12 



THE CIViL ENGINEER AND ARCHITECT'S JOURNAL. 



[January, 



lie has cliospn the most appropriiite materials, and has with con- 

 siderable skill a|i])lied to liis construction the improved system 

 which cast-iron ]irescnts. I have not stopped to consider whether 

 he has adopted all the expedients which we should consider neces- 

 sary for counteracting tlie expansion and contraction to he ex- 

 pected in ironwork ; particularly as regards the movement which 

 might he expected at the feet of the rihs of the dome, and which 

 possihly we might have regulated hy rollers, and by allowing space 

 for the development to be expected in a warmer temperature. 

 The interval of ten years must have proved the efficacy of his 

 provisions, and I should ill requite the courtesy of our generous 

 donor were I to analyse with the severity of a critical eye the pro- 

 portions and details of this remarkable monument. The unspar- 

 ing nature of the materials employed prove the pious liberality of 

 the em])eror and tlie nation. The careful skill with which the 

 architect lias fulfilled his part, and the deeji feeling for decorative 

 art with which he has embellished the cathedral of the Russian 

 capital, and the brief space of time in which he has erected the 

 lofty pile, must ever render the church of St. Isaac one of the 

 most striking edifices of the nineteenth century. 



GENERAL SCALE FOR MEASURING EARTHWORK. 



Sin — Enclosed herewith I send you a printed description of a 

 new method of measuring earthwork, thinking that you might 

 insert it as a communication in your valuable Joiii-iia/, for the 

 benefit of such of your subscribers to whom I have not the oppor- 

 tunity of remitting this circular, which explains a simple and novel 

 application of a scale to earthwork measurement. As the circular 

 so fully explains the use of the scale, it is not necessary for me to 

 mention anything concerning its practical use; but as the mathe- 

 matical principle is not so obvious as students of these kind of 

 j)roblems may desire, I beg to supply this demonstration for their 

 benefit. I was led to perceive this principle, as I have apjilied it, 

 <iuite accidentally while investigating a totally different problem — 

 ^'iz., the geometrical extraction of the cube root, of which I have 

 obtained a very simple and approximate solution. The principle 

 on which the construction of the scale depends, is as follows: — 



Let RDF be a circle; A, its centre; H, a point without the 

 circle in the diameter B E produced ; and let each semicircle be 

 divided into n number of parts at C, D, F, G, &c. : then, 



ATj « -f A H « = B H X H F X H D ; 



or equal to the continual product of the lines drawn between H 

 and alternate points of division of the circle. 



The diagram shows the semicircle divided into threr equal parts; 

 and if A II = H, A B = /(, ri = 3, the above equation becomes 



II ' + h:< — II F = X B II, because H F = II D. 

 Also, B H = A II - A B = H - A; 

 H •■* 4- h^ 



•'• "F' = "h-J = n"- + m + hK 



But on referring to the 176th page, line 11, of my work on the 

 "Prismoidal Formula," it will be seen that this expression for H F- 

 is identical with the variable part of the second term of the gene- 

 ral rule for the contents of a prismoid. Hence we derive the 

 application of this problem to the computation of earthwork. 



If you inspect the diagram at the head of my circular, the cor- 

 respondence is evident: the point A corresjjonds with tlie gradient 

 or formation line; A E is the height of cutting at that point = A; 

 A H is the last height [dotted below the gradient := II ; and H F 

 is the diagonal along which the scale is applied to measure the 

 slopes. For those who desire an authority without the tnudde of 

 investigation, for the foregoing diagram, a reference to "iMathema- 

 tics for Practical Men" (Weale, 1818), p. 108, will suffice. 



I have only another observation to make concerning the conve- 

 nience of this scale. It is engraved for a plot of 20 feet vertical ^ 

 1 inch : but if the plot is otherwise, then, after the measurements 

 have been taken by the scale, it is necessary to multiply or divide 

 the resiilts by the proper ratio due to the difference of plotting. 

 Thus, su))pose the plot were 40 feet to 1 inch ; then all measure- 

 ments for the base or middle are too little by 40 : 20, or 2 to 1 ; 

 and too little for the slopes or sides by Vio : V20, or Vg to 1. 

 If the ])lot were 10 feet = 1 inch, then all the measiirements are 

 too great — for the base, as 1 to 2; for the slopes, as 1 to V'2. 



Apologising for occupying your time thus, though with a view to 

 benefit others, 



I remain, Sir, 

 Wanfiteiid, Essex, Yours truly, 



December, iSth, 1848. J. B. Huntington. 



The following is a copy of the circular referred to by Mr. Hun- 

 tington : — 



B Surface B 



Let the above diagram represent a section of a railway plotted 

 in the usual manner, with a vertical scale of 20 feet to 1 inch. 

 Divide the section into prismoids in the ordinary manner, by per- 

 pendiculars (B D) throughout. The present mode of measuring 

 earthwork is to measure the several heights, 1 B D, 2 B D, 3 B D, 

 4 B D, &c., and then to compute the mean areas by referring 

 to tables prepared for the purpose by Macneil, Bidder, and others, 

 whose methods have been explained in the appendix to the Second 

 Edition of " Huntington's Tables." In measuring with a scale 

 divided into feet, it unavoidably happens, in a large majority of 

 cases, that the heights B D do not measure exactly integral feet, 

 but some fraction or decimal part of a foot, more or less ; that is, 

 the plotted height of the section rarely coincides with the divi- 

 sions of a scale. It becomes generally necessary in using Tables 

 to omit these fractions, and to compute the quantity due to the 

 nearest number of integral feet found in the table; so that by al- 

 lowing the measurement to be sometimes more and sometimes 

 less than the truth, a compensati(ui is provided, and a tolerably 

 accurate result is obtained. But where cuttings or embankments 

 are very great, it will be found that the number of cubic yards 

 computed by the above method will vary by a large per centage 

 from the true amount, because the allowance for compensation is 

 always discretional with the measurer, whose judgment must be 

 constantly exercised with a doubtful pros])ect bef(U'e him, as to 

 whether the fractional measurement should become nearest the 

 foot above or below. 



In order to avoid this chance — indeed, I miglit almost say, cer- 

 tainty of error — I considered whether it were luit possible to con- 

 struct a scale so as to determine the cubic quantity, by making the 

 degrees of the scale exnctlji mincide witli the plotted heights; 

 there would then be no necessity to give or take; and if I could 

 divide the scale so minutely that, with the further assistance of 

 sub-division by the eye, the graduations should become less than 

 any fraction of a foot, for which tabular nundiers .are prepared, I 

 might fairly assume, that the coincident quantity thus read from 

 the scale, must he far more accurate than by the methods usually 

 adopted. In 1839, I first made some scales on this principle for 

 the use of the Eastern Counties Railway, adapting them to the 

 particular base and slnjies of that railway. I hive described them, 

 with a cut, in my work on "Eartliwork," &c. Since then, having 

 been asked whether I could make a general scale, to effect the same 



