Mr. Maw ovth's Arrangemeni o/'^^^Macriirou.s Crustacea. 183 

 Hence by substitution 



cos (A' - B) = ^ + (cos B - ^l cos A') cos A' 



^ ' sin A \ sin A / 



sin B -r> A / sin B o » i 



= .'. -.— TT -r cos B cos A ■. — — cos * A' 



sin A' sin A' 



sin B „ A I sin B . . „ . A > 



T + cos B cos A : — — , -j- sin B . sin A 



sin A' sin A 



= ••• cos B cos A' + sin B sin A' 



XXIX. A new biliary Atrangement of the Macrurous Crus- 

 tacea. By A. H. Hawouth, Esq., Fello-iSO of the Linnccan and 

 Horticultural Societies of Lo7ido7i, and (f the Imperial Na- 

 tural History Society of Moscow, 8fc. ^c. 



[Continued from p. 106.] 



To the Editor of the Philosophical Magazine and Journal. 



Sir, 

 ILTEREUNDER I transmit you the promised continuation 

 ■■• -'■ of my new binary arrangement ot" cnistaceous animals, 

 including the great branch Macuura; which, if you could 

 print in the manner of my first and second tables, would much 

 better display the horizontal analogies and affinities than my 

 last or third table can ; Xhe first articles of every dichotomy in 

 any given group having ever the least affinity to each other, 

 and the last articles the most. Wherefore the said first arti- 

 cles (as animal — vegetable) are often merely analogies (in point 

 of relationship to each other); but these insensibly, as we 

 go down the table and arrive at the genera, lessen and 

 blend into the closest affinities. But I allow that the mode 

 in which you have printed my last or third table shows more 

 advantageously to a mere reader, the current location, or na- 

 tural distribution di \X\g. genera -, which, notwithstanding what 

 is in modern, not old times, supposed to the contraiy, I now 

 believe to be a continuous one, that is unravelable in the way 

 of a straight line; but arising dichotomously from one root 

 (which I have termed Matter) and proceeding in a rcpetiteh' 

 double, and, in point of magnitude or quantity, unequal series ; 

 resembling as it were an inverted branching and exuberant 

 tree, whose foliation and flowers may be compared to our arti- 

 ficial genera, and natural, and therefore permanent species. 



As soon as I can procure some books which must be con- 

 sulted before I can proceed much further with this business, 

 you shall have the requisite continuations; and in the mean 

 time I remain, sir, yours, &c. 



Qucen'i Elm, Chelsea, March 1826. A. H. Haworth. 



