132 Mr. Beverley on the Double Altitude Problem. 
neither has he, in that paper, given a solution to the problem 
which he professes to solve. 
The observations of Messrs. Riddle and Henderson are well 
founded; and I wonder you have not heard from more of your 
correspondents on the same subject: for after all he has ad- 
vanced or may advance in its favour, it is evident he has proposed 
one problem and solved another. I do not hesitate a moment 
in saying, in the words of Mr. Riddle, that in his first paper 
«he has altogether misapprehended the nature of the pro- 
blem.” And though he has been practising it these six months, 
we have not yet received from him a direct analytical solution 
of a double altitude. The one he has given us at page 50, 
vol. Ixvii., which is identical to the one at page 345, vol. Ixvi., 
is the same in substance as those given in Kelly’s Spheroids, 
Bonnycastle’s Trigonometry, &c. &c.—as it represents no more 
than the several trigonometrical operations in algebraical terms. 
The horary angles cannot be determined by any less la- 
borious an investigation than the latitude itself; neither do 
the “ Horary Tables” show those horary angles at all. They 
only show the horary angle when the latitude, altitude, and 
declination are given, or the latitude when the horary angle 
is given. They might, however, be of excellent use in single 
altitudes, if they were about sixty times as extensive as they are. 
In Mr. B.’s first paper, I cannot see how far he can con- 
ceive himself justified in endeavouring to depretiate the very 
valuable labours of Mr. Douwes and Dr. Brinkley, while at 
the same time he is pursuing a problem of a quite different and 
inferior nature, and which is no more than the declination, 
two altitudes of the sun, and the times from noon when those 
altitudes were taken, given to find the latitude. 
Yours, &c. 
Brompton, near Scarborough, Tuomas BEVERLEY. 
Feb. 13, 1826, 
(Mr. Beverley proceeds at great length to the discussion of 
this problem, and states the mode of its solution as given in his 
forthcoming Mariner’s Celestial Guide: but as so much has 
been said already upon the subject, we are desirous of bring- 
ing it to a close. We shall have great pleasure in hearing 
from Mr. Beverley on any other scientific subject, and are 
sure that he will not attribute our shortening his communica- 
tion to any want of respect for the talent with which he has 
treated the subject.—Ebir. ] 
XXII. Pro- 
