74 



Mr. J. N. Lockyer's Spectroscopic 



[Recess, 



Let x=a sin 0, y=a sin f, then the general equation of the rth order 

 may be written 



a sin (m6-\-n<p) + a sin (m'd— ri<p) + a" sin (m"Q+n"<f) + . . . =a sin0. 



Let a number of machines like the foregoing be placed side by side with 

 their ordinate wheels rolling in one another, and their abscissa wheels duly 

 connected. Let one abscissa wheel describe an angle md, and the cor- 

 responding ordinate wheel the angle wp, then a nut placed on the corre- 

 sponding addition wheel, at a distance a from its centre, will cause a 

 horizontal bar to descend vertically through a space a sin (md + n<p). In 

 the same way a nut properly placed on the subtraction wheel will cause a 

 horizontal bar to descend vertically through a space d sin (md—n<p). By 

 means of the adjacent machines we may in like manner cause bars to 

 descend through the vertical spaces, a" sin (>w'0-f n'<f), a" sin (m'B— n'<p), 

 &c. Now let motion be communicated to the ordinate wheels, and let all 

 the vertical motions due to the addition and subtraction wheels be com- 

 bined together and made to act vertically upon a nut in one of the abscissa 

 wheels ; then the angles 0, <p, will satisfy the equation 



a sin (m6 + n<p) + a' sin (mB— n<f) + a" sin (m'd + ri<p) . . . =a sin 0, 

 which is the general equation of the rth order. 



Therefore two bars moved respectively horizontally and vertically by nuts 

 in the wheels describing the angles 0 and p will trace by their intersection 

 the required curve. 



COMMrNICATIONS RECEIVED SINCE THE END OF THE SESSION. 



I. " Spectroscopic Observ ations of the Sun." — No. V. 

 By J. Norman Lockyer, F.R.S. Received July 8, 1869. 



Since the date of my last communication under the above title the weather 

 has, if possible, been worse for telescopic work than during the winter and 

 spring ; my opportunities of observation, therefore, have been very limited : 

 still the sun has occasionally been in such a disturbed state, and our 

 atmosphere has at times been so pure, that several new facts of importance 

 have come out. 



I will state them here as briefly as possible, reserving a discussion of 

 them and my detailed observations for a future occasion. 



I. The extreme rates of movement in the chromosphere observed up to 

 the present time are : — 



Vertical movement 40 miles a second 



Horizontal or cyclonic movement .120 „ 



II. I have carefully observed the chromosphere when spots have been near 

 the limb. The spots have sometimes been accompanied by prominences, 

 at other times they have not been so accompanied. Such observations show 

 that we may have spots visible without prominences in the same region, 



