tecting their class interests, will practically leave the traffic of the Thames much the same as at present, i.e., in confusion. The portto-port rule is supposed to be in force now, but is admittedly unworkable.

W. P.

ANOTHER NEW AND SIMPLE DEMONSTRATION OF THE RULES FOR COMPUTING THE AMPLITUDE, AND THE TIME OF RISING OR SETTING OF A HEAVENLY BODY.

By THOMAS DOBSON, M.A., Head Master of the Marine School of South Shields.

HE following two general theorems require no previous knowledge beyond that of the elementary definitions of Plane Trigonometry. They are quite as useful as Napier's Rules of Circular Parts, and much less complex and embarrassing in application. In any right-angled spherical triangle, the side opposite to the right angle being called the hypothenuse, either of the two other sides may be called the perpendicular with respect to the angle opposite to that side, and the remaining side will then be termed the base; with this understanding we have

sin perp sin hyp x sin angle at base....(1)

=

and, sin base = tan perp x cot angle at base....(2) Demon.-Let O be the centre of the sphere, A B C a right-angled spherical triangle, C the right angle; draw 0 BMO C, M N O A, and consequently B NO A.

Then, by the definitions of Plane Trigonometry,

N

= sin Ax sin A B;

Applying these theorems to the triangle E S D in the figure;

1

But E is the colatitude, and sin E = cos lat =

sec lat

It may be well to add here a demonstration of a third general theorem of frequent use, viz. :

cos hyp = cos perp Xcos base......(3)

ON ONOM

D

=

= cos A Cx cos B C.

SHOAL PATCHES ON THE GREAT BANK OF
NEWFOUNDLAND.

N

N consequence of several shoal patches having been reported on the Great Bank of Newfoundland in the vicinity of Virgin rocks, an examination of the locality has been made by Staff-Commander W. F.

Maxwell, Admiralty Surveyor, with the following results: -

VIRGIN ROCKS.-The least water found on these rocks was three fathoms; shoals occupying a space six miles long and one mile broad, having depths upon them varying from five to twenty fathoms have also been found upon the bank on which the Virgin rocks are situated.

EASTERN ROCKS.-A shoal having a depth of nine fathoms was found to be situated East (true) from Virgin rocks distant fourteen miles.

JESSE RYDER ROCK.-The position of this reported danger (in lat. 46° 29′ N., long. 49° 41′ W.) was carefully examined throughout one day, but no indication of it was found either by variation in the soundings, or change in quality of the bottom.

BERTEL BANK.-The position assigned to this bank (lat. 44° 43′ N., long. 49° 52′ W.) was also carefully examined, but no sign of it was found.

Note. The masters of various fishing vessels, who have had many years experience on the Great Bank of Newfoundland, stated that to their knowledge, no trace of shoal ground exists near the reported positions of Jesse Ryder rock and Bertel bank.

The United States Hydrographic Office has also recently published a "Sketch of the Eastern Shoals," based on information derived from the most responsible and trustworthy of the fishermen on the Great Bank. The accompanying copy of this sketch has been obligingly furnished to us by Messrs. Imray and Son, Chart Publishers, 89, Minories.

The Nine-Fathom patch, together with other spots supposed to be shoaler than the general soundings of the locality, is laid down on the sketch, which otherwise sufficiently explains itself, and will be found useful to masters navigating this part of the Atlantic. The approximate position of the Nine-Fathom patch is lat. 46° 25' N., long. 50° 32′ W.

JESSE RYDER ROCK.-The position of this reported danger (in lat. 46° 29' N., long. 49° 41′ W.) was carefully examined throughout one day, but no indication of it was found either by variation in the soundings, or change in quality of the bottom.

BERTEL BANK. The position assigned to this bank (lat. 44° 43' N., long. 49° 52′ W.) was also carefully examined, but no sign of it was found.

Note. The masters of various fishing vessels, who have had many years experience on the Great Bank of Newfoundland, stated that to their knowledge, no trace of shoal ground exists near the reported positions of Jesse Ryder rock and Bertel bank.

The United States Hydrographic Office has also recently published a "Sketch of the Eastern Shoals," based on information derived from the most responsible and trustworthy of the fishermen on the Great Bank. The accompanying copy of this sketch has been obligingly furnished to us by Messrs. Imray and Son, Chart Publishers, 89, Minories.

The Nine-Fathom patch, together with other spots supposed to be shoaler than the general soundings of the locality, is laid down on the sketch, which otherwise sufficiently explains itself, and will be found useful to masters navigating this part of the Atlantic. The approximate position of the Nine-Fathom patch is lat. 46° 25' N., long. 50° 32′ W.