chlorine was united not to calcium, but to lime; and that, therefore, the bleaching salt of Mr. Tennent is in reality a chloride of lime, as it has hitherto been supposed to be. When it is heated, the lime parts with its oxygen, and is converted into calcium, and the chloride of lime becomes a chloride of calcium. Of course it loses its peculiar properties, and, when dissolved in water, is nothing else than a muriate of lime.

Hence the reason that during the preparation of the bleaching powder, it is necessary to keep the temperature of the lime very low. If it be allowed to acquire heat, the chloride of lime is converted into chloride of calcium, and becomes useless for the

purposes of the bleacher. Probably unslacked lime might be

united with chlorine, if its temperature could be kept low. But when the attempt is made on a large scale, so much heat is always generated that the lime is speedily converted into calcium, and the object frustrated.

2. I find that barytes, strontian, potash, and soda, may be united to chlorine as well as lime, so that chlorides of these bases exist. They are easily obtained by double decomposition from chloride of lime. When heated, they give out oxygen gas, and are converted into chlorides of barium, strontium, potassium, and sodium. It is probable that many of the metallic oxides are capable of forming chlorides likewise. Indeed from the trials which I made, I have little doubt that solution of chloride of lime may be employed with advantage to procure several of the metallic chlorides in quantities and with facility. But the discussion of these and many other points, I must leave till a future opportunity.

ARTICLE III.

On the Reduction of Lunar Distances for finding the Longitude.

SIR,

By Dr. Tiarks.

(To Dr. Thomson.)

Chateangay Woods, North America, Sept. 19, 1818. THE method of determining the longitude by observations of lunar distances is by far not so commonly practised as it might be expected, considering the number of instruments fit for such purposes which are in common use. The calculations which such observations require are a great obstacle with most people. Mendoza's tables, by which they are very much abridged, do not seem to be in general use; and the methods contained in the common books, besides being often very inaccurate, require not unfrequently more labour and rules than the direct formulæ. Seamen commonly compute by different methods, in order to guard against mistakes; but in cases of a disagreement of the

results, they are uncertain in which calculation the mistake lies, and, as I have observed myself, have often neither patience nor time enough to find out the errors which are easily committed in logarithmic calculations.

It appeared, therefore, to me, that a method susceptible of an easy check, like those which Prof. Gauss has introduced into astronomical calculations, would be desirable both for astronomers and navigators. The method which I propose for this purpose seems to deserve notice; and I can recommend it the more as the practical seamen to whom I have had an opportunity of communicating it, have found it easy and useful.

Reduction of the apparent Distances of the Moon from a celestial Body to the true Distance.

and the angle at the zenith in the triangle formed by the moon, the celestial body, and the zenith = Z.

We have immediately the two following equations:

Sin. h. sin. H + cos. h cos. H. cos. Z = cos. D

Sin. h'. sin. H' + cos. h. cos. H'. cos. Z' cos. D; therefore,

cos. D' sin. h'. sin. H' +

cos. . cos. I'

(x)

cos. H. cos. H · {cos. D — sin. h.sin. H} and from this by adding and subtracting on the left cos. H'. cos.h'

cos. '. cos. H'

cos. D' cos. (H′ — h′) +

cos. h. cos. H

{cos. D cos. (H− h)}

— 2 sin. (D + H− 1) . sin

but cos. D-cos. (H − h) being equal — 2 sin.

cos. h. cos. H

cos. h. cos. H

we have by (8).

cos. D'

sin., (S h) sin. (SH)]=cos. ₫ (A), and

cos. (H'-h) 2 cos. p, or by substituting 1 + cos.

24 for 2 cos, 2

It

H'

= sin. ( + ("")) . sin.

may be remarked, that when l' > H',

stituted in the equations B and C.

2

(C)

is to be sub

The equation (A) gives 4, and D' is found by (B). The term, to the left, (of the equation (C)) is the same as cos. o previously found, which must be equal to the other term of (C), for the calculation of which, D' is required. If, therefore, D' as found by (B), makes this term equal to cos. o, the calculation is correct, otherwise not. An example may illustrate the whole.

It is clear that it would be very easy to prepare printed forms to be filled up, and that the calculations would become more accurate, and not liable to mistakes.

I am, Sir, your obedient servants vid

T. L. TIA RKS, 1

Stonehouse, Sept. 20, 1818.

YOUR inserting the following problems, &c. in the Annals of Philosophy, will much oblige your most obedient servant,

JAMES ADAMS.

Problem 1.-To find the difference of the natural cosines of

two arcs by logarithms.

A-B

Per trigonometry, cos. B cos. A 2. sin.

M
A+B

sin.

2240

Problem 2.-To find (A + B) — B, by logarithms.

B

Find an arc corres

ponding to the log. sin. which denote by C;

A+ B

Then 2 log. cos. C + log. (A + B) = log. { (A + B) — B }. This solution depends on the property sin. A + cos. A = rad. Problem 3.-To find 1 (1+m) by logarithms.

Then

+ m

which re

{2 log. cos. D + log. (1 + m) } = log. {1-(1+m)}. This solution also depends on the property sin. A + cos.2 A = rad.2.

Problem 4.-To reduce the observed distance of the moon and sun, or moon and star, to the true, by the addition of log. sines, and cosines, only.

Let M and S represent the true places of the moon and sun, or star, mand s the apparent places, m s the apparent distance, M S the true distance, Z the zenith, and H R the horizon of the place of observation.

Put half the sum of the apparent distance and differ

And the difference of the true altitudes

Then per Simpson's Trigonometry, p. 74.

cas. (Zm✩ Z s) — cos,

sin. Z msin, Zsibodo kousin, Z S. sin, Z M

:}

= A

= B

= C

cos. S M = cos. (MR - SH) cos. (H

cos. S H. cos. MR

cos. m R. cos. s H