April 6, 1888.] 



SCIENCE. 



167 



opposite points when extended, which we know to be conditions 

 that must be filled. 



The plane table is essentially a direction instrument. Theoreti- 

 cally we can do perfect work without knowing a single distance, 

 and afterwards, by measuring some length between objects marked 

 on the sheet, determine a scale for the whole. This being the case, 

 the angle at the occupied station, between two points marked on the 

 sheet, will be the same wherever the points may happen to be on 

 the paper. It is the practical application of the geometric functions 

 of similar triangles. But the distortion of a sheet destroys these 

 perfect proportions, for we have to preserve directions bet^veen 

 fixed objects, and knowingly increase or diminish the angle con- 

 tained between the directions. As at X, we know that it is in its 

 proper position on the line between ae, eg, etc. ; but we know also 

 that the angle aXh is smaller than it is in nature, and the angle 

 aXc is larger. 



This forcing the position does not produce any appreciable error 

 in the work represented, as in short distances, like filling in detail 

 around the station, the distortion cannot be measured, and in long 

 distances it can be eliminated. It is evident that a station made by 

 three points on the lines of contraction will give the table the true 

 orientation, for the effect of the distortion upon three points so 

 situated is only that of a change of scale, and a change of scale 

 does not affect orientation. But the position of the station made in 

 relation to the other points on the table is not true, ov^fing to the 

 change of scale not being the same on both lines of contraction. 

 From the conditions presented, Mr. Ogden deduced the following 

 rules : — 



(1) A station made with three points that are on the lines of 

 contraction, the resecting lines forming nearly right angles at their 

 intersection, will give the true position in relation to all points on 

 the sheet (as h, b, and d). 



(2) A similar condition of right-angular intersection at the 

 station, but the lines forming diagonals to the lines of contraction, 

 will give the worst possible position for the station (as a, c, and e). 



(3) A station made with three points on one of the lines of con- 

 traction will give the correct orientation of the table (as«, h, and_^). 



(4) In estimating errors of the points due to distortion, those 

 situated on the lines of contraction require no allowance, however 

 distant. 



Mr. Ogden then explained the treatment in cases where only 

 three points were visible, — first, when all of them are on the lines 

 of contraction ; second, when two of them are on the lines of con- 

 traction, and one of them not ; and, third, when neither of them is 

 on the lines of contraction. 



The effects of distortion, as Mr. Ogden explains them, throws 

 some light on the relative accuracy of plane-table triangulation. 

 This class of work is good and reliable if the paper does not change 

 its conditions ; but it is evident that a triangulation extended over 

 a sheet that has contracted since the base was plotted on it, and 

 the first few triangles laid down upon it, will be continued on vary- 

 ing scales. We have but to conceive the triangles extended in the 

 form of a parallelogram, working two sides of it from each of the 

 separate bases to a common point, to see the theoretical outcome of 

 such conditions. 



Plane-table triangulation is liable to be further complicated by 

 frequent changes of scale or different degrees of contraction as 

 the work progresses, which prevent the possibility of computing 

 the resultant errors. Some check can be obtained by subdividing 

 the sheet into squares of uniform size, which will show, at least, 

 how much the paper has changed when the work is finished. Such 

 squares are an assistance in the information they give while the 

 work is in progress ; and by carefully watching the changes in them 

 it would be possible to apply corrections for the points of a plane- 

 table triangulation that would eliminate the worst of the errors 

 incident to such work. 



The uniformity in the contraction of a sheet of paper may also 

 be taken advantage of in measuring the length of a diagonal line 

 by drawing lines on the lines of contraction at right angles with 

 each other ; and, having obtained the true lengths of the two sides 

 of the triangle, the third may be computed with at least as much 

 accuracy as it could have been measured on the paper if the scale 

 had not become distorted. 



ELECTRICAL SCIENCE. 

 Alternating versus Continuous Current Distribution. 



The subject which most engrosses the attention of electric- 

 lighting people at present, is the question of the relative values of 

 continuous and alternating currents for electrical distribution. In 

 England the matter was brought up by the papers of Messrs. 

 Kapp and Mackenzie on transformers, while in this country a 

 pamphlet issued by the Edison Company, attacking the alternating 

 system, has been followed by two interesting papers read before 

 the Chicago Electric Club, — one by Mr. Leonard in favor of the 

 continuous, the other by Mr. Slatterly favoring the alternating sys- 

 tem. 



The difficulty in all of this material is that it is distinctly partisan. 

 In spite of this, it is valuable. The trouble, of xourse, in getting 

 reliable data on the subject, lies in the fact that those who have had 

 most experience of the practical difficulties or advantages of a sys- 

 tem are those who are directly interested in its working, and who- 

 must have some bias in its favor. 



In the discussion before the Chicago Electric Club, Mr. Leonard, 

 taking the matter up first, considers the following points : first cost, 

 economy, reliability, value of possible sources of revenue, safety,, 

 effect on existing property. Under the first head he calculates the 

 cost per lamp of the copper necessary for conductors in the 

 direct system at different distances from the station : for example,, 

 with an average loss of eight per cent in the conductors, and a dis- 

 tance of six thousand feet, the cost is $3.87 per lamp. With this 

 he compares the cost of the corresponding investment in the alter- 

 nating system, — copper and transformers, — and makes it Si- This 

 is on the assumption that copper is sixteen cents per pound. As 

 it is principally in the cost of conductors that the alternating claims 

 advantage over the direct system, Mr. Leonard's figures would go- 

 to prove the advantage of the latter for mean distances up to six 

 thousand feet from the station. Passing to depreciation of the dis- 

 tributing plant, Mr. Leonard claims that the conductors in the direct 

 will depreciate in value less than the conductors and converters of 

 the rival system. The reliability of the direct system would seem 

 greater than that of the other ; for the apparatus is less complicated,- 

 and a breakdown of one engine or dynamo in a station will not 

 affect the lights. The possible sources of revenue seem to Mr. 

 Leonard more numerous in the continuous system. At present the 

 alternating system can supply only light and — if it is ever needed 

 — heat : its rival can be utilized for all the purposes to which elec- 

 tricity can be applied. The danger of high potential alternating 

 currents is dwelt upon, and fatal results were cited. 



Mr. Slatterly, in replying to the paper, disputes some of Mr. 

 Leonard's points. The estimates, based on sixteen cents per pound 

 for copper, would hardly apply to copper at nearly twenty-five cents, 

 its present price. The alternating system has the advantage that 

 it can be used at a)iy distance from the station, and the latter can 

 be built on inexpensive ground, not in the middle of a crowded dis- 

 trict where property is costly. Mr. Slatterly claims for the alter- 

 nating system that the accidents that have happened are due to in- 

 experience, and their occurrence was not a fault of the system. On 

 the question of danger he states that alternating currents are not so 

 dangerous as continuous currents of the same potential. As re- 

 gards distribution of power, Mr. Slatterly thinks that an alternating 

 electro-motor will soon be forthcoming. 



In considering electrical questions with a view of deciding be- 

 tween two systems, we should consider two things, — economy 

 under present conditions, and the probable progress in the near 

 future. As things stand at present, we may say that the direct 

 system has the disadvantages of a limited area of distribution, and 

 the necessity of locating in a central position, where land is expen- 

 sive : the alternating system has the disadvantage of a considerably 

 greater loss in distribution, of greater complexity and consequent 

 liability to accident, impossibility of distributing power, and danger. 

 These considerations would point to the direct system being best 

 in the central portions of cities, while the alternating system should 

 be used for towns and for the suburbs of cities ; possibly, too, as- 

 an auxiliary to arc-lighting stations. 



In the future the alternating system can hope for the perfection 

 of a motor and the general improvement of the apparatus : the 



