1822.] the Quantity of Rain falling in adjacent Places. 21 
fall of rain will be found to differ much less than hitherto 
recorded. Nothing will contribute more to ascertain the fact 
than an uniformity of guages, as well in situation, as size and 
shape. It is desirable that in all cases there should bea guage on 
the level of the surface of the ground. A pit must be prepared 
just fitted to the bottle in which it may so stand that the edge 
of the funnel shall be but half an inch above the surface, and 
care taken that the rim of the basin be truly horizontal. If any 
obstacle to the free course of the wind occurs within 100 or 200 
yards of the guage, its height, breadth, and direction, should be 
noticed ; and in respect of those placed on the tops of buildings, 
the length of pipe between the funnel and receiver, and whether 
within or without the house, should be mentioned ; as well as the 
height of the guage above the ground, and above the level of the 
sea. It is also desirable that the barometrical tables should be 
always reduced to the temperature of 32°, or, if not, that the 
omission should be stated; and the thermometrical tables which 
Sle the true maximwm and minimum of every 24 hours are pre- 
erable to the observations of fixed periods, which very often fail 
to show either. 
Iam, Sir, your most obedient servant, 
H. Boase. 
Articte VI. 
On Finding the Sines of the Sum and Difference of Two Arcs. 
? By Mr. James Adams. 
(To the Editor of the Annals of Philosophy.) 
SIR, Stonehouse, near Plymouth, June 8, 1822. 
Ir having occurred to me that by making a small alteration in 
the methods given by Mr. Leslie in his Geometry, and by Mr. 
Woodhouse in his Trigonometry, the demonstrations of the two 
fundamental formule for compound ares may be rendered still 
more simple than those usually given, I will thank you to 
insert the following in the Annals of Philosophy, when con- 
venient. I am, Sir, your most obediert servant, 
James ADAMS. 
; —_ 
To find the Sine of the Sum of two Arcs. 
Let the quadrilaterals A B D E be inscribed in acircle and 
semieircle, whose centres are C, and diameters A E, the dia- 
gonals of which being AE, BD, in fig. 9 (Pl. XIII), and 
AB, DE, in fig. 10. Bisect the ares EB, ED, BD, in: the 
‘points ¢, r, w; and draw the radii Ct, C r, and Cw, which will 
