace of it. . . , n i ^^a 



The analysis of Hungarian Libethenite performed upon small selected 

 cystals, for which 1 am indebted to the kindness of my friend Dr. 

 Krantz, gave the following results : — 



Oxygen. 



Oxide of copper 66"29 13*26 



Phosphoric acid 26-46 14-92 1 ^^.^^ 



Arsenic acid 2-30 0-79 J 



Water ^i 3-58 



99-09 

 The relation of the oxygen is therefore 4 : 5 : 1, and Libithenite is, 

 as is well known, isomorphous with olivenite. 



Phosphochalcite from Linz on the Rhine consists of— 



Oxygen. 



Oxide of copper 69-97 14-1 



Phosphoric acid 19-89 ^^'\t\ 11-75 



Arsenic acid 1*78 0-6o J 



Water _^ 7-11 



99-85 



