R. O. WEST ON LISSAJOUS' CURVES. 43 



I have made is largely due to the excellent diamond point 

 for which I am indebted to the kindness of Messrs. R. and 

 J. Beck. This very delicacy is, however, in some cases a 

 drawback, as it increases the difficulty of obtaining an illumination, 

 which will show the figures in a striking way. Some of the lines 

 which I have obtained have been measured by Mr. Webb as 55,000 

 to the inch. I have cut a few specimens more deeply, and they 

 undoubtedly " come out " better, and even brilliantly, but they are 

 necessarily coarser in line, and more widely spaced. A point of 

 interest with respect to these curves is their possible value as test- 

 objects ; and Mr. Wenham, to whom my acknowledgments are due 

 fur many practical and valuable suggestions, tells me that some of 

 of them are quite sufficiently closely ruled for this purpose, and he 

 considers that the intersection of some of the lines, and the gradual 

 approximation of others, gives them a value above that of parallel 

 rulings. With reference to this, I may mention that in some of the 

 figures every degree of sharpness of curve is obtainable, from a line 

 returning almost upon itself, at an exceedingly acute angle, to curves 

 so flat as to present in parts virtually the appearance of parallel 

 straight lines. Another point is that, unlike diatom-markings, 

 which, after abundant controversy, can hardly yet be said to be indu- 

 bitably understood, the nature of all lines cut in glass may, up to a 

 certain point, be said to be known. It seems clear, from the nature 

 of the case, that they must be formed by some such V-shaped grooves 

 as are illustrated in section, thus : — y — y — y — though, whether, in 

 traversing transversely such a series of ridges and furrows, the trac- 

 ing-point descends into the furrows, I cannot positively say. From 

 some appearances which I have observed, I am inclined to think that 

 the point leaps from ridge to ridge ; but I believe the apparatus 

 could be modified to produce with certainty a vertically waved line, if 

 desirable. A curious feature in some figures is that though all the 

 lines would seem to be in the same plane (except in so far as affected 

 by the consideration just named), it sometimes happens that an 

 alteration of focus is requisite to bring out the transverse lines. I 

 should mention that, with one or two excej>tions, each of the figures 

 is a single continuous line from beginning to end. These exceptions 

 consist of one figure super-imposed on another. 



I have alluded to the difficulty of exhibiting these objects. They 

 are almost drowned in the glare of direct transmitted light. For 

 general effect Mr. Curties, who has devoted not a little time and 



