1843.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



225 



Logarithm of 21986496588 

 Constant logarithm 



10-3421561 

 9-3267737 



Logarithm of 10"-3605 . . . . 1-0153824 



Dalby's rule, from the simplicity of the wording, and from the few 

 figures exhibited in the operation, appears to be more convenient 

 in practice than the one which we have given as an improvement, but 

 this is not the case ; for to find the logarithm of 219811496588, or the 

 number corresponding to 1-0153824 from a table of logarithms, will 

 employ more time than the complete working of the problem by the 

 method here proposed, which may be thus investigated. 



Let E be the area of a triangle in square feet ; r=the radius of cur- 

 vature at the place on the earth's surface where the triangle is situated, 

 and A°, B°, C°, be the angles of the triangle considered as spherical, 

 reckoned in degrees and decimal parts of a degree. By the well- 



known theorem of Gerard, 2 £. = 4*7- ' 



■{' 



360 



} (A) 



Suppose the triangle to be one employed in the trigonometrical 

 survey of England, then the length of a degree may be considered 

 equal to 60859-1 X 6 feet, without involving much error. Therefore 

 the circumference of the globe to which this triangle is supposed to 



„ „ . 360 X 6x60859-1 

 belong = 360X 6 X 60859-1, and r = 5 



, (A) becomes 

 .'. 2E = 



2-tE 



,2E=4-r( 



360x6x60859 



2t 

 360 X 6' X (60859-1)' 



•>)■(- 



+B°+C°— 180° 



360 

 (A° + B° + C° — 180°) 



„ - = A° + B° + C° - 180 r , which we shall call 

 360 X 6- x (60859- 1) 2 T T 



e, or the spherical excess in degrees and decimal parts of a degree, 

 ■which when reduced to seconds will stand thus: — 



q«00 , - 3600 X 2*E _ .E 



ow _ g60 ^ 6 , x (60859 . 1)2 — 1>8 x (G o859-l) 2 



but «• = 3-1415926 &c. 

 E 



" ' 1-8 X (60859-1) 2 1-8 X (60859- If (182577-3)2 

 3-1415926 15-707963 



(B) 



but (1 ^l 57 /'fi - = 2122138300-6, from whence the rule is derived. 

 15*707963 



It is evident that Dalby's rule is in error when half the length of a 



degree is greater or less than 182577-3 English feet in the place where 



the triangle is measured; for by putting (B) into a logarithmic form 



we have Dalby's rule. But the constant divisor or its logarithm can 



be readily attained by substituting (B) for 182577-3 feet, half the 



length of any other degree in feet. However, the difference must be 



very great when the spherical excess is effected, of such triangles as 



occur in practice. 



LIFE OF SIR DAVID WILKIE. 



Poor Allan Cunningham ! he had a poetical imagination and a 

 grateful heart. He never forgot an obligation, and felt every kindness 

 so warmly, that it was natural he should overestimate his friends who 

 were interested in his welfare ; he loved Sir Walter Scott, he adored 

 Chantrey, and believed Wilkie (if the truth were confessed) to be 

 greater than Raphael. The basis of biography is fact, bare, naked , 

 disinterested, unqualified, undistorted, unpoetized, unexaggerated fact. 

 Unless all the facts connected with the character described be correct, 

 the conclusions must be false, and confidence destroyed. I fear the 

 manufacturers of reminiscences, conversations, and biographies of late 

 years have not been remarkable for adherence to this essential prin- 

 ciple. 



"When Foote tells me a story," said Johnson, "it makes me laugh, 

 but it passes from my mind from its falsehood; when Reynolds tells 



me anything, I have an idea the more, for I know it to be a true repre- 

 sentation of nature." Let every biographer print these words in 

 letters of gold over his study door, and let him read them with atten- 

 tion whenever he feels inclined to give his imagination the reins at 

 the expence of his understanding. 



It may be said of all Cunningham's lives of artists that there is 

 scarcely an anecdote told of. any of them which happened in my 

 time, which is not so poetically treated as to amount to a misrepre- 

 sentation, though nothing was further from his desire or his principle. 

 In the very first volume he states Wilkie was refused admission 

 into the Academy of Edinburgh by Mr. George Thompson, and I, as 

 well as others, felt the injustice as well as ignorance of Mr. Thompson. 

 Now Mr. Thompson is ilive, and luckily he is so, and he has given, 

 in the Morning Chronicle, a flat contradiction to the assertion, and 

 says it is " not true." Sir George Beaumont told me Boswell would 

 race the town for days to ascertain the correctness of yes or ho ; as 

 Mr. Thompson was alive, it was Mr. Cunningham's duty to have ascer- 

 tained the fact, before he made so unjust an attack on a very worthy 

 person. 



No. 8, Norton Street, says Cunningham, was Wilkie's first residence, 

 then a coal shed ; now it was not a coal shed at the time, 1806, but a 

 little front parlour! Wilkie's bed-room, sitting-room, and painting- 

 room, and there he painted the Village Politicians. 



He says again : something of Wilkie's reputation preceded him to 

 London, for Jackson wrote to Haydon, &c. then in Devonshire. We 

 never heard a word of him till he came to the Academy, and when 

 he came, Jackson wrote to me. "Touched with Jackson's letter, 

 Haydon came to London and went to the Academy. Wilkie, the 

 most punctual of mankind, was there before him," says the author. 

 Now Wilkie did not come the fast day at all, and the next day not till 

 near one — one hour and a half after his time ! Because he painted to 

 get his living, always before he came to the Academy, and Jackson, 

 whom Lord Mulgrave maintained, and my father maintaining me, 

 enabled us to be much more punctual than Sir David. 



" Haydon," says Cunningham, " is an admirer of the grand stvle ; 

 but Wilkie, with a wider reach of mind, used to argue, " that 

 though the rose excelled in beauty all other flowers of the field, 

 we were not to despise the daisy, which had a loveliness of 

 its own." Very like Wilkie's conversation. I imagine my dear 

 old friend at that time, pale, thiu, shrewd, legal, unpoetical and 

 cold, talking the purest Fifeshire, scarcely understood in Auld 

 Reekie, alluding in a strain of poetical language to the comparative 

 beauty of the rose and the daisy ! A wider reach of mind, too! So 

 that I, who was devoting myself to see nature in the abstract, to clear 

 the essential from the superfluous, and restore man, woman, and 

 animal, to the essential properties in form of their respective species, 

 as their great Creator sent them forth in Paradise to increase and 

 multiply; I — who was thus fitting myself first, to master them as a 

 species, and second, to put them in actions and expressions, to convey 

 high moral lessons, to inspire the youth or elevate the country — was 

 not of so wide a reach of mind as David Wilkie, who took man, 

 woman, and animal as accident, disease, or dress had distorted them, 

 painted them as they were in their humblest moments, without refe- 

 rence to moral objects at all, without relation, without abstraction, 

 without choice ! 



He talks, too, very much of the smart pert students of the Royal 

 Academy of that time. Except one poor fellow who is now insane, 

 there was not a pert or smart student there — and the most loquacious, 

 the most whispering, the most disturbing arguing student that ever 

 lived, to whom we were all obliged to cry "Silence " repeatedly, was 

 Sir David Wilkie. Wilkie was remarkably fond of loud whisper- 

 ing arguments, touching away with his port-crayon as he talked. 

 "In my mind's eye, Horatio, I see him now." As to pertness, who 

 was pert? Were Collins, Jackson, Mulready, Hilton, Pickersgill, Etty, 

 and myself, were we pert? — we were the students, and our present 

 station is an answer to such absurdity. 



Page 76, Vol. I., he says, "Haydon was invited to breakfast; he 

 knocked — a voice said 'Come in'; and he found Wilkie partly 



