2 REPORT—1852. 
did not attempt a commercial arithmetic, as that would have required a fuller know- 
ledge of their weights, measures, &c. than he found it convenient to acquire ; but 
as these are all decimal, it will be easy for any one to do what remains. His main 
object was to make arithmetic an instrument of that intellectual culture, which, in 
common with all missionaries, he deemed of so much importance. With this view 
he has given the reasons of all the rules, except that for finding the greatest common 
measure of two numbers. and that of Mr. Horner for extracting any root of a number, 
which are obviously too difficult for the pupils for whom his book was intended. 
Dr. Moncrieff’s attempt has already had such a measure of success as to encourage 
a hope that the stream of Eufopeah improvement may, with less difficulty than we 
have hitherto supposed, be made to flow into the stagnant waters of Chinese science 
and literature. 

On Criteria for real and imaginary Roots of Biquadratie Equations. 
By W. GarTLANnD. 
This is an extension and simplification of Sturm’s method, but does not admit of 
being given in an abstract. 

On Biquaternions. By Sir Wit11AM R. Hamittoy, LL.D. M.R.LA. 
The author briefly explained the term which he had been obliged to introduce into 
this new system ; showed the simplicity and the reasons for the leading operations 
in it; and by a few very simple experiments on the rotation of planes round axes 
inclined to each other, explained the simple interpretation of some of those results 
which appeared at first to be inconsistent with the principles of the ordinary analysis. 
i = é 
On the Gradient of Density in saturated Vapours, and its Development as a 
Physical Relation between Bodies of definite Chemical Constitution. By 
J. J. WATERSTON. 
_ The object of the present communication was to give a short notice of certain de- 
velopments of a general law of density in saturated vapouts, which the author had 
lately, in a paper laid before the Royal Society, collected evidence from observation 
to support. Density is, by him, taken to signify, not specific gravity, but the quotient 
of the pressure of the vapour by its temperature, reckoned from the zero of gaseous 
tension; the standard of temperature being that of the air-thermometer. The 
general law is, that the temperature and sixth root of the density of a saturated 
vapour form the co-ordinates of a straight line. In other words, at the same tem- 
perature, or at the same interval of temperature, any two vapours in contact with 
their generating liquids, have densities that are either equal, or that have a constant 
proportion to each other. The author gave diagrams illustrative of the application 
of this law to several vapours. The point of convergence of the right lines he calls 
nodes. He gave twenty-four distinct examples of its application to steam, alcohol, 
wether, and several other vapours, laid down the formule by which the computations 
could be conducted, and pointed out the method of determining the value of the 
constants. 
Lieut, Heat, Evectricity, MAGNETISM. 
Notice of a Tree struck by Lightning in Clandeboye Park. 
By Sir DAvip Brewster, A.A, D.CL., PRS. & ViPRS, Edinb. 
During one of the thunder-storms which passed over the county of Down in August 
last, a birch-tree of considerable magnitude was struck by lightning. The tree stood 
in a thick mass of wood, and was not the tallest of the group. The lightning-bolt 
struck it laterally about 15 feet above the ground, exactly at the cleft where the two 
principal branches of the tree rose from the trunk. A large part of the bark and a 
piece of the solid wood were driven to some distance, and the electric fluid passed 

