On the Rules for Algelraic MullipUcation^ 15 



Description of the Dxiiuing. 



Plate I. fig. 1, 1, 1, 2, 3, ditiVrent sand plants, showing how 

 they appear when a breadth of the leaf is cut. 



Fig. 2, being the upright hairs, while the figure ks show the 

 horizontal ones. 



Fig. 3, shows the sort of borders that covers eacli face of the 

 leaf and is often seen with the upright hairs. 



Fig. 5, is a leaf which is too small in proportion, but is de- 

 signed to show that one side of the leaf is gcacrally filled and 

 emjnied at a time, as here represented, only that to show them 

 well the hairs are drawn too large. 



Fig. 6 and 7, the hairs showing full and empty. 



Fig. 8, an ujjright hair, various figures of this sort. 



In Parasite Plants. 



Fig. 9, the manner in which the pumps are formed : some hare 

 three or four points in one case ; some have only one ; but they 

 have all the loose part a, a, which falls over the point, and glues 

 itself to the plant it is designed to live on : — a piece of the ivy, 

 %. 10. 



Fig. 12, a breadth of the leaf as cut from the xylophylla plant. 



II. On the Rules for Algebraic Multiplication. By Sir 

 H. C. E>GUiFiELD, Bart. F.R.A. and L.S. 



To Mr. Tilioch. 



Sir, — JL HE following had been several years ago composed, but 

 it is only a few months since the approbation it received from 

 some friends well qualified to appretiate it induced me to send 

 it to you for publication, if vou should judge it worthy. Since 

 it was written I have seen the work of Maria Agnesi, the cele- 

 brated female professor of mathematics at Bologna. She has 

 in the part relative to subtraction made use of a reasoning si- 

 milar to that adopted by me ; but she has not extended it to 

 niultiplicatiou. A friend pointed out to me the work of Mr. 

 Woodhouse, entitled Principles of Analytical Calculation. 



In this excellent work, peculiarly valuable for the clearness 

 and precision with which it is wTitten, I found with great plea- 

 sure that the mode of treating the subject of multiplication was 

 in effect similar to my own, though expressed v\ith more con- 

 ciseness, and perhaps not so evident to mere beginners. I there- 

 fore have still thought that what I now send you may be of 

 use to that class of readers, and in that hope transmit it to 

 you. I am, sir. 



Your obedient servant, 



Tilney Street, Nov. 1, 18U. H. C. EnglefielD. 



