340 



KNOWLEDGE. 



September, 1913. 



Method 4. Let A B (Figure 366) be one side of 



the required polygon. Bisect A B in M, and at M 



draw M P perpendicular to A B and of indefinite 



/ 1ft0° 



length. Now, when *=19, tan (90°— — 



= 6. 



almost exactly ; so that if a point 19 be marked on 

 M P distant from M three times the length of A B, 

 this will give very accurately the centre of the circle 

 circumscribing the regular nonadecagon drawn on 

 A B as base. Mark this point. Trisect M B (or 

 A M) and, commencing from 19, mark off divisions 

 along M P each equal to f, M B. These points give 

 the centres of the circumscribing circles. The 

 polygons are then drawn as in the former methods. 

 In Figure 366 are shown polygons containing 17 

 and 19 sides thus obtained. Both are extremely 

 accurate. The equation connecting x and y for this 

 method can be obtained thus: Let y — mx-\-c. 

 Then clearly 



m = -3, and 19m + c = 6-000; 

 whence c = — -3. 



Therefore y= -3r — -3. The values of y thus 

 calculated are given in Column 10 of Table 59, and 

 the differences between them and the true values of 



y are shown in Column 11. Below .*=15, these 



differences are higher than with Methods 2 and 3, 



and below x = 9 they are greater than with Method 1. 



This method is not recommended, therefore, for 



polygons with less than 15 sides. But when the 



number of sides lies between 15 and 20 inclusive, it 



is the most accurate method. The graph of the 



equation y = «3* — -3 is shown in Figure 367 



(Graph D). It practically coincides with that of y 



180°^ 

 90° 



tan 



between x — 16 and x — 20. 



We have not considered it necessary to continue 

 the investigation for polygons containing more than 

 20 sides, though doubtless similar methods for 

 accurately constructing such polygons could be 

 devised. 



In Table 59 that method which is most accurate 

 for each polygon is indicated by an asterisk. If, when 

 using any of these methods, one has a list of errors, 

 such as given in Columns 5, 7, 9, and 11 of Table 59, 

 an even more accurate construction may be obtained 

 by estimating with the eye the true position of the 

 centre of the circumscribing circle above or below 

 the approximate position given by the method 

 employed. 



SOLAR DISTURBANCES DURING JULY, IQI3- 



By FRANK C. DENNETT. 



During July the solar disc has shown very little disturbance, 

 though rather more than in the two previous months. On 

 eight days (2, 5, 19, 21, 22 to 24 and 27) the disc appeared 

 quite clear. On nine (7 to 14 and 30) spots or pores were 

 visible. No observations were made on the 18th, and on the 

 remaining thirteen days faculae were visible. The longitude 

 of the central meridian at noon on July 1st was 137° 20'. 



No. 9. — First seen on the 9th as two spotlets, the larger 

 leading. On the 10th there were at least three umbrae in the 

 western portion of the group and two, with a dull companion, 

 in the eastern. The disturbance reached its maximum on the 

 11th, being some 40,000 miles in length; the components were 

 smaller on the 12th, and less in the evening than in the 

 morning. Only two pores were seen on the 13th, one still 

 remaining on the 14th. Faculae were seen in the same area 

 on the 16th and 17th. 



No. 10. — A little group of pores seen on the morning of the 



30th, which had faded greatly by the afternoon, and were 

 gone entirely by the next day. 



On both the 7th and 8th tiny black pores and bright flecks 

 were visible in various places on the disc under best 

 conditions, but none sufficiently conspicuous to measure. 



Faculae during the month were very far from being 

 conspicuous. There were some near the western limb on the 

 1st, and within the north-eastern on the 3rd and 4th. On the 

 20th a facula near longitude 295°, S. Latitude 35°, was 

 approaching the south-western limb. Faculae were within 

 the eastern limb on the 25th and 26th, also within the north- 

 eastern limb on the 28th and 29th. On the 29th faculae were 

 also situated at about 206°, 20° North, and 56°, 5° South. 

 There were faculae near the eastern limb on the 31st. 



Our chart is constructed from the combined observations 

 of Messrs. J. Mc Harg, A. A. Buss, E. E. Peacock, W. H. 

 Izzard and F. C. Dennett. 



DAY OF JULY, 1913. 



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